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Louis N. Ridenour, Editor-in-Chief 


The qnafily of the maierial used in the manufacture 
of Urn hook is qoverrwd hy cordinaed postwar shortages. 




Board of Editors 

Lotus N. Ridbnotib, Bditor^-irirChief 
George B. Collins, Deputy Editor-4n-Chief 

Britton Change, S. A. Goudsmit, B. G. Herb, Hubert M. James, Julian K. Knipp, 
Jambs L. Lawson, Leon B. Lintord, Carol G. Montgomery, C. Newton, Albert 
M. Stone, Louis A. Turner, George E. Valley, Jr., Herbert H. Wheaton 

1. Radar System Engineering — Ridenour 

2. Radar Aids to Navigation—HoZZ 

3. Radar Beacons — Roberts 

4. Loran — PiercBj McKenzie^ and Woodward 

5. Pulse Generators — Glasoe and Lehacqz 

6. Microwave Magnetrons — Collins 

7. Klystrons and Microwave Triodes— Knipp^ and Kuper 

8. Principles op Microwave Circuits— Dicke, and Purcell, 

9. Microwave Transmission Circuits — Ragan 

10. Waveguide Handbook — Marauvitz 

11. Technique op Microwave Measurements— 

12. Microwave Antenna Theory and Design — Silver 

13. Propagation op Short Radio Waves— K err 

14. Microwave Duplexbrs — Smullin and Montgomery 

15. Crystal Rectifiers- T orres/ and Whitmer 

16. Microwave Mixers- P ot^nd 

17. Components Handbook— 

18. Vacuum Tube AMPUPiBRs—VaZZey and Wallman 

19. Waveforms- CAance, Hughes, MacNichol, Sayre, and Williams 

20. Elbothootc Time Mbastjbbmbnts— C ftonce, HMzer, MocNicha 

and Williams * 

21. EtBCTOONio INSTEUMBOTB-Greenwod, MacRae, Reed, and Holdam 

22. Cathode Bay Tdbb Displays— S oBer, Starr, and Valley 

23. AXicrowave Receivers^” V an "Voorhis 

24. Threshold Signals — Lawson and Uhlenheck 

25. Theory op Servomechanisms— J ames, NichoU, and PkiUipe 

26. Radar Scanners and Radomes— C ad^, KardUz, and Turner 

27. CoMPTPnNO Mechanisms and Linkages- 5»o5£>do 

28. Index — Linford 




With a chapter by ERIC DURAND 



C. G. Montgomery D. D. Montgomery 


Fiusr Edition 
Second Impression 


■ lA Lib., 


McGraw-Hill Book Company, Inc. 


AU rights reserved. This hook, or 
j>arts thereof, may not be reproduced 
in any form without permission of 
the publishers. 



T he tremendous I’esearch and development effort that went into the 
development of radar and related techniques during World War II 
i*esulted not only in hundreds of radar sets for military (and some for 
possible peacetime) use but also in a great body of information and new 
techniques in the electronics and high-frequency fields. Because this 
basic material may be of great value to science and engineering, it seemed 
most important to publish it as soon as security permitted. 

The Radiation Laboratory of MIT, which operated under the super- 
vision of the National Defense Research Committee, undertook the great 
task of preparing these volumes. The work described herein, however, is 
the collective result of work done at many laboratories, Army, Navy, 
university, and industrial, both in this country and in England, Canada, 
and other Dominions. 

The Radiation Laboratory, once its proposals were approved and 
finances provided by the OfiBice of Scientific Research and Development, 
chose Louis N. Ridenour as Editor-in-Chief to lead and direct the entire 
project. An editorial staff was then selected of those best qualified for 
this type of task. Finally the authors for the various volumes or chapters 
or sections were chosen from among those experts who were intimately 
familiar with the various fields, and who were able and willing to write 
the summaries of them. This entire staff agreed to remain at work at 
MIT for six months or more after the work of the Radiation Laboratory 
was complete. These volumes stand as a monument to this group. 

These volumes serve as a memorial to the unnamed hundreds and 
thousands of other scientists, engineers, and others who actually carried 
on the research, development, and engineering work the results of which 
are herein described. There were so many involved in this work and they 
worked so closely together even though often in widely separated labora- 
t.ories that it is impossible to name or even to know those who contributed 
to a particular idea or development. Only certain ones who wrote reports 
or articles have even been mentioned. But to all those who contributed 
in any way to this great cooperative development enterprise, both in this 
(iountiy and in England, these volumes are dedicated. 

L. A. DuBridge. 


T his volume describes the design of the various microwave circuits 
that have been used as mixers in the microwave region at the Radi- 
ation Laboratory. The mixers convert the microwave signal into a 
signal at a lower frequency, where conventional lumped-constant circuits 
and multiple-element vacuum tubes are used. For information con- 
cerning the design of a complete microwave superheterodyne receiver, 
of which the mixer is a part, Vol. 23 of this series is recommended. Low- 
frequency amplifiers of many types, for use following the mixer, are 
described in Vol. 18. A complete treatment of crystal rectifiers, which 
are the hearts of the mixers described in the present volume, is given in 
Vol. 15, Duplexing circuits often required in pulse radar, and the tubes 
used in them are described in Vol. 14. Low-level oscillators, which are 
used as local oscillators for the mixers, are treated in Vols. 7 and 11. 
Because the frequency of the local oscillator determines the sensitive 
frequency of the mixer, automatic frequency control has been considered 
to be closely related to the mixer; for this reason, the chapter on this 
subject by Eric Durand has been included in this volume. 

I wish to take this opportunity to thank H. F. Webster for his cooper- 
ation in the design of the mixers developed at the Radiation Laboratory 
from 1943 to 1945, and Florence M. Carroll and Rosemarie Saponaro 
for theii’ veiy great assistance in the preparation of the manuscript. 

The publishers have agreed that ten years after the date on which 
each volume in this series is issued, the cbpyright thereon shall be relin- 
quished, and the work shall become part the public domain. 

R. V. Pound. 

Cambkidge, Mass. 

June , 1946 


FOREWORD BY L. A. DttBridqb v 



1*1. Definition, of Terms 2 

1-2. Effect of Type of Signal on Receiver Design 4 

1*3. Qualitative Discussion of Duplexing Components 6 

1-4. Figures of Merit for Receivers 10 

Classification and Description of Types of Microwave Recbiverb . . 17 

1-6. The Low-lcvel Detector 17 

1-6. The Square-law Detector 19 

1-7. The Minimum Detectable Signal Power 21 

1-8. The Superheterodyne Receiver 24 

1-9. The Frequency Converter 26 

1*10. The Triode Mixer 28 

1-11. The Diode Mixer 32 

1«12. The Crystal Mixer 34 

1-13. The Local Oscillator 35 

M4. The Reflex Klystron 37 

1-15, Radio-frequency AinpUficrs 43 

1- 16. Receivers of Other Types 44 


2*1. Physical Description of Rectificaiiou 48 

2- 2. High-frequency Effects in Oystal IhictifiorH 62 

2-3. Figure of Merit of (Jrystal-video Receivers 64 

2-4. The (Crystal Converter 66 

2-6. Linear-network Representation of the Crystal (’-on verter .... 69 

2-6. The Threcs-terininal -pair-network Rt‘.pres(uif.ation 61 

2*7. The R(dation between the Input Admittance and the Jx)a<l 

Admittance 66 

2-8. The Dependence of Input Adinittanee on the l-f Ijoad Admittance 68 
2-9. Dependence of the l-f Admittance upon R-f Mahdiing (^omlitions 71 
2*10. Dependence of ( Jon version I johs on linage-frecpiency Termination 75 
2*11. Measurement, with an Admittance Rridge, of the Dependence of 

Conversion Ivoss on the Image Rcdlecition 80 

2-12. The Effect of Rxdlectiou of the Second i larnioiuc 83 

2-13. The Welded-contact Gcrinaniuin Crystal 87 

2-14. The (Jonverter Noise Temperature 93 

216. Crystal Burnout 96 



2-16. Correlation between TR Leakage Power and Crystal-burnout 

Power 97 

Testing and Specifications op Cbystals 100 

2*17. Conversion-loss Measurement 101 

2*18. Noise-temperature Measurement 105 

2*19. Bumout-test Apparatus Ill 

2*20. TheD-c Crystal Checker 113 

2*21. Specifications and Relevant Information on Available Types . .114: 


3*1. The Basic Mixer Circuit 120 

3*2. The Design of a Crystal Mount 122 

3*3. Crystal Mounts for the 3-cm and the 10-cm Bands 124 

3*4. The Filter in the I-f Output Lead 128 

3*6. Tunable Crystal Mounts 131 

3*6. Admittance Scatter in a Mount of Fixed Tuning 134 

3- 7. Local-oscillator Coupling Mechanisms . . . . « 136 

3*8. Capacitive Local-oscillator Coupling in Coaxial-line Mixers . . . 140 

3*9. A Local-oscillator Coupling Circuit for Coaxial-line Mixers . . . 142 

3*10. Local-oscillator Coupling in Waveguide Mixers 144 

3*11. A Directional Coupler for Coupling the Local Oscillator to the 

Mbcer 146 

3*12. A Single Channel for Local-oscillator Coupling 150 

3*13. An Exact Equivalent Network for the Coupling Channel. ... 155 

3*14. An Iris for Local-osciQator Coupling 160 

3*15. Signal-input Circuit 166 

3*16. Mounts for 1N26 Crystals and a Waveguide Mixer for the 10-cm 

Band 171 

3*17, Self-protection of the Mixer Crystal 172 

3*18. Harmonic Chokes and Shutters 174 

3*19. I-f Output Admittance . . 178 

3*20. The Completed Mixer 185 


Beacons and Automatic F^qubncy Control 190 

4*1. The Beacon Problem 190 

4*2. Single-channel Automatic Frequency Control 191 

4*3. Separate-mixer AFC 193 

4*4. The Coupling of the Transmitter Sample 196 

4*5. Two-channel Mixers for All-waveguide Systems 199 

4*6. A Mixer Employing Directional Couplers 201 

Load-dependent Properties op Oscillators 202 

4*7. The Rieke Diagram 203 

4*8. Frequency Discontinuities Caused by High-Q Load Circuits . . . 209 

4*9. The Design of Load Circuits Containing Transmission Cavities . 215 

4- 10. Load Circuits with Reaction Cavities 218 

4*llr The Prevention of Frequency Discontinuities by Padding. . . . 219 


Examples of Mxtltiplb-ftjnction Mixers. 223 

4-12. Provision for Beacon Local Oscillator 223 

4*13. R-f Provision for Beacon AFC 227 

4- 14. Representative Mixers with Multiple Functions 231 


6-1. Generation and Effect of Local-oscillator Noise 235 

6*2. Magnitude of Local-osciUator Noise for Typical Tubes 237 

5*3. Effect of Local-oscillator Noise on Over-all Noise Figure .... 239 

5*4. Reduction of Local-oscillator Noise by the TR Cavity 241 

5*5. Reduction of Local-osciUator Noise by Resonant Filters 243 

5*6. Reduction of Local-osciUator Noise by the TJse of a Cavity as Part 

of the OscUlator Tank Circuit 245 

6 *7. Effect of D-c Bias on the Mixer Crystal 249 

5- 8. Results of Experiments on the Effect of D-c Bias 251 


6- 1, Simple Microwave Balanced Mixer 267 

6-2. General Properties of the Magic T 259 

6-3. The Matching of the Magic T 262 

64, Description of the Magic T in Terms of Voltages and Currents . 264 

6*5. The Magic-T Balanced Mixer 269 

6*6. Additional Features of the Magic-T Balanced Mixer 275 

6*7. Special Crystal Mounts for the Balanced Mixer 279 

6-8. A Double Balanced Mixer for Separate-channel AFC 283 

6- 9. Other Special Circuits 287 


7- 1. Soiirccs of Frequency Drift 290 

7-2. Properties of Ijoeal Oscillators for Frequency Control 292 

7-3. C’-kssilication of AFC Systems 294 


74. The AP"C Feedback Ix)op 295 

7*5. The Transmitter Sample 296 

7*0. Mixers, liocal Oscillators, and 1-f Amplifiers 299 

7-7. Discriminators 302 

7*8. Discriminator Theory 308 

Noniiuntino Systems 312 

7-9. C’ontrol CUrcuitsfor Nonhuiitiiig Systems 312 

Dhujt-in 11 iTNTiNo System 314 

7-10. Basie Theory 314 

7*11. Standard Gas-discharge-tube AFC 315 

7-12. Design Theory for Gas-discharge-tubc Control (Urcuits 317 

7*13. Diodo-transitron Control Circuits 326 

Thermal Hunting Systems 331 

7-14. Background and Basic Theory 331 


7*16. The Whitford AFC 333 

7*16. Nibbe-Durand AFC System 337 


7-17. The Beacon Problem 341 

7- 18. Reflector-modulation Schemes for Reflector AFC 342 

7*19. Beacon AFC for Thermally Tuned Tubes 347 


8’1. Production Tests for Losses of Signal Power 362 

8- 2. Local-oBciUator Coupling 364 

8*3. Over-all Noise-figure Measurements 366 

8-4. Radio-frequency Noise Generators 361 

8-6. Apparatus for Measurement of the Effect of Image Reflection . . 364 

8*6. An Apparatus for Measurement of the Admittance Loss of a Mixer 367 

8-7. Tests of the AFC Mixer 372 




The term receiver^’ is customarily applied to an entire device which, 
when connected to a source of radio-wave energy, converts the informa- 
tion conveyed by the radio wave into a form in which it is directly 
usable. By this understanding, a conventional radio broadcast receiver 
includes everything from the antenna to the loudspeaker. In a television 
receiver, the information is presented on a cathode-ray tube; in facsimile 
transmission, the receiver supplies energizing voltages to a suitable 
reproducing device. It is conventional to discuss the design of such a 
receiver as a completely unified system, because similar techniques and 
components are used throughout the receiver. 

The problem of design of receivers for microwaves, however, falls more 
naturally into two subdivisions; first, the design of components involving 
microwave techniques, and, second, the design of those involving more 
conventional, low-frequency techniques. Because these two categories 
of components are so widely different in nature, it has been thought 
advisable to treat these two aspects of microwave receiver design in 
separate volumes of this series, with the present volume restricted in 
scope to those components that involve mic^rowavo t(^chni([ues. Volume 
23 of this series covers the details of assembly of the microwave and low- 
frequency components into a complete receiver unit for use in specific 
microwave radio systems. In addition, the dc^tails of amplifier design 
are covered in Vol. 18 of this series. The scope of the present volume will 
include a discussion of those components of a mi(U‘owavc receiver which 
involve microwave energy. 

If a transmission system from a receiving antenna is connected to the 
input terminals of an assembly of these mi(‘.rowavc components, energy 
in a form to be treated with lower-frequency te(‘.hni(iues is derived from 
the output terminals. There are many different ways in which such an 
assembly of components can be made, the choice l)eing dependent upon 
the particular requirements that the receiver must satisfy. Since the 
experience upon which this volume is based is largely with receivers 
specifically designed for radar, by the Radiation Ijal)oratory in conjunc- 
tion with outside companies, the emphasis will l)c rather heavily weighted 
toward the design of microwave components for this service. It is 
hoped, however, that the information will be found of value to those 
interested in the design of microwave receivers for other applications. 




[Sec. M 

14. Definition of Terms. — ^Before proceeding with a discussion of the 
properties of microwave receivers, it will be well to make specific state- 
ments as to the meaning of certain terms that will be used frequently in 
the following sections. Most of these terms are in common usage in 
radio practice, but they will be defined more generally here, in some 
cases, to make their application to microwave devices apparent. In 
other cases, a confusion exists in the meaning of terms, and their usage 
in the following sections will be clarified by these definitions. 

The conventional meaning of the term receiver has already been dis- 
cussed and this meaning will be used throughout the present volume. 
The classification may be begun by analogy to low-frequency techniques, 
and by the definition of those terms which have relevance to the present 
work. A conventional radio receiver usually begins with a radio-fre- 
quency amplifier. This term, abbreviated ^'r-f amplifier,” will be used to 
denote a device that reproduces at its output terminals a signal having 
the same frequency and modulation components as those impressed 
upon its input terminals, but at a higher power level. The r-f amplifier 
must be operative directly for signals at the frequency of the received 
wave, which means, for the present discussion, that it must be a micro- 
wave device. 

It wiU frequently be necessary to use the concept of bandwidth” in 
the following sections. In a qualitative sense, this term will be used to 
mean the extent of the range of frequencies within which the particular 
device in question has a relatively uniform amplitude-response character- 
istic. The exact amount by which the amplitude response may vary 
within this band will be defined in a manner which depends upon the 
device in question. An exact definition of noise bandwidth ” will be given 
in a later section of this chapter dealing with figures of merit for receivers. 

By the tuning range” of a component will be meant the extent of the 
range of frequencies to which the component can be adjusted with uniform 
response. ^ The question of tolerances arises in this connection and the 
specification of tolerances will be discussed when particular devices are 
described. If a component is tuned to a frequency within its tuning 
range, the magnitude of its response and its bandwidth should be sub- 
stantially independent of that tuning. 

Any microwave circuit which, is retuned, restricts the tuning 
range of the receiver to a range less than that of most microwave circuits 
will be considered as a preselecting circuit. A tuned r-f amplifier would 
thiis be a preselectoiv-a concept which is in agreement with common 
usage at low frequencies. Also under this definition would be included 
any selective filter m the microwave section of the receiver which must be 
crfthe procedure for changing the frequency setting 

Sec. 1-1] 



In conventional radio practice, the superheterodyne receiver is the 
most widely used and most flexible type of receiver. A fundamental 
group of components used in a receiver of this type is the group making 
up the frequency converter, often called simply the '^converter.*' This 
group of circuits can be defined as one that has the property of giving, 
at its output terminals, a signal containing the same phase and amplitude 
relationships among its components as those found in the signal impressed 
upon its input terminals, but having a center frequency differing from 
that of the input signal. As usually employed in a superheterodyne 
receiver, the converter changes the frequency of signals from the radio 
frequency derived from the antenna into a lower, or intermediate, 
frequency. In some applications, however, it is desirable to use a con- 
verter that increases the signal frequency. The bandwidth of a converter 
specifies the range of frequencies at the input terminals which will be 
converted into the same range at a different center frequency at the 
output terminals. 

The most common converter is one that combines a wave from a local 
oscillator with the signal wave in a mixer” circuit. Because the com- 
ponent derived from the mixer is usually the difference, or beat, frequency 
l)etween the signal and the local oscillator, an oscillator so used is often 
called a beating oscillator. In low-frequency practice, a tube containing 
elements that, when associated with the proper circuits, can be used as a 
mixer, as well as elements that can be used to form the beating oscillator, 
is termed a converter tube. A tube that does not contain elements to 
form a beating oscillator, but that does contain separate elements for 
the injection of signal voltages and for the injection of local-oscillator 
voltage, is called a mixer tube. Often, the two sets of voltages are 
injected on a single element after their superposition has occurred in a 
common circuit. The tube may then be considered as a detector, and 
for this reason the term '^first detector” is often applied to this part of a 
superheterodyne receiver. 

A detector ” will be defined, therefore, as a device that produces in its 
output circuit a voltage that has a-c components derived from amplitude- 
modulation components of the wave, or superposition of waves, at its 
input terminals. In addition, there is a d-c component of the voltage at 
its output terminals which depends upon the averaged amplitude of the 
suporposcul waves at the input terminals. When a detector of this sort 
is used as a part of a mixer, only the a-c components in the desired 
freciuency range are utilized. Since a detector usually consists of a 
device in which the currents induced are not linearly related to the 
exciting voltages, components of many other frequencies are also gener- 
ated, but these are not utilized. It is for this reason, however, that the 
element that functions as a detector can also be used as a harmonic 


[Biflc. 1-2 

generator, ^ce both functions are the result of its nonlmeanty A 
Ltector is used directly as a receiving element in nonsuperheterodyne 
receivers in which the incoming wave is converted directly from a micro- 
wave dgnal to a voltage containing only the modulation components. 

1.2 Effect of Type of Signal on Receiver Design.-The great ma]onty 
of receivers for microwaves in present use are designed for the reception of 
conasting of pulses of short time duration. In appHcations such 

as pulse radar, the pulses are usually 
not longer than a few microseconds 
(10"® second) and in some cases are 
as short as one-tenth microsecond. 
An understanding of the factors that 
enter into the design of receivers for 
short pulses may be gained from the 
consideration of a single pulse of micro- 
wave energy, as shown in Fig.1-1. 

If the amplitude of the pulse is 
as unity and its time duration 
as T, the pulse amplitude can be de- 
scribed as a time function which is 
zero for \t\ > t/2 and is equal to 
cos(<i)oi + <t>) lor \t\ < tI’I, where wo is 
2 t times the frequency of a continuous- 
wave signal that has been turned on 
at i = -t/2 and off at « = t/2. The term (#> is an arbitrary phase factor 
included for generality. The Fourier transform, p(w), for such a function 
is given by 

Fig. 1*1. — Graphical representation of a 
rectangular r-f pulse. 


cos (woa: -|- ix. 

( 1 ) 

The limits of integration are —t/2 and -1-t/2 because the time function 
is zero everywhere outside this range. The result of oerforming the 
integration is 

ff(«) = 


sin (w-coo) J (“ + 



CO + CO() 

( 2 ) 

which shows that the postulated pulse or wave train contains frequency 
components extending infinitely far in both directions from co{)/2t. If 
the carrier frequency, ci)o/27r, is large compared with 1 /t, the second term 
in Eq. (2) is negligible, and the frequency components have amplitudes as 
shown in Fig. 1*2. 

Sec. 1*2] 



The response of a receiver to a pulse of this sort obviously depends upon 
the bandwidth of the receiver. A detailed discussion of this dependence 
is outside the scope of this volume. Suffice it to say that, usually, the 
optimum band\vidth is approximately the width of the principal maxi- 
mum of the frequency spectrum. 

The best width and shape for the 
bandpass characteristic of the re- 
ceiver depend primarily upon the 
degree of fidelity with which the 
pulse must pass through the re- 
ceiver and the sensitivity require- 
ments that must be met. In any 
case, most of the energy in the pulse 
is contained in the principal maximum. In order to receive most of the 
energy carried in pulses from 0.1 to 1.0 /xsec in duration, the receiver 
bandwidths required are 20 to 2 Mc/sec. 

The effect of this requirement on the design of the microwave com- 
ponents must now be considered. Because the carrier frequencies 
concerned are usually from 3000 Mc/sec upward, it is apparent that a 
microwave component must have a loaded Q of 100 to 1000, for the 
bandwidths stated, before it begins to affect the receiver bandwidth. 
Circuits as sharply resonant as this are rarely encountered, and the band- 
width requirement for the microwave components is therefore seldom 
difficult to meet. On the other hand, it is relatively simple to achieve 
resonant circuits that are sufficiently sharp to obtain a certain degree 
of preselection, if desired. The bandwidth requirement affects the 
microwave receiver because it is so small rather than because it is large. 
For a bandwidth of 2 Mc/sec, the receiver must remain stable in fre- 
quency to 2 Mc/sec in at least 3000 — and perhaps as many as 30,000 — 
Mc/sec. Thus a frequency stability of 1 part in 15,000 may be required. 
This would correspond to maintaining an ordinary broadcast receiver 
to within 50 cps at a rec,civing frequency of 750 kc/sec, whieffi requires 
some care. For this reason, automatic frequency (control has become a 
standard part of almost all microwave rciccivers, and thus provision for 
it is an important factor in the design of microwave components. 

In receivers for radar sc^rvice, the automatic freciuency control is so 
arranged that the nuieiver is maintained at the local transmitting fre- 
quency, although this freciuency may vary. Ifence, in the following 
chapters, great emphasis will be placed on the various methods by which 
automatic frequency control of this kind can be achieved. There will 
also be a discussion of the various techniques that have been devised for 
absolute frequency control for receiver bandwidths of this order. An 
exception to the policy of excluding the discussions of low-frequency 

Fig. 1*2. — Fourier frequency transform of a 
rectangular r-f pulse. 



[Bbo. 1-3 

circuits from this volume is made in the case of automatic frequency 
control. The low-frequency circuits used as a part of the frequency- 
control schemes are discussed in Chap. 7. The reason for including 
this discussion is that frequency control and stability are fundamentally 
connected with microwave oscillators and for that reason may be con- 
sidered a part of a microwave component. 

If microwave frequencies are ever to be used for transmission and 
reception of ordinary audio-frequency signals, and, therefore, conven- 
tional audio-frequency receiver bandwidths are desired, the frequency- 
stability problem will become of prime importance. It may then be 
necessary to maintain a receiver at an absolute frequency within 1 part 
in 10® or more. For this service, an entirely different approach to fre- 
quency control is required, and a certain amount of work in this direction 
has been done. Circuits developed for such purposes are fully discussed 
in Vol. 11 of this series because their major application, so far, has been 
in special laboratory equipment. 

Because most of the receiver components discussed in this volume were - 
designed to operate in pulse radar, the effect of a ‘‘duplexing system” 
on their design will be prominent. A duplexing system includes those 
parts of a radar set which make possible the use of a common antenna for 
transmission of large signals and reception of weak signals at different 
times. Such a system makes use of the fact that the amounts of trans- 
mitted and received power are of very different orders of magnitude, to 
facilitate the flow of transmitted power to the antenna and not into the 
receiver, and the flow of received power into the receiver circuit. Because 
these duplexing components are of very great importance in the design of 
modem radar, and because an exposition of the problems and design of 
the many types that have been developed is a large task in itself, only a 
rudimentary discussion of their functions and general nature will be 
given here. For a complete discussion of this subject the reader is 
referred to Vol. 14 of this series where it is treated in detail. Because 
duplexing systems have had so great an influence upon the design of the 
microwave receiving components, however, it will be necessary to give a 
qualitative description of some of the more important types. 

1'3. Qualitative Discussion of Duplexing Components. — As stated in 
the previous section, the duplexer components form a unit that makes 
possible the use of a common antenna for transmission and reception. 
In pulse radar this is done by making use of the fact that transmission 
and reception are accomplished at different times and at different power 
levels. The great majority of the receiving components to be described 
have been designed to work with duplexers of this kind, but it might be 
well to digress for a moment to add a few words about the more general 


class of duplexers with which transmissioii and reception may be accom- 
plished simultaneously. 

It is not the task of the present volume to discuss the desirability of 
common transmitting and receiving antennas, for this is certainly a 
question that must be decided for a particular system. At microwave 
frequencies, small but highly directive scanning antennas are usually 
employed and the exact alignment of two such antennas is not easy to 
maintain. In addition, the usual desire is for maximum directivity 
compatible with the available space, and, therefore, a single large antenna 
is more desirable than two antennas of half the area each. The further 
fact that this single antenna has twice the gain of the two smaller ones for 
both transmitting and receiving, makes the use of a duplexer, even with 
the loss of some transmitted and received power, definitely advantageous. 

A box representing a generalized duplexer is shown in Fig. 1-3. The 
box has three pairs of terminals. One of these pairs is to be connected 
to the antenna, one to the receiver, and one to the transmitter. For 
the best duplexing action the product of the available transmitted power 
sent to the antenna and the available received signal power delivered to 
the receiver should be as large as possible 
and none of the transmitter power should 
be coupled into the receiver. It can be 
shown that if the duplexer contains only 
linear circuit elements and if the received 
and transmitted frequencies are identical, 
the maximum value this product can have 
is 0.25. For example, if one-half the 
available transmitter power is radiated by the antenna, not more than 
one-half the available received signal power can be delivered to the 
receiver. This loss just compensates for the gain obtained through the 
use of a single antenna instead of two, each one-half the radiating area. 
Duplexers of this kind can be made up from such bridge circuits as the 
''magic T” and its equivalent circuits, described in Sec. 6*2. 

A duplexer for a radar system is different from this, in that simultane- 
ous transmission and reception are not required. In a radar system, the 
transmitted power is very high, and the prime requirement of the 
duplexer is that it protect the sensitive elements of the receiver from 
damage by this power. Because of the extremely fragile nature of the 
best receiver elements, great effort must be made to achieve adequate 
protection. An attenuation from 70 to 80 db is needed between the 
transmitter and receiver when the transmitter is actuated. This attenu- 
ation is realized through the use of a resonant chamber Riled with an 
appropriate gas at low pressure. The resonant chamber is so designed 

Fig. 1-3. — Generalized roproaoiita- 
tion of a duploxer. 



[Sec. 1-3 

that a narrow gap exists between two posts. In the gap, the electric 
field is built up to a value considerably greater than that in the normal 
t r an smi ssion line. If the field at this gap is less than sufficient to break 
down the gas by ionization effects, the resonator transmits an incident 
wave at its resonant frequency with little attenuation. Boc-ausc the 
resonant frequency is adjusted to be that of the received signal, the (cavity 
acts as little more than a preselection circuit for tlic r(K*.(uvc^i’. l''he 
resonator is sometimes made up of a combination of several individual 
resonators and corresponds to a multituned circuit passing a widci band of 

from T-junefion 



tuning screw 

Retaining ring 




Vacuum tight 
solder joint 



Ijg diam. flange 

To mixer 

1" dlam. flange 

^’IG. 1-4.— Cross-sectional view of a 1B27 Til switch. 

In thi, owe, 8V«, it, n„|i„„ ,„,.y 

that necessary to sustain the arc- thus if r*'*' 

resonator to the receiver is sufficiWl-B- ’ n ‘wiplinK of the 

iato the receiver to t 

the arc is always greater tw j required to strike 

higher power is transmitted for a ve^^short^ t' i‘^ 

each transmission period Thi^ nnw ^ beginning of 

aMMth.p,»tm<BtIikeIytod»mng8the.-«oivcr, SnA 


a resonator is called a TR switch, because of its function as a self-actuating 
transmit and receive switch. The design of this switch always involves a 
compromise between the leakage power that reaches the receiver during 
transmission and the attenuation suffered during reception. For a 
detailed discussion of this problem and for details of the design and gas 
content of the resonator, the reader is referred to Vol. 14 of this series. 
Fig. 1-4 shows a cutaway perspective view of a resonator commonly used 
as a TR switch. 

When the arc of the TR switch is firing, a wave incident at the input 
side of the TR cavity is almost completely reflected. The cavity may 
therefore be placed in a side aim, as a T-connection to the main Ime that 
connects- the transmitter to the antenna. The phase of the reflection 
coefficient is such, with an iris-coupled cavity, that it is equivalent to a 
short circuit in the plane of the input iris. To obtain transmission of the 
transmitter signal past the junction without reflection, the length of line 
from the wall of the waveguide to the input iris is chosen to be approxi- 
mately an integi'al number of half wavelengths. For coverage of a wide 
frequency band, the cavity is mounted with its input iris in the wall of the 
main waveguide. With a loop-coupled TR switch the phase of the 
reflection coefficient is determined by experiment, and the cavity is 
(‘.onnoctod in such a way as to act as a short circuit at the end of a stub 
line, an odd number of quarter wavelengths in eciuivalent length, on the 
side of the main coaxial line. 

During reception, the duplexer must also ensure that almost all of the 
available received signal power is transmitted through theTR cavity into 
the receiver. The transmitter, when not oscillating, has a resonant 
frequency differing from its os(*illation frecpiency, and it therefore 
reflects, almost completely, a received signal wave arriving through the 
line from the antenna. The lin(^ length between the transmitting oscilla- 
tor and th(^ side branch that contains the TR cavity and receiver can be 
chosen in such a way that waves traveling along the line from the antenna 
are transmitted into th(^ TR cavity and receiver without sei*ious reflection 
or absorption duo to the ])resenco of the piece of line terminating in the 
transmitter. For coaxial liiK's, the piece of line between the T-junction 
branch and the transmitter is ecjuivalent to a short/-circuited stub line, 
an odd number of (piartcu’ \vavelengths in length, such as is used for a 
right-angk', stub supi)ort. Tn (nirly radar eciuipment this line length was 
made variable to allow proper* adjustmemt for the particular transmitter 
tube in use. Jjahu*, it was found that a fixed Ieng1;h gives sufficiently 
good results for all transmitter tTd)es in a small frecpiency band. To 
ensure this, a specification test of the “cold impedance” of transmitter 
tubes intended for \is(^ with systems having a fixed distance between the 
TR cavity and the transmitter was set up. 



[Sec. 14 

An improved method for ensuring transmission of received signals to 
the receiver, is one that utilizes a second gas-filled cavity resonator, 
called an anti-TR or RT switch. This switch is so placed on a stub line, 
or in the wall of the main line between the transmitter and the branch 
leading to the TR switch that, when an arc is struck in its gap, during 
transmission periods, it causes little reflection of the transmitter wave. 
The cavity is timed to resonate at the transmitter frequency and it is 
tightly coupled to the input Ime. As a result a large standing-wave ratio 
for low-level signals is produced in the main line between the branch 
containing the TR switch and the branch containing the anti-TR switch. 
The spacing between these two branches is chosen in such a way that 
received signal power is coupled into the receiver with little reflection 
or absorption due to the line terminating in the transmitter, regardless of 
the cold impedance of the transmitter. 


To antenna 

— T" 

, J To transmitter ^ 

- 4 .- 

^ 1 ^ 


E vector is JL to plane 


of the page 

TR tube 

Fia. 1-5. — Schomatic representation of a duplexer. 

A sketch of the relevant parts of a typical duplexer is given in Fig. 1-6 
where the dimensions shown refer to equivalent electrical lengths. This 
is an example of only one of many forms in which duplexers have been 
made. For a thorough treatment of the subjects of TR switches, anti-TR 
switches, and complete duplexers, the reader is referred to Vol. 14 of this 

1-4. Figures of Merit for Receivers. — ^At low frequencies, the sensi- 
tivity of a receiver can be specified in various ways. Since atmospheric 
and man-made static is almost always present to some degree, the useful 
sensitivity is usually considerably below any limits imposed by purely 
phyacal or thermodynamical considerations. At microwave frequencies, 
such static is almost completely absent and the minimum detectable 
signal is determined almost completely by the masking effect of random 
noise. Such noise is developed because electric currents are not steady, 
but are made up of the flow of large numbers of electrons. Thermal 
agitation of the particles in a resistor gives rise to a random noise voltage 
across the terminals of the resistor. For this reason, the quantity called 

Sec. 14] 



the “noise figure” has become the figure of merit for microwave receivers, 
and deagn considerations that affect the noise figure of the receiver 
are of the first importance if the detection of the smallest possible signal 
strength is a prime requirement. 

Within any electronic circuit there exist sources of noise in the form of 
nmnll potentials developed by thermally excited fluctuation of electrons in 
the circuit elements. This thermal-agitation noise has been studied by 
many people and is often called “Johnson noise” after J. B. Johnson, ‘ 
one of the first to study the phenomenon. It has been shown that the 
mean square of the noise voltages in the frequency range vi to vz, devel- 
oped by a circuit element because of thermal agitation, is given by 

W^^kT\Rdv, (3) 


where k is Boltzmann’s constant, T is the absolute temperature of the 
circuit element in degrees Kelvin, R is the resistive component of the 
impedance of the circuit element, and v is the frequency of the noise- 
voltage component. For an interval of frequencies so small that R may 
be regarded as constant, Eq. (3) becomes 

W = ^TR dv. (4) 

Any network made up of linear passive circuit elements such as resis- 
tors, condensers, and inductances, or them microwave equivalents, may be 
considered as a noise-voltage generator with an open-circuit mean-square 
noise voltage given by Eci. (4) in the narrow frequency band dv, where R 
is the resistive part of the impedance measured across the terminals of the 
network. Since the power available from such a generator is 



" AR’ 

( 5 ) 

the available noise power in the frequency band dv is 

dP = kT dv. («) 

For a linear four-tei-minal network with a signal generator connected 
to the input pair of terminals, a gain G may be defined. The network 
may be considered as a now source of the signal developed in the signal 
generator, and it will deliver maximum power when the output load has an 
impedance that is the complex conjugate of that measured across the out- 

1 J. B. Johnson, “Thermal Agitation of Uloctricity in Conductors,” Phya. Rev., 32, 
97 (1928); H. Nyquist, “Tliermal Agitation of Electronic Charge in Conductors,” 
Phya. Rev., 32, 110 (1928), J. B. Johnson and F. B. Llewellyn, “Limits to Amplifica- 
tion,” Elect. EnpW; W, 1449 (1934); F. C. Williams, “'I'hermal Fluctuations in 
Complex Networks,” Wireless Section, I.E.E., 13, p. .53, Mandi 1938. 



[Sec. 1-4 

put terminals of the network. If So and S are the available powers from 
the network and from the signal generator, respectively, the gain of the 
signal-generator-network combination is defined as 

G = (7) 

This definition says nothing about the impedance match between the 
signal generator and the network; in fact, the value of G depends upon 
the impedance of the signal generator as well as on the network. It is 
a maximum when the impedance of the signal generator is the complex 
conjugate of the impedance measured across the input terminals of the 
network, when the output terminals of the network are connected to a 
load having an impedance equal to the complex conjugate of that at the 
output terminals. 

Associated with the output impedance of the signal generator, there 
will be thermal-agitation noise, as discussed earlier in this section, the 
available noise power being given by Eq. (6). From the four-terminal 
network there will also be an available noise power in the frequency 
band dv. If dN is the noise power available from the signal generator, 
and dNo is the noise power available from the output terminals of the 
network, it is found that 

So S ’ 

where F is equal to, or often greater than unity. The quantity F is 
called the “noise figure of the network and is a measure of the signal- 
power loss in the network, as well as of the detrimental effects of addi- 
tional thermal-agitation noise, vacuum-tube noise, and noise from other 
sources added to the signal within the network. This quantity is thus the 
figure of merit for a receiver. For a perfect receiver, F is equal to unity, 
which means that a signal arriving at the output terminals is masked by 
noise no more nor less than it was as delivered from the antenna. The 
noise power available from the antenna of a receiver may be regarded as 
being developed in the radiation resistance of the antenna. As a con- 
sequence, its magnitude depends upon the temperature of the region of 
space from which the antenna receives radiation. Since receiver noise 
figures are usually considerably greater than unity, however, the part of 
the output noise power of the receiver which arises from the antenna 
resistance is small for an apparent antenna temperature near room 
temperature. R. H. Dicke^ has designed an ingenious device that 
measures very precisely the apparent temperature of the resistance of a 

' R. H. Dicke, ^‘Th© Measurement of Thermal Radiation at Microwave Fre- 
quencies,” RL Report No. 787, Aug. 22, 1946. 

Sac. 1-4 



receiving antenna, as a means for measuring the attenuation of microwave 
frequencies in the atmosphere. The noise figures of receivers are usually 
defined for an antenna resistance assumed to be at room temperature. 

A combination of Eqs. (6), (7), and (8) leads to the result 

dNo = FGkTo dv. (9) 

Both the quantities F and G depend upon the impedance of the signal 
generator, but in general, the impedance that gives minimum noise 
figure is different from the impedance that results in maximum gain. 
Because the noise figure is the important quantity, receiver design should, 
always be such as to minimize it, even at the expense of gain, for the gain 
can be increased easily at high level where any noise power introduced 
is negligible. 

In general, the noise figure is a function of frequency. An ''effective'^ 
noise figiu’o for the system may be defined in the following way. The 
output power from the network is read on a meter. We define Go as the 
product of the gain of the network and the fraction of the available power 
from the network delivered to the output meter. Power is delivered to 
the output meter only when the power available from the network 
ex<*.oods thermal-agitation noise, if the network and the meter are at the 
same temperature, for otherwise the transfer of energy from one body to 
another at a higher temperature would be implied. The noise power 
deliven-ed to the oiit])ut meter is 

N„ = kTo FGodv. (10) 

The use of the gain Go instead of G makes the integral convergent. As 
can 1)0 scon from lOq. (9), the product FG must be equal to or greater 
than unity at all freciviencics since, from Eq. (6), dNo must be at least as 
great as k'J'o dv. 

If F were unity at. all frciiuencios the output noise from the network 
would 1)0 

N'o=^ k-To GodP. (11) 



[Sbc. 1-4 

An effective noise bandwidth. B may be defined, for the combination, as 


where Gq mu is the maximum value of the gain with respect to frequency. 
The effective noise figure, from Eqs. (10), (12), and (13), is then 




This noise figure can be measured by determining iVo, Gq ^bx, and B. 
The quantity B may be considered as the bandwidth of an equivalent 
circuit having a constant gain equal to Go m« within the band and zero 
gain outside the band. This bandwidth can be calculated for bandpass 
circuits of many t3q)es if the bandwidth between the points at which 

jy Go max 

^0 = — o — 

is measured and the type of circuit is known. 

Network 1+2 

I 1 

Fig. 1-6. — Block diagram of cascaded networks. 

It is often necessary to use two or more networks with noise figures 
greater than unity, in cascade. To discover how the noise figure of the 
combination depends upon the noise figures of the individual networks, 
we may consider a situation such as that shown in Fig. 1-6. A signal 
generator is connected to network 1, this in turn connects to network 2, 
which finally connects to the output meter. Networks 1 and 2 can be 
treated as a single network, (1 + 2). From Eq. (9), 

dNoii+2) = F(i+2)(j(i+2)fcTo dv ( 15 ) 

where the quantities are all the same as before except that they refer to 
the combined network (1 + 2) . The gain of the combination must 
be equal to the product of the individual gains Gi and 0^, where Gi depends 
upon the output impedance of network 1, in accordance with the defini- 
tion of gain, Eq. (7). Therefore, 

di\ro(i+2) = P {i+2)GiGikT(t dv. ( 16 ) 

The available noise power from network 1 is 

dN 01 = FiGJcTq dv, 

Sec. 1-4] 



whereas that part of the available noise power from network 2 caused by 
noise output from network 1 is just 

dKa+% = = FiGxG 2 kTo dv, ' (17) 

The part of the available output noise power from network 2 which 
arises in network 2 and in the output impedance of network 1 is 

dNo 2 = F^ 2 kTo dv. (18) 

The part of this originating in network 2 is 

dKw) = dNo 2 - G^kTo dv, * (19) 

since the contribution resulting from thermal noise available in the output 
impedance of network 1 is feTo dv times the gain of network 2. These 
noise components are added and subtracted directly as power because 
they are completely I'andom and therefore can have no phase coherence. 
The total noise output (iiV‘o(i+ 2 ) from the combination must be the sum 

dN 0(1+2) = H" ^-^0(1+2) • (20) 

Putting Eqs. (17), (18), and (19) into Eq. (20) we have 

dN o(x+ 2 ) = F,a,G 2 kTo dv + F^^kTo dv - G^kTo dv. 

From this and l^q. (10), an expression is obtained for the over-all noise 
figure in the narrow frcciuency range dv given by 


Again, by use of the concept of the gain of network 2 associated with an 
output meter G 02 , ho that the integrals may exist, an expression analogous 
to Eq. (14), for the elTcctive over-all noise figure, is 

^ ( 1 + 2 ) 

( 22 ) 

If the network 1 is v(wy wideband compared with the combination of 
network 2 and the output meter, andO'i and Fi may therefore bo regarded 
as constants in the above integrals, then 

If* _ If 4 . ^'*-1 

/'(i+s, = /'i + -f,--’ 


where F* is defined by Mip (12). Eejuation (23) suggests the possibility 
of setting up apparatus to measure the noise figure of a single network 
used as network 1 in the combination. To do tiiis a measurement of 



[Sec. 14 

^(i+?) and of Gi must be made for the network in question in the apparatus 
so that, if F* is known by a previous measurement, Fi may be calculated. 
Since Ff will be a function of the output impedance of network 1, this 
function and the output impedance of network 1, under the conditions of 
the experiment, must be known or measured. 

To facilitate the calculation of over-all noise figures and the measure- 
ment of pertinent parameters for devices that can be simulated by linear 
passive networks, the concept of noise temperature ’’ has come into use. 
The noise temperature of a device is independent of the gain of the 
device, directly a measure of the noisiness of the network compared 
with a simple resistance. The noise temperature is defined as the ratio 
of the noise power available from the network to that available from a 
resistor at room temperature. It was shown by Eq. (9) that the available 
noise power in a frequency band dv is 

dN 01 = FiOikTodv. 

The same quantity for a resistor is 

dNo = kTo dv, (24) 

and the ratio dNoi/dNo = t, becomes 

t = FiOi. (26) 

By substitution of this expression into Eq. (23), 

^ ci+2) (-60; 

The noise temperature of a network may be measured by simply com- 
paring its noise output power with that of a resistor. The gain of the 
network may then be measured at a much higher signal level, provided 
the network is the same for a signal at this level as for noise, and these two 
quantities together will then be the figure of merit for the device. The 
effective over-all noise figure for a combination may then be computed 
from Eq. (26), provided the output impedance of the first network, and 
F* for the second network corresponding to this impedance, are known. 

An expression of the form of Eq. (23) may be derived in an analogous 
manner for more than two networks in cascade. Because the noise 
figure and gain of each network are functions of frequency (as is also the 
noise temperature), an expression for the over-all noise figure of a com- 
bination can be expressed only as an integral. In practice, however, one 
of the circuits very often has a pass band much narrower than that of the 
others, and an expression similar to Eqs. (23) or (26) is useful. Micro- 
wave receiving components very often have pass bands 10 per cent or 
more in width, whereas the pass band of the entire receiver is about 

Smc. 1 - 5 ] 



0.01 per cent; therefore Eqs. (23) and (26) are useful. If all but the last 
of n networks in cascade have pass bands wide compared with that of the 
last network, their gains and noise figures may be regarded as constants in 
integrals similar to those in Eq. (22). The effective over-all noise figure 
foi* the combination may then be written 

^^'<1+2+ . . . +n) = + 

^2 “ 1 









Because of the appearance of the gain factors in the denominators of these 
successive terms, it is clear that in a receiver, the contribution to the 
effective over-all noise figure from stages occuning after a reasonable 
gain has been achieved is negligible. Another way of saying this is 
simply that the noise contribution of the early stages, because it is 
amplified, masks any contributions to the total output noise which might 
he made by later stages. It is clear, then, that the microwave com- 
[)<)nonts, since they must necessarily be the first in any cascade of circuits 
making iq) a microwave receiver, play the dominating role in determining 
the figure of merit for the receiver. 


1*6. The Low-level Detector. — The simplest kind of receiver at any 
fnKiuenc.y (‘insists of a detector followed by an amplifier, as indi- 
<‘.at(Kl in l<"ig. 1*7. At microwave frequencies, the detector for such a 
re(^eiver must respond directly to the microwave energy. The detector 
lM‘ 0 (luc(’!S, at its output terminals, voltages derived from amplitude- 
modulation components in the envelope of the radio-frequency waves 
impressed upon its input terminals. All of the amplification in such a 
rcu-iciver occurs at the modulation frequency. A receiver of this kind 
ix^sponds to signals having carrier frequencies anywhere in the pass band 
of the r-f c.ompononts, including the detector. The ability to reproduce 
modulation voltages is determined primarily by the characteristics of 
the dotecitor and modulation-frequency amplifier, since the pass band of 
the othc^r r-f components is usually wide compared with the frequency 
spectrum of the received signal. 

A number of devices may be used as detectors for a receiver of this 
kind. Because they must respond directly to the microwave signal, 
however, only special kinds of vacuum tubes, in which the interelectrode 
spacings are very small, are useful. Transit-time effects make ordinary 



[Sbc. 1*6 

vacuum tubes almost completely unresponsive. In addition, such 
vacuum tubes must be built in a form that enables them to become inte- 
gral parts of the circuits associated with them. There exist a few tubes 
that meet these requirements — ^the GE ^'lighthouse ’’ and "oilcan^’ diodes 
and triodes for example. Such tubes, however, even with their small, 
but not negligible, interelectrode spacings, are useful only in the low- 
frequency part of the microwave region, principally above 10 cm. The 
design of circuits for the use of these tubes is too strongly dependent on 
the specific nature of the tube available to be described here. The pri- 
mary problem associated with the design of detectors using these tubes is 
the matching of the signal energy available from the antenna into the 
r-f input circuit. This problem can be solved by the use of standard 
microwave techniques, and circuits for this purpose will be found in 
literature dealing specifically with such tubes. A tube intended for use at 
microwave frequencies is so designed that it may be used as an integral 

Fig. 1*7. — Blook diagram, of receiver with low-level detector. 

part of the microwave circuit. In the lower-frequency part of the micro- 
wave region, only diodes are used as detectors; in the higher-frequency 
part of the region (10,000 Mc/sec and above), no satisfactory diodes exist. 
The diode is not the most satisfactory detector for most purposes, and is 
Avidely used only in applications where its ability to withstand high-power 
signals without damage is an important property. 

A detector for microwave signals can be made from one of several 
devices that change in electrical resistance when heated by incident micro- 
wave energy. One such device is a WoUaston wire. An ordinaiy 5- or 
10-ma Littelfuse contains such an element and can therefore be used as a 
detector. Another device of this sort is the thermistor, which also suffers 
a change in resistance when heated by microwave energy. The thermis- 
tor has a negative temperature coefficient of resistance, whereas the fuse 
wire has a positive coefficient. Either of these devices may be arranged 
in a circuit with an r-f matching transformer, in such a way as to absorb 
signal energy from an antenna. A steady current is passed through 
the fuse or thermistor, and incident r-f energy causes a change in the 
voltage produced across the element. 

The use of a detector of this kindisrestricted primarily to laboratory 
equipment. Its power sensitivity and noise figure are not so good as 
those of some other devices, and it cannot be used to detect modulation 


frequencies above a few thousand cycles per second because the thermal 
time constant limits the rate at which it can respond. Detectors of this 
kind are \videly used in test equipment, however, because they are easily 
procured and have some convenient properties. Because these detectors 
are capable of absolute calibration when used as bolometers in bridge 
circuits, they are most frequently used in low-level power-measuring 
equipment. A discussion of these applications is outside the scope of 
this volume, and is to be found in Vol. 11 of this series. 

A sensitive detector for microwave power is the very highly developed 
microwave version of the familiar crystal detector. Crystal detectors 
were early recognized as being especially suited to microwave circuits 
because of their extremely small physical size. A large amount of 
research has been devoted to the development of crystal detectors in 
fixed adjustment and packaged in small cartridges. A large advance in 
the understanding of the mechanism of operation of these devices and 
studies of the factors making possible the manufacture of high-quality 
crystals have led to mass production of cartridge units that are considera- 
bly superior to their earlier prototypes. The principal work on these 
devices has been toward the development of rectifiers for use as frequency 
converters, but advances in the development of low-level detectors have 
also been significant and have benefited considerably from the other 
development. Because the development of crystal detectors and units 
for mixers is a very large field in itself, it will not be possible to give it more 
than a cursory treatment in the next chapter. The reader is referred to 
Vol. 15 of this scries for a thorough review of the subject. The use of 
receivers of the variety under discussion here is not sufficiently wid(v 
spread or complex to warrant a separate treatment in this volume. In 
the following section some of the considerations that affect the figure of 
merit for such a receiver will be discussed. 

1-6. The Square-law’ Detector. — ^Both diodes and crystals function as 
detectors because of the nonlinear relationship between the cuiTent 
induced in them and the magnitude of the voltage impressed. In general, 
a smaller current is induced by a voltage of one sign than by a voltage 
of the other sign. If the current through a crystal is plotted as the 
ordinate on a linear scale, and the impressed voltage is plotted as the 
abscissa, a ciuve of the type shown in Fig. T8 is obtained. This plot will 
be seen to show considerable curvature or nonlinearity in the region of 
the origin, and it is upon this curvature that the action as a low-level 
detector depends. If an alternating voltage, such as is shown on the 
negative current axis, is impressed across this ciystal, the current that is 
passed through the unit has the form indiciated in the plot on the right- 
hand voltage axis. Because there is less current flowing during the 
negative half-cycles than during the positive ones, there is a net positive 



ISbc. 1-6 

current having magnitude related to the magnitude of the impressed a-c 
voltage. If the envelope of the a-c voltage varies with time, the net 
current varies in a related fashion and so has components derived from 
the amplitude modulation of the impressed voltage wave. This is a 

picture often used to explain detec* 
tion and can be found in any refer* 
ence book. 

The current in a nonlinear device 
can be expressed, analytically, as a 
function of the voltage, and ex* 
panded in a Taylor series. The 
nonlinearity is expressed by the 
terms in powers of the voltage 
higher than the first. For very 
small voltages, the term in the 
second power of the voltage is large 
compared with the higher*power 
terms. Therefore the rectified cur- 
rent produced from a veiy small 
signal must be proportional to the square of the impressed a-c voltage. 
For this reason, low-level detectors are often referred to as ^‘square law’’ 
detectors. The induced current is proportional to the incident r-f power. 
A diode or crystal detector is an entirely passive circuit, in that there is 
no source of energy other than the input signal. The maximum possible 
gain of such a detector, according to the definition of gain in the pi‘evious 
section, is unity. Because the detector is a square-law device, its gain 
decreases with decreasing signal strength unless a change of the output 
impedance accompanies the decrease in current flow. 

The detector, as a generator of modulation-frequency signals, may be 
considered as a current generator producing a current f, in shunt with an 
admittance g, as shown in Fig. 1-9. . The value 
of i is proportional to the input power to the 
detector and the value of g is also dependent 
upon the input power level. At very low 
levels, the value of g is relatively independent 
of the power level, and an effective measure 
01 tne gain oi tne device can be obtamed. queucy equivalent of a detoc- 
Because of the square-law dependence of the 

magnitude of the current generated, this gain is directly proportional to 
the input r-f power. It is clear that the concept of the noise figure for 
such a detector is not very useful since the noise figure, too, depends 
upon the input-signal level. A quantity that is a measure of the quality 
of a square-law detector can be defined in terms of the magnitude of the 

Fig, 1‘8. — Graphical representation of 



current produced by the generator per unit of incident power and the 
magnitude of the generator conductance associated with it. 

1*7. The Minimum Detectable Signal Power. — Because the conver- 
sion eflSlciency (gain) of a diode or crystal detector at low level is so small, 
the device may be described in terms of a two-terminal-pair network in 
which the transfer admittances are very small compared with the self- 
admittances associated with the input and output terminal pairs. In 
such a network the input admittance is almost completely independent of 
the load admittance presented to the output terminals. Maximum power 
is therefore delivered through the network when the admittance of the 
r-f generator connected to the input terminals is the complex conjugate of 
the self-admittance of these terminals, and the load admittance is the 
complex conjugate of the self-admittance of the output terminals. The 
design of the microwave unit associated with the detector is largely con- 
cerned with transforming the self-admittance of the input terminals into 
line admittance so that the detector may be connected to a matched 
antenna line with maximum power transfer. This specific subject will 
not be discussed explicitly in this volume, but the techniques involved are 
similar to those outlined in following chapters on ciystal-mixer design. 
One special problem connected with the experimental design comes about 
because admittances must be measured with signals sufficiently small to 
approximate the low-level condition. If the signal strength is sufficiently 
small, no change in the measured input admittance should result from a 
further decrease in the signal strength. Since, to satisfy this condition 
for crystal detectors, the power delivered to the crystal must \isually be 
less than 1 /zw, equipment for measurement of the input admittance by 
the standing-wave-ratio method must have high sensitivity. 

In the absence of currents through a ciystal the noise voltage at its 
output terminals is thermal-agitation noise, as discussed in Sec. T4 and 
given by l^q. (3). To evaluate the degree of sensitivity possible with a 
receiver using a crystal detec.tor, the detector can be considered to l)e 
connected to a noise-free amplifier, and the amount of r-f power necessary 
to produce a signal power ccpial to the noise power at the output termi- 
nals of the amplifier can be found. Tt has been shown that the current 
induced in the crystal is proportional to the r-f signal power. This state- 
ment may be expressed as 

i = J-, (28) 

where i is the short-circuit current, P is the available r-f signal power, 
and b is a proportionality constant dependent on the crystal. Since P 
is defined as the available power rather than that dissipated in the ciystal, 
b includes any losses caused ])y mismatch bestweem the signal sour(*.e and 



[Shc. 1-7 

the crystal. If the output terminals of the crystal are connected to the 
input terminals of the noise-free amplifier of gain 0, the output signal 
power from the amplifier will be 


ig 4b^g 


For this quantity to be equal to the output noise from the receiver it is 
required that 

gj = GkTB, (30) 

where B is the effective noise bandwidth of the amplifier, as defined in 
Sec. 1-6. This equation can be solved for the required r-f power, giving 

P = 2&VgV^, (31) 

where the expression has been separated into two terms because the first 
relates to the detector unit and the second to the amplifier. This expres- 
sion holds only for a noise-free amplifier, which cannot be achieved in 
practice; therefore an expression for a realizable situation must take the 
amplifier noise into account. The expression can be used, however, to 
obtain some qualitative information about receivers with low-level 
detectors. A more rigorous treatment of the subject will be found in 
Vpl. 15 of this series. In Chap. 2 of this volume, an extension of this 
discussion to include the effect of amplifier noise will be given. 

Equation (31) may be compared with a similar expression for an ideal 
receiver-^that is, one with a noise figure equal to unity. For sTich a 
receiver the r-f signal power required to equal noise power in the output 
terminals is just 

Po = kTBu (32) 

The bandwidth Pi is the effective noise bandwidth of the over-all receiver. 
For a square-law detector. Pi is the effective noise bandwidth of the 
modulation-frequency amplifier. This immediately brings out one 
feature of a receiver of the detector type. Because the efficiency of the 
detector is so small, the output noise is independent of the r-f bandwidth 
of the receiver. In reality, there are two different pass bands to be 
considered: first, the width of the region of radio frequencies to which the 
receiver is sensitive, and second, the pass band of the amplifier, which 
determines the kind of modulation components to which it will respond. 
For an ideal receiver, the effective noise bandwidth is equal to the scpiaro 
root of the product of the bandwidth before detection and that after 
detection, because it is the fluctuation in detected noise power, which can 
pass through the circuits following the detector, that tends to mask a 
small signal. The performance of a receiver in which a low-level detec- 



tor is used approaches that of the ideal receiver more closely if the r-f 
baudwidth is large compared with the Simplifier pass baud thau if the two 
pass bauds have siiuilar widths. This is the type of service iu which 
receivers of this kiud have beeu most widely employed. Fot use at 
beacou stations, for instance, a receiver that responded to pulses of 
about 2-j«seo duration anywhere in a frequency band of about 120-Mc/sec 
width, was required. The simplicity of a receiver with a crystal detector 
was considered worth the loss in ultimate sensitivity compared with 
other receivers. For very large bandwidths, greater thn-n about 160 
Mc/sec, only receivers with the low-level detectors have so far been used 
to receive in the whole band continuously, because amplifiers have not 
yet been made for bands wider than about 70 Mc/sec. If intermittent 
response to each frequency in the band is acceptable, a sweeping super- 
heterodyne Eoay be used. 

If the receiver is to be responsive to a band of frequencies only suffici- 
ently wide to carry the desired modulation components, then the band- 
width before detection and the over-all receiver bandwidth are similar. 

P 26 

Po VkTB 


The smaller this quantity, the more closely does the receiver having a 
low-level detector approach the ideal noise-free receiver. It will be seen 
that, again, wide pass bands are favored; thus, for example, the low-level 
detector might be satisfactory for receivers designed to respond to 
extremely short pulses. In general, however, for receiver bandwidths 
of 1 or 2 Mc/sec (before detection) the minimum detectable signal power 
is larger, by a factor of about 10®, than that obtainable with receivers of 
other typers. Receivers of the low-level-detector type have not been used 
extensively, except at beacon stations. 

One way of reducing the minimum detectable signal for this type of 
receiver is to precede the detector with r-f amplifiers having sufficient 
gain to make noise generated ahead of the detector contribute a signifi- 
cant part of the total output noise from the detector. In this case the 
over-all noise figure of the system becomes dependent on the noise figure 
of the r-f amidifying system. If the amplification is sufficiently great 
to make r-f noise contribute all but a negligible part of the detector out- 
put noise, the receiver noise figure is completely determined by the noise 
figure of the r-f amplifiers. Since these amplifiers are usually made 
with resonant circuits, they also act as preselectors. The receiver is then 
similar to the tuned r-f receivers commonly used at lower frequencies 
before the advent of the superheterodyne. Because the minimum signal 
power detectable by a low-level detector is relatively large, a high gain 



[Smc. I'S 

would be required of a noise-free amplifier. In the example cited, the 
gain would have to be greater than 10®. A gain this large would require 
several stages of amplification by tubes available even at the lowest fre- 
quencies in the microwave region. In this low-frequency region, improve- 
ment can be made by use of r-f amplifiers, but the system becomes 
relatively complex and a smaller minimum detectable signal can be 
obtained with a superheterodyne receiver. It would be advantageous 
to use noise-free amplifiers ahead of a superheterodyne receiver. Because 
a superheterodyne receiver having a moderate bandwidth can detect a 
much smaller signal than can the low-level detector, less gain would be 
required of a noise-free amplifier to make the over-all noise figure 
approach unity. A discussion of existing types of r-f amplifiers will 
therefore be deferred until the superheterodyne receiver has been 

1'8. The Superheterodyne Receiver. — ^The superheterodyne receiver 
makes use of a frequency converter, which changes the signal into one 

Fig. mo, — B lock diagram of a superheterodyne receiver. 

centered at a different frequency. The signal is then amplified at this 
new frequency before demodulation by a detector. Because the ampli- 
fication usually occurs at a frequency lower than the signal frequency 
(that is, the converter produces a downward frequency conversion), the 
amplifier is called an intermediate-frequency or i-f amplifier. A detector 
at a relatively high level is used, following the amplifier, to detect the 
modulation components carried by the signal, and modulation-frequency 
amplifiers are usually used to make the signal large enough to drive the 
reproducing device. A block diagram for such a superheterodyne 
receiver is shown in Fig. 1-10. 

At conventional frequencies, the advantages of a superheterodyne 
over receivers of other types are numerous. The fact that the i-f ampli- 
fier is operated at a fixed frequency allows the receiver to be designed 
with almost any shape of bandpass characteristic desired, with full utili- 
zation of the gain available from the tubes used, compatible with the band- 
pass circuits. The r-f selectivity, except for image-frequency effects, is 
completely determined by the selectivity of the i-f amplifier. Because 
this amplifier need not be tuned, highly selective circuits can be used. 

Sec. 1-81 



The tuning of a superheterodyne receiver is accomplished by adjustment 
of the frequency converter and of any selective circuits occurring between 
the receiver and the antenna terminals. 

Another property of this receiver is that the signal level at the second 
detector is sufficiently high to make the noise contribution from this 
part of the system completely negligible. Under this condition, the 
detector may be chosen on the basis of its fidelity in reproducing modu- 
lation, rather than on the basis of its noise figure. Relatively little 
modulation-frequency amplification is needed because the output level 
of the detector is high. 

As a receiver for microwave signals, the superheterodyne has another 
property, which is not so important at other frequencies. Ordinarily, 
the radio frequency and intermediate frequency are of the same order of 
magnitude but this need not be so. For a microwave receiver, the fre- 
quency converter is usually made to convert the microwave signal into 
one at a relatively low frequency, with the result that conventional 
lumped-constant circuits and ordinary pentode and triode vacuum 
tubes may be used in the i-f amplifier. A receiver having a noise figure 
approaching that of a low-frequency amplifier can be made, provided the 
frequency conversion can be accomplished with a device having a small 
noise figure. Under such a condition, an r-f amplifier would not improve 
the over-all noise figure of the receiver unless it had considerable gain and 
a noise figure smaller than that of the frequency-converter and the i-f 
amplifier combined. 

Another property of the superheterodyne receiver, especially for 
mic.rowavc frequencies, is its susceptibility to frequency control. In most 
microwave receivers, the intermediate frequency is less than 1 per cent 
of the radio frequency; consequently, the effect of time and temperature 
drifts in the highly selective circuits upon the receiver frequency setting 
is smaller, by a factor of 100, than it would be if the selectivity were 
accomplished at the radio frequency. Furthermore, since there is little 
to be gaincnl in making any r-f circuits as selective as the i-f ones, the 
control of the receiver frequency can be accomplished by control of the 
<‘.onvert(u- alone. Thus, the superheterodyne receiver is especially well 
adapted to microwave frequencies and has been used almost exclusively 
exc.ept in cases where the receiver bandwidth must be greater than can be 
accomplished with i-f amplifiers. The recent advances in the develop- 
ment of i-f amplifiers (see Vol. 18 of this series) have resulted in amplifiers 
with noise figures near unity and bandwidths much greater than were 
previously used. The emphasis of this volume will be on the subject 
of circuits for frequency conversion and the circuits associated with the 
frequency control of the frequency-conversion device. The design of 
microwave low-level crystal-detector circuits will not be discussed sped- 



[Sec. 1*9 

fically, but tbe method of attack should be apparent from the methods 
discussed in connection with frequency converters. 

1'9. The Frequency Converter. — In low-frequency superheterodyne 
receivers the frequency conversion is accomplished through the combined 
use of a local oscillator and a mixer. The local oscillator is simply a 
continuous-wave oscillator operating at a frequency somewhat different 
from that to which the receiver is to be sensitive. In the mixer, a super- 
position of the local-oscillator wave and the input signal takes place. A 
beat, or heterodyne, frequency equal to the difference frequency between 
the two waves exists as an amplitude-modulation component on the 
superposition of waves within the mixer. The mixer produces at its 
output terminals a voltage or current corresponding to this heterodyne 
frequency. Signal frequencies that differ from the local-oscillator fre- 
quency by the intermediate frequency, produce a heterodyne frequency 
equal to the intermediate frequency and so are amplified by the i-f 
amplifier. If the signal is not a continuous wave but is a modulated 

wave, it may be considered as a 
combination of Fourier compo- 
nents, each of which produces its 
own heterodyne frequency. The 
output signal from the mixer con- 
tains a component for each compo- 
nent in the incoming signal. The 
amplitude, frequency, and phase relations between these components 
are preserved as the signal passes through the mixer. The signal 
entering the i-f amplifier therefore contains the same modulation as 
the r-f signal, but is centered at the intermediate frequency. Only 
those components lying within the pass band of the i-f amplifier will 
continue through the receiver, and it is for this reason that the band- 
width of the receiver is just the bandwidth of the i-f amplifier, provided 
no narrower circuits are used in the mixer, or ahead of it. A block dia- 
gram for a converter of this type is shown in Fig. ITl. 

If the local-oscillator frequency is /« there are two frequencies that 
give rise to the intermediate frequency // 3 . These are/« + and/o, — 
since the difference between each of these and/« is equal to the intermedi- 
ate frequency. For this reason, the combination of a converter and an i-f 
amplifier is sensitive to two r-f bands, each of a width equal to the band- 
Avidth of the i-f amplifier, and differing in center frequency by twice 
the intermediate frequency. This situation gives rise to one of the 
principal imperfections encountered in the superheterodyne receiver, 
the so-called image response. At ordinary frequencies, there is usually a 
tuned circuit associated with the signal input terminals of the mixer, 
which is adjusted to favor one of the two signal frequencies, and which is 


Fig. 1*11. — Block diagram of a converter. 

Sbc. 1'9] 



caused to follow the tuning of the local oscillator in such a m anner as to 
TYig^T' the required frequency difference. The frequency to which this 
circuit is tuned is termed the signal frequency for the receiver. The other 
frequency to which the converter unit is sensitive, and which is discrimi- 
nated against by the input circuit, is called the image frequency. There 
is no particular convention as to which of these is the higher frequency. 
Sometimes the choice is made so that the image frequency falls in a region 
where there are few strong singals to be expected. In this way, inter- 
ference by signals at the image frequency is minimized. In low-frequency 
receivers, the intermediate frequency is often chosen to be quite high to 
secure a large image suppression, without requiring highly selective cir- 
cuits in the r-f part of the receiver. However, the condition that the 
intermediate frequency be low enough to allow the use of conventional 
tubes and lumped-constant circuit elements limits the choice of inter- 
mediate frequencies for microwave receivers. 

It should be noted that, if no difficulties with interference or confusion 
of si gnals are encountered because of the two frequency bands of sensitiv- 
ity of a converter, there is little to be gained through the use of preselec- 
tion unless the noise figure of the converter is nearly unity. If a converter 
has a noise figure of unity, the entire noise power available at its output 
terminals originates on the r-f side of the converter. The ratio of a signal 
to noise power at the output terminals of the converter can be doubled by 
the use of a preselection circuit that eliminates the noise contributed 
from the image-frequency region. If a large part of the output noise from 
an imperfect converter arises Avithin the device itself, however, preselec- 
tion can have little effect on the available i-f noise power. Since this is 
true of all known frequency converters for microwave signals, the effective 
noise bandwidth of such a receiver is considered to be that of the i-f 
amplifier, whether or not preselection is used. In addition, a circuit 
that reduces the sensitivity of the receiver to image-frequency signals 
from the antenna does not necessarily suppress the i-f noise power availa- 
ble from the converter and may even increase it. Some of the small 
variations in converter noise figure which can be produced by special 
treatment of the image-frequency voltages are discussed in Chap. 2 in 
connection with the linear-network representation for a converter. 

Because a mixer usually contains a nonlinear circuit clement for the 
detection of the heterodyne frequency, there exist in its output circuit 
many frequency components of second and higher orders, corresponding 
to sums, differences, and products of all of the input frequencies and their 
harmonics. These components, too, can give rise to spurious responses 
in the receiver, especially if very strong signals outside the receiver band 
are allowed to enter the mixer. Preselection, which restricts the allowed 
frequency range to one comparable with the i-f bandwidth, is very desira- 



[Sbo. 1*10 

ble if such signals are anticipated, even if the fidelity and the minimum 
detectable signal, in the absence of interfering signals, are unaffected. 
Since most of the circuits to be discussed were designed for use in pulse- 
radar systems, preselection is achieved by means of the resonant TR 
cavity of the duplexer that precedes the converter. If the receiver is to 
be used for some other purpose, the design should therefore include 
a preselecting resonator that has characteristics similar to those of the 
TR cavity but need not be capable of electrical breakdown. Many of the 
circuits demand the use of such a resonator, independently of any pre- 
selection function for the over-all receiver, to allow satisfactory operation 
of the LO coupling circuit. For this reason, the TR cavity used with each 
mixer discussed wiU be indicated. 

As mentioned in Sec, 1-1, m which the terms “mixer” and “con- 
verter” were defined, some special vacuum tubes have been developed for 
performing these functions at conventional frequencies. Converter tubes 
combine the function of local oscillator and mixer in one envelope. 
Mixer tubes and the mixer sections of the special converter tubes accom- 
plish the mixing in the electron stream flowing to the plate of the tube. 
All of these electronic mixer tubes require that the drift time of the 
electrons through their many elements be short compared with the period 
of the r-f waves which they mix. Their performance consequently falls 
off at even lower frequencies than does that of the simpler conventional 
tubes. At moderately high frequencies, it has been found advantageous 
to return to the older technique of accomplishing the superposition of 
waves in circuits external to the tube and using a tube of simpler construc- 
tion, such as a triode or diode acting as an amplitude-modulation detector, 
to perform the mixer function. At microwave frequencies there is almost 
no other course, and even the drift time between cathode and grid in a 
triode, or cathode and plate in a diode, is excessive except in some very 
specially designed tubes in the lower-frequency part of the microwave 
region. Since the developments to be described in this volume arc 
chiefly concerned with the frequencies from 3000 Mc/sec upward, these 
tubes will receive practically no attention elsewhere in this book, but it 
might be well for historical purposes and for purposes of orientation to 
mention briefly some of the more successful types. 

1‘10. The Triode Mixer. — ^The effective noise figure of two cascaded 
networks, given in Eq. (26), depends inversely upon the gain of the first 
network, and directly upon the noise power available from it, as measured 
by t. If a triode or multielement tube is to be used as a mixer, the gain 
that can be realized falls off with increasing frequency because of the time 
required for the electrons to cross the gaps between the elements. One 
phenomenon caused by the transit time is an apparent grid-to-cathode 
conductance, which increases as the frequency is increased. This con- 

Sec. 1*10] 



ductance sets an upper limit to the grid-to-cathode voltage that can be 
developed from a given signal power, with the result that the gain decreases 
with increasing frequency. In order that this effect may be minimized, 
the interelectrode spacings must be made very small, and in order that 
the grids may function as electronic shields, they must then be made of 
very fine mesh. The manufacturing tolerances that must be maintamed 

Plate structure 

Low-loss glass 
Grid structure 

Low-loss glass 

Base and cathode 

Fig. 1-12. — Cross-soctional view of a typical lighthouse tube. 

and the difficulties of working with such extremely small parts have pre- 
vented the development of usable tubes of this sort for frequencies higher 
than about 3000 Mc/sec, except on a restricted, experimental basis. 

At frequencies up to 3000 or 4000 Mc/sec, tubes of the lighthouse 
type (plane-parallel electrodes) have been used as mixers. The noise 
figure of a mixer using such a tube 
has never been made so small as the 
noise figure for crystal mixers. 

Hence, the use of lighthouse tubes 
in this servi(^e has never become 
widespread exc.ept in th('. very low- 
est frequency region (below 1000 
Mc/sec). The design of tlu^ c.inuiit 
for such a device is determim^d 
largely by the particular tube avail- 
able. Usually a resonant circuit between the grid and cathode is employed 
to match the availal)le signal j)ower into the grid condiic.taiic.e of the tube. 

A sketch of a typical lighi.hoiise tube, such as the GL44(), or the 2C40 
tube, is shown in Fig. I - 12. The grid of this tube is a rectangular wire 
mesh, mounted on tlu^ grid ring and made of wire 0.002 in. in diameter, 
with the centers of the wii-es spaced 0.010 in. apart. The cathode-to- 
grid spacing averages 0.005 in. and the grid-to-plate spacing is 0.010 in. 
All of the elements arc; plane-parallel, including the cathode which is 

Fig. l-l,'i.-— CJirc.uit. (liagi'iitii of a ligliU 
liouHO-tiibo mixer. 


[Sec. 1-10 


indirectly heated. A typical low-frequency circuit using a lighthouse 
triode as a mixer is shown in Fig. 1-13. 

The tube is biased near cutoff by the self-biasing resistor in the cathode 
circuit and then driven relatively hard by the injected local-oscillator 
voltage. Consequently, on the negative half-cycle very little change in 
plate current occurs, whereas on the positive half-cycle considerable 
plate current flows. The average plate current, therefore, depends 
upon the magnitude of the voltage at the grid, and since this voltage is 
composed of the local-oscillator voltage plus a small signal voltage, the 
beat or difference frequency will exist as a component of the plate current. 
As long as the signal voltage is small compared with the local-oscillator 
voltage, as measured at the grid, the beat-frequency current flowing in 
the plate circuit must be directly proportional to the signal amplitude. 
The mixer, therefore, is a linear device, as contrasted with the square-law 
low-level detector. Because the tuned circuit must be resonant for the 
signal frequency, the efflciency of transfer of the local-oscillator signal to 
the grid is relatively low. Considerably greater local-oscillator power 
must be available than would be otherwise necessary. Moreover, the loss 
of signal power into the local-oscillator circuit must be kept small. This 
particular requirement is one that has an important influence upon the 
design of all mixers to be described, for it must be met if the minimum 
noise figure possible with a given type of mixer element is to be achieved. 
The resonant circuit in the plate lead of the mixer tube of Fig. 1T3 serves 
to develop an i-f voltage from the beat-frequency component of the plate 
current and so is made to resonate at the intermediate frequency. 

A sketch of the basic parts of a microwave mixer circuit designed by 
P. A. Cole for operation near 3300 Mc/sec, which is equivalent to the 
low-frequency circuit, is shown in Fig. 1-14. The resonant grid-to- 
cathode circuit is made up of the radial cavity, which is somewhat lessened 
in radius by the lumped-capacitance loading due to the grid-to-cathode 
capacitance of the tube at its center. The signal voltage is coupled in by 
means of the coaxial line, the center conductor of which crosses to the 

opposite wall of the resonator. The signal power may be matched into 
the cavity by proper choice of the distance from the center of the cavity 
to the point at which the coaxial line enters the cavity. The greater this 
distance, the larger the voltage stepup from the coaxial line to the grid. 
The signal hne also affects the resonant frequency of the cavity, and, 

consequently, the cavity diameter is not independent of the position of 
the.ji^^9u^ line. These two dimensions are determined experimentally. 

eve the small coupling between the grid-to-cathode region and 
lUt line, the distance from the outside edge of the resonator to 
t line is made considerably shorter than the distance to the 
[This procedure may be considered to be analogous to the use , 

Smc. 1 - 10 ] 



in the circuit of Fig. 1-13, of a much larger stepup ratio for the local- 
oscillator circuit than for the signal circuit. A matched termination on 
the local-oscillator line then contributes only a small admittance at the 
grid of the tube. Consequently, little signal power is lost in this con- 

ductance, compared with that delivered to the grid-to-cathode conduct- 
ance of the tube. '^Fo ensure that the local-oscillator line is matched, a 
cable with a distributed loss of several decibels between the local oscillator 
and the mixer is used. In addition, the cable sei'ves to minimize the 
effects on the local oscillator of the large reflections at the mixer of local- 


oscillator signals. Such reflections exist because the local-oscillator line 
is not terminated in the characteristic admittance of the line. In this way 
the behavior of the local oscillator is less affected by the mixer circuit than 
it would be in the absence of the dissipative cable, but the available local- 
oscillator power required is increased. 

The circuit of Fig. 1-14 includes no provision for tuning the resonator 
as would, in general, be required for a tunable receiver. This particular 
circuit was designed for operation with a very wide i-f amplifier to cover 
the entire range from 9.0 to 9.2 cm with fixed tuning. The Q of the reson- 
ant circuit was found to be just low enough to allow this. The resonant 
wavelength was 9.1 cm with a tube of average input capacitance. 

If the mixer must be tunable, provision for adjustment of the effec- 
tive resonator radius can be made. This can be done by the inclusion of 
screw plugs of large diameter so placed around the outside wall of the 
resonator that, when they are screwed into this wall, they fiU the region 
between the top and bottom resonator walls for a part of the circumfer- 
ence. The average radius is thus reduced, and hence the resonant fre- 
quency of the circuit is increased. The coupling ratio for the signal input 
line will not remain constant, nor will the cavity losses. It is not advisa- 
ble therefore to attempt to cover a very great tuning range by such a 
means. Because triode mixers are not used extensively In the microwave 
region, the many methods by which tunable cavities and measurements 
on them may be made will not be discussed here. The reader who is 
interested in this subject is referred to Vol. 7, which deals with micro- 
wave vacuum tubes, and Vol. 14 on TR tubes, where these matters are 
considered in detail. 

The triode mixer of Fig. 1*14 was found to have a noise figure of about 
100 or, as usually expressed since it is a power ratio, 20 db at the center 
of the band and about 23 db at 9.0 cm and 9.2 cm. The exact value 
depends, of course, on the particular tube used, but this value is not so 
small as the noise figure of receivers using other types of mixers. The 
noise figure of the triode mixer is high because, although it has a larger 
conversion gain than some other mixers, the noise power available in the 
plate circuit is large. All tubes develop noise through the '‘shot effect” 
and because some electrons are stopped by the grid. The over-all 
noise figure of a triode mixer decreases if the radio frequency is decreased, 
because the grid-to-cathode conductance decreases with frequency as a 
result of the decreased transit angle of the electrons. This allows a larger 
gain to be obtained with the mixer with almost no change in the available 
noise power, if the intermediate frequency is held constant. 

l-ll. The Diode Mixer. — Another tube that can be used in a con- 
verter is a diode. At low frequencies, where the transit angles are negli- 
gible, both the gain and the noise of the diode mixer are smaller than those 



Plate structure 


1.15. — Cross-sectional -view of 
typical diode used for a diode mixer. 

Sbc. 1.11] 

of a triode mixer. Like the triode, the dicde, to be useful at microwave 
frequencies, must have a small interelectrode spacing, in order to mini- 
mize the transit time. The diode must be so constructed that the tube 
can be made an integral part of the microwave circuit. The construction 
of diodes with plane-parallel elec- 
trodes, such as are used in the light- 
house tubes, has proved to be one 
of the most successful methods. 

Figure 1*15 shows the construc- 
tion of a typical diode. The cath- 
ode is plane, and forms the top of a 
cylinder that contains an indirect 
heater element, as in the triode. 

The anode is a cylindrical post, 
separated by a very few mils from 
the cathode, with its face parallel 
to that of the cathode. A typical 
low-frequency circuit for a mixer 
containing a diode is shown in 
Fig. 1-16. In addition to a d-c component, the diode plate current 
contains the beat-frequency component, because the diode passes a 
current only during the positive half-cycles of the input voltage, which 
consists of the superposition of the small signal on a relatively large 
local-oscillator voltage. If the beat frequency is equal to the intermedi- 
ate frequency, an i-f voltage is developed across the i-f resonant circuit in 
the plate circuit. As is true for the triode, the magnitude of this voltage 

is proportional to the amplitude of 
the signal voltage if the signal volt- 
age is very small compared with, the 
local-oscillator voltage. The circuits 
used between the cathode and plate 
of the diode may be the same that 
are used between the grid and cath- 
ode of the triode. If the shell of the 
tube is actually connected to the 
cathode, a bypass condenser must be 
built into the circuit l)etwccii the resonator and the shell to prevent short- 
circuiting of the i-f voltage. In some tubes, this condenser exists within 
the tube itself. This allows the resonator to be connected directly to the 
base part of the tube. The same is true for the triode circuit, where bias 
voltage must be developed for the cathode. 

The noise figure of the diode mixer used in combination with an i-f 
amplifier of noise figure /''2 is given by Eq. (26), where the gain G is always 

Signal < 













) I-f output 



t'l J 


by pass _ 

o •' 


Kiu. MO.- A 

cirouit for use of a diodo 
Uti 11 niixor. 



[Sec. M2 

less than unity, representing actually a loss, and the noise temperature t is 
greater than unity. Since the gain is less than unity, the noise figure of 
the succeeding i-f amplifier is relatively more important than for a mixer 
with a large gain. The best operating point, with respect to driving 
power from the local oscillator, results if a compromise is made between 
gain and noise temperature. The gain increases with increasing driving 
power, but the rate of increase becomes small for large local-oscillator 
drive. The noise temperature also increases with increasing driving power 
because of the larger current flow in the plate circuit of the tube. In 
addition, the output impedance varies with driving power, and there exists 
a limit to the amount of driving power that can be coupled into the mixer 
from a given local oscillator. If this limit is exceeded, the signal loss into 
the local-oscillator circuit becomes significant. The optimum driving 
power must consequently be chosen — ^usually experimentally — for the 
particular combination at hand. At 3000 Mc/sec, the minimum over-all 
effective receiver noise figure that can be achieved with a diode mixer is 
about 18 db. At higher frequencies, poorer noise figures are found, 
because of the increased transit angles. 

As a consequence of its relatively poor noise figure the diode mixer is 
not widely used; therefore it will not be discussed in detail here. For 
information about cavity circuits, the reader is referred to literature 
dealing writh tube design. Diode and triode mixers may be successfully 
used in the lower-frequency regions if noise figure is not a primary con- 
sideration and if resistance against damage by excessive input power is of 
great importance. A disadvantage in addition to that of noise figure is 
that these tubes must always be used in resonant circuits, in order that 
the shunting effect of the grid-to-cathode or plate-to-cathode capacitance 
may be eliminated. If a wide tuning range is desired for the receiver, the 
resonant circuit must be tuned at the same time as the local oscillator. 
To accomplish tuning, the physical size of the resonators must be variable, 
and the manufacture of the circuits and the operation of the receiver are 
therefore diflicult. These difficulties can be eliminated by the use of 
mixing elements of other types. 

1*12. The Crystal Mixer. — The crystal rectifier has been developed 
to the extent that it is the most effective mixer element for the super- 
heterodyne receiver at microwave frequencies. The qualitative descrip- 
tion of the operation of a crystal as a mixer is similar to that of the diode 
and, as in the case of the diode, the i-f voltage is linearly dependent upon 
the signal amplitude, for signals small compared with the local-oscillator 
power. Because the part of the crystal in which rectification takes place 
is physically very small, transit-time effects are minimized and may be 
neglected, for most purposes, even in the microwave region. The con- 
siderable effort that has gone into the design of crystal-rectifier elements 

Sec. 1*13] 



for this purpose during the war has resulted in a very great improvement in 
the various parameters that determine the usefulness of a crystal mixer. 
At the beginning of the development the crystal was found to be slightly 
better in over-all noise figure than any vacuum-tube mixer then available. 
The subsequent improvement has been so great that the crystal now com- 
pares even more favorably with the improved vacuum tubes now availa- 
ble. In fact, one result of the improvement in crystal rectifiers has been 
the replacement of vacuum-tube r-f amplifiers and mixers by the simpler 
crystal mixers, even at frequencies as low as 700 Mc/sec. The subject of 
the design of the ciystal unit is treated in Vol. 15 of this series. A short 
discussion of the properties of these units relevant to the design of mixer 
and converter circuits, as developed at the Radiation Laboratory, is to be 
found in Chap. 2 of this volume. In subsequent chapters, specific mixer 
designs are discussed. Suffice it to say, here, that rugged receivers using 
crystal units as mixers can be made that have over-all noise figures as low 
as a factor of 5 (7 db), at frequencies up to 25,000 Mc/sec. When it is 
realized that such noise figures were rarely achieved, even at frequencies 
of a few megacycles pci* second, before the war, the significance of the 
crystal as a mixer element for use at microwave frequencies and the justi- 
fication for placing the emphasis of tliis volume almost completely on a 
receiver of this typo become apparent. 

1*13. The Local Oscillator. — An important component of the super- 
heterodyne converter, which lias not yet been discussed but the existence 
of which has been assumed, is the local oscillator. Here, again, is a field 
of development which is so highly specialized and so extensive that it (^an 
not be discussed from the point of view of tube dc^sign in this volume. 
The physical and elecjtrical chara(*.teristics of the available local-oscillator 
tubes, however, have a considerable influence on the design of the mixei* 
units that will bo discussed. It is necessary, therefore, to describe 
briefly tubes of the more common types. 

The usefulness of the triode and of the more complex space-charge 
tubes is limited l)y the transit times l)etw('.(n the various elements when 
the tubes are to be used as oscillators, just as when they are used as ampli- 
fiers and converters. If a tul)e of this typo is to be us(hI as an oscillator, 
it is necessary that the gain of the tube as an amplifi(U' be greater than 
unity in order that T)ositiv(^ f(H’!d])a(^k can sustain oscillations. The only 
tubes of this type whic.h can be used successfully as oscillators are those 
that arc specially designed with small interelec±rode spacings and with a 
shape that allows them to be made an integral part of the cavity type of 
oscillator circuit. Tlie lighthouse tube is probably the best example of 
this construction available in quantity, but the highest frc(iuency at 
which most lighthouse tul)es oscillate is in the neighborhood of 3000 
Mc/sec. In order to make an oscillator for frequencues higher than this. 



[Sec. M2 

it is necessary to make use of entirely different principles. At present the 
most widely used local-oscillator tube is the klystron. This tube utilizes 
the principle of velocity modulation of an electron beam. In addition to 
its ability to oscillate at very high frequencies, the velocity-modulation 
oscillator, through the introduction of the reflex principle, has become the 
simplest kind to manufacture and to operate. It also has the advantage 
of being both electronically and mechanically tunable in a very simple 
manner. A klystron oscillator of the original two-cavity kind is shown 
schematically in Fig. 1-17. An electron gun, similar to those used in 
cathode-ray tubes, with focusing electrodes to form a small-diameter 
beam directed upward through the grids of the cavities, is indicated at 
the bottom of the figure. The beam is accelerated by the large potential, 
positive with respect to the cathode, on the cavities. The field is so 
shaped, and the grids of the cavities are so constructed, that the beam 

potential ~ 


Output line 

L 1 — Catcher 


5 - 

Drift distance 


cavity 1 
Electron gun with beam- 
forming electrodes 

Fig. 1*17. — Schematic diagram of a two-cavity klysitron oscillator. 

passes on through all of the grids with very small interception of electrons 
by the grids. The beam is finally collected on the positive electrode at 
the upper end of the tube. The cavities are made to be resonant at a 
common frequency and their shape is such that, if they are excited by a 
wave of the resonant frequency, a large field is developed between the 
two grids of each cavity. These grids may be considered as forming the 
capacitive part of a shunt-resonant circuit. The electric field, if it exists, 
is directed parallel to the path of the electron stream, and so will alter- 
nately accelerate and decelerate the electrons passing through the grids. 
In accordance with the usual procedure in describing the operation of an 
oscillator, the excitation of the cavities will be assumed to exist and the 
device will be examined to see if the excitation can be maintained. Sup- 
pose that cavity (1) contains some r-f energy. This cavity will velocity- 
modulate the stream sinusoidally with the frequency of the resonance of 
the cavity. As the stream drifts on toward cavity (2), the density of the 
electrons will no longer be uniform, since those slowed down by the field 
in the grid space of cavity (1) will be overtaken by those acjcelerated in that 
region. The spacing between the two cavities can be so chosen that there 
are bunches of electrons passing through the grids of the cavity (2) with a 

Sec. M4] 



recurrence frequency equal to the resonant frequency of cavity (1). The 
first cavity is therefore called the buncher cavity. If the second cavity 
is resonant at the same frequency and if, furthermore, the phase of the 
voltage in this cavity is properly adjusted, the field between its grids 
opposes the transit of electrons between them at the time the bunches 
arrive. In this way the electron stream is made to give up energy to 
the r-f field, since very few electrons transit the grids at a time when they 
would be accelerated and so take energy from the field. The second 
cavity is therefore called the catcher. Thus the passage of electrons 
through cavity (2) is made to maintain the energy in this cavity in suflfi- 
cient strength to allow some of this energy to be coupled out to excite 
cavity (1) and some to be coupled out as the useful power from the oscilla- 
tor. The proper drift time between the first and second cavities is 
obtained by choice of the acceleration voltage on the beam, and by the 
spacing between the cavities. It is, of course, influenced by the relative 
phase of the excitation of the two cavities, which in turn depends upon 
the line length of the feedback loop. A simpler embodiment of the 
velocity-modulation principle, for use as a low-power local oscillator is 
the reflex klystron. This tube operates in much the same fashion, but 
has only one cavity, used as both buncher and catcher, and is therefore 
easier to make and to operate. The two-<*.avity klystron, and even three- 
cavity klystrons, are used as power oscillators, amplifiers, and even as 
frequency multipliers. The various oscillator tubes and their uses are 
discussed in Vol. 7 of this series. 

1-14, The Reflex Klystron. — The reflex velocity-modulation oscillator 
may be described with the aid of Fig. 1*18. The beam of electrons passes 
through the cavity grids and enters 
the retarding field of the reflector 
which is at a negative potential 
with respect to the cathode. The 
retarding field is sufficiently strong 
not only to prevent the electrons 
from arriving at the reflcc.tor but 
also to return them through the i^kj. i-is. Kunotiomii dinwinK of the 
grids of the cavity. If an r-f field klystron, 

exists between the grids of tlie cavity, the electrons will be velocity- 
modulated by this field, and thus will be caused to form bunches as 
they drift toward the reflector and then back to the grids. The time 
between the first and second passages of a parti(*.ular gi’oup of electrons 
is dependent upon the magnitudes of the retarding field, and this field can 
be chosen to make the arrival of bunches l)ack into the grid region con*e- 
spond to the times when the field is directed against the backward 
transit of the electrons. The bunejhes, therefore, give up energy to the 



[Sbc. M5 

r-f field and maintain oscillation at the cavity frequency. The bunches 
form aroxmd electrons which, while traveling toward the reflector, pass 
through the cavity at a time when the r-f field is going through zero from 
the accelerating to the* decelerating direction. This is because the accele- 
rated electrons penetrate more deeply into the refiecting field and there- 
fore take a longer time to return to the cavity than do the unaccelerated 
electrons. The decelerated electrons, correspondingly, take a shorter 
time to return. For oscillations to be maintained, the total diift time 
of an electron that is not acted on by the field in the first transit must be 
{n + I) cycles, where n is an integer. For a given acceleration potential, 
there are several values of the reflector potential which will give rise to 
oscillations, corresponding to several different values of w. These are 
referred to as reflector-voltage modes. As the reflector voltage is increased 
in the negative direction with respect to the cathode, the mode number 
n decreases and, because the electrons are returned at higher backward 
velocities as the reflector voltage is increased, the output power increases 
with increasing reflector voltage. There is a limiting reflector voltage, 
however, for which the drift time becomes too short to give good bunch- 
ing. Thus, for a particular tube and accelerator voltage, there is a reflec- 
tor-voltage mode that gives maximum output power. It may be said 
that the velocity-modulation tube surmounts the difficulty of transit- 
time effects, first by causing the pertinent electrode gaps to be transited 
by accelerated electrons instead of by electrons starting from rest and, 
second, by making use of the drift time outside of these electrodes as 
the means of producing bunching. 

The reflex oscillator is simpler in operation than the two-cavity tube 
because there is only one adjustment that must be made to satisfy the 
condition for oscillation. This adjustment consists of setting the reflector 
voltage to give the proper phase to the reflected electron bunches. Oscil- 
lation occurs not only for a discrete set of voltages corresponding to an 
exact integral value for n, but also if the reflector voltage is varied 
slightly either side of the exact value. Operation under this condition 
reveals one of the most useful properties of the reflex oxcillator, namely, 
that of electronic tuning. The slightly incorrect reflector-voltage 
setting gives rise to slightly out-of-phase currents in the cavity resonator 
and these currents can be resolved into components, one in tlie correct 
phase and one at 90® to this. The 90® component is purely reactive in 
character and results in a change in the oscillator frequency in just the 
same way as would a change of the capacitance between the grids. Since 
the orthogonal component can either lead or lag the in-phase com- 
ponent, the frequency may be altered in either direction from the cavity 
frequency, depending upon whether the reflector voltage is made slightly 
greater or slightly less than the value making n exactly an integer. As 

Sec. M41 



the reflector voltage is altered from this value, there results, in addition 
to the frequency change, a decrease in the amplitude of oscillation, 
because the in-phase component of the induced cavity current falls off, 
and the oscillator finally falls out of oscillation. Most of the reflex 
oscillators currently used as local oscillators in frequency converters are 
so designed that a considerable range of frequency can be covered by the 
electronic tuning before the output power falls to half its value at the 
center of the reflector-voltage mode. Figure 1*19 shows a typical plot of 
the reflector-voltage modes of a reflex oscillator. The abscissa is the 
reflector voltage, increasing in the negative direction toward the right. 
The ordinate for the solid curves is the output power, and the ordinate for 
the broken curves is the frequency relative to the resonant frequency 
of the cavity. Since the mode of highest output power does not give the 
maximum timing range, the choice of the operating mode is made as a 

Fiu. 1*10.- -Typical rofltHil-of-voltaKo charaotoriHtioH for a roflox klystron. 

compromise between large output power and larg(^ electronic-tuning 

Since the reflector does not collect electrons, it draws no current. 
Consequently, the electronic tuning device can be a veiy-high-impedance 
source of voltage. For this reason, the provision for frecpieney control 
of a converter can be acconiplish(Hl very simply and clTectively througli 
the control of the reflector voltage of the local oscillator. In many 
eases, of course, the freqmuicy range of the reflector tuning is not sufficuuit 
to cover the required tuning range of the receiver and mecdianic^al tuning 
must be incorporated as well. Mechani(‘-al tuning is accomplished by 
altering the size or shape of the cavity of the oscillator. In some cases, 
the tube itself contains only the grids, and the rest of the cavity is 
attached to flanges external to the glass wall of the tube. Tlie timing of 
such a tube is accomplished through the use of plungers or tuning screws 
in this external part of the cavity. There are usually several such screws 
around the circumference of the cavity as well as an output loop and 
coaxial line, or an exit iris with a waveguide, by means of which power 
is extracted. The tul^c now most commonly used is of metal construc- 
tion and contains the entire cavity as an integral part. The tuning of 

Table 1*1. — Locai/-oscillatob Tubes 



(Sbc. I.i4 





[Sec. 1*14 

this tube is accomplished through mechanical deformation of the cavity, 
which alters the grid spacing and, therefore, the capacitance and resonant 
frequency. A cross-sectional view of a typical tube of this kind is shown 
in Fig. 1*20. 

A recent development in reflex oscillators is the incorporation of a 
means for accomplishing the mechanical deformation of an internal 
cavity by an electronically controlled mechanism. One method consists 
, of the inclusion of a small triode, Avith a separate cathode, grid, and plate, 
within the envelope of the oscillator tube. The plate of the triode is 

made of a bimetal strip, the shape 
or dimensions of which are deter- 
mined by its temperature. The 
temperature is, in turn, controlled 
by the triode grid voltage which 
determines the current passing into 
the plate and, consequently, the 
power dissipated by it. The plate 
is so connected to the cavity of the 
oscillator that the temperature of 
the plate determines the grid spac- 
ing of the cavity and, conseciuently, 
the frequency of the oscillator. In 
this way, electronic tuning over a 
very wide range — 10 per cent or 
more — has been acc om])! ished 
through the control of th(j triode 
grid, which draws no curixmt. This 
frequency control cannot bo used 

Fig. 1-20.— CrosH-sectionai view of the jf response must h(i instantauc- 
2K25 reflex klystron. . *1 • i j.! ^ 

ous, because it involves a thermal 
timft constant. When the triode tuner is used in combination with reflec- 
tor-voltage control in a frequency-control circuit, however, completely 
automatic frequency control over a -wide region can be accomplished. 
This subject is discussed in Chap. 7. 

Table 1-1 is a list of some of the tubes available at present wbicih are 
useful as local oscillators. All but the first of those arc reflc'.x klystrons. 
Information is given concerning the frequency range, l>eam voltage and 
current, negative reflector voltage, output power, and the electronic 
tuning range for a typical tube. These numbers arc the average and not 
the liTniting values acceptable under the. specifications of the tubes. For 
the specification limits the manufacturers’ technical sheets or the Army- 
Navy specifications should be consulted. Present manufacttirors are 
listed with the following abbreviations; 


BTL Bell Telephone Laboratories, 463 West St., New York, N.Y. 

WE Western Electric Co., 120 Broadway, New York, N.Y. 

Sperry Sperry Gyroscope Co., Great Neck, N.Y. 

Raytheon. . .Raytheon Manufacturing Co., Waltham, Mass. 

RCA Radio Corporation of America, Camden, N.J. 

GE General Electric Co., Schenectady, N.Y. 

1*16. Radio-frequency Amplifiers. — It might be wondered whether 
the superheterodyne receiver could not be improved in noise figure by the 
addition of a preselecting r-f amplifier. It was pointed out in Sec. 1*9 
that the only advantage afforded by preselection alone is the suppression 
of spurious frequency response, and that the noise figure is changed 
very little. The preselection can be accomplished without tubes as 
amplifiers, with only small loss in noise figure, through the use of appro- 
priately selective r-f circuits. This feature is not of importance unless 
image rejection is needed. 

Tubes such as two-cavity klystrons can be used as r-f amplifiers and, 
in fact, were so used in some of the very early experimental radars in the 
microwave region. This was done, however, because of the lack of good 
duplexing components. The minimum detectable signal for the receiver 
probably was not clocreasocl by their use. These tubes usually have poor 
noise figures and are now rarely used as r-f amplifiers except at high level 
for transmitting purposes. 

The only other types of amplifier available are the triode and the 
more complex spa(‘.e-c.harge tubes. At freciuetuucs of 3000 M c/sec 
and below, the 2040 tube l)c used su(*.cessfully as an r-f amplifier, 
giving an increasing r-f gain and doe.i*easing noise figure as the frequency 
is decreased. An elTe(4.iv(i over-all noise figure, at 700 M c/sec, of 5 db 
has been achiev(Ml with two such r-f amplifiers in (cascade, each tuned, 
preceding the convertor. In view of the fact that a receiver with about 
the same efTec.tive over-all noise figure can b(^ made with a c.rystal con- 
verter, however, it hardly secerns worth while to add the complexity 
of such amplifiers to a rcMUMver, since all such cavity (*.irc,uits arc relatively 
difficult to tune and power must bo provided for the tubes. It is true 
that excellent image r(^j(x*.iion can be achieved with such a re(*xnver, and 
that the receiver is considerably less susceptible to damage l)y excessive 
input power. If these c()nsid(u*ati()ns are im])()rtant, the use of r-f 
amplifiers may be dc^sirable. The simplicity of tuning and of opc^ration of 
the crystal c()nv(M*t(^r, without r-f amplifiers, might be (‘.onsi<l(M*ed worth a 
sacrifice of a few d(^ciljels in noise figun^. In any event, it is more difficult 
to maintain a n-ir.civer using two r-f amplifiers at its oi)i.imnm perform- 
ance, and it is likely tluit in ac.tiial use the sim[)ler (n*ystal c.onvcrter 
will have a better noise figure than the amplifi(u*s. When the r-f amplifiers 



[Sec. M6 

were first developed they were incorporated in many existing receivers, 
and improved performance .resulted. This was true, however, largely 
because those receivers had very poor noise figures in comparison with 
what can now be achieved with the crystal converter. 

For use at frequencies of 3000 Mc/sec and higher there are no vacuum 
tubes commercially available that can be used as r-f amplifiers to give 
noise figures even comparable with those easily achieved with the crystal 
converter. A project at the Radiation Laboratory for the development 
of such a tube led to the construction, by H. V. Neher, of a few experi- 
mental models of an amplifier tube for the 3000-Mc/sec region. These 
are the only tubes known to the author which can be used as r-f ampli- 
fiers in receivers with noise figures comparable with those achieved with a 
crystal converter. These tubes were tetrodes, having a screen grid in 
addition to the cathode, grid, and plate. The construction was a planes 
parallel one similar to that of the lighthouse tubes. The resonant cavitie. 
were built into the tube envelope, which was the size of that of the 6L6 
As an example of the extremely fine workmanship involved in them, the 
fact may be cited that the grid structures were made with wires 0.0002 
in. in diameter and spaced 0.001 in. apart. At the time these tubes 
were first available on a laboratory scale it appeared that some decrease in 
over-all receiver noise figure would be possible through the use of one as 
an r-f amplifier 'with the existing crystal-mixer superheterodyne receivers. 
Before any large-scale production was accomplished, however, improve- 
ment in the crystals available in quantity production and reduced i-f 
amplifier noise figures had resulted in a smaller noise figure for the simple 
crystal-mixer superheterodyne receiver than could be achieved with, 
the amplifier tube. The intended production of this tube in factory 
quantities was consequently dropped to make the production facilities 
available for more urgently neecied devices. The details of the desigi\ 
and results achieved with this tube are described in a Radiation Labora- 
tory report.^ 

1*16. Receivers of Other Types- — Other receivers are sometimes used 
at lower frequencies. A brief description of them is given to show why 
they have not as yet been commonly used at microwave frcquencietrv. 

Some development work has been done on the design of frequency 
converters of basic types other than the space-charge tube. Because 
tubes using accelerated electron beams have largely replaced other typon 
as local oscillators, it might be supposed that some sort of tube using thiw 
principle could be designed to solve the mixer problem. Thus far no 
development along these lines has given results comparable with thus 
crystal mixer, and little need be said about them here. As with thus 

1 H. V. Neher, ^'The Radiation Laboratory S-Band Amplifier,” RL Report No, 30tt 
July 10, 1943. 

Sec. 1 - 16 ] 



low-level amplifier, the major limitation of beam tubes seems to lie in 
the excessive noise they introduce. A very large conversion gain would 
overcome this difficulty, but suflficient conversion gain to achieve noise 
figures comparable with those of the crystal converter has not yet been 
obtained. It appears that the limiting frequency of the aceelerated- 
electron-beam tube might be met before that of the crystal mixer. The 
transit angle of the electron beam must be kept small, as the frequency is 
increased, either by a corresponding reduction in the grid spacings or by 
an increase of the velocity of the beam through the use of higher poten- 
tials. Both of these expedients make the tube increasingly difiicult to 
build. Although the crystal probably does have an ultimate limiting 
frequency where transit angles become significant, this frequency has not 
yet been approached. So far, the application of the crystal mixer has 
been successfully extended to higher-frequency bands through the use of 
smaller paits in the cartridge construction and a smaller contact area on 
the crystal. By this means it has been possible to extend the frequency 
range of crystal mixci-s up to 25,000 Mc/scc with almost no saciifice in 
noise figure over the best value that can be achieved at the lowest micro- 
wave frequencies. The sacrifice that is made in doing this is in the 
resistance of the unit to damage from high-powor signals. 

A receiver that has boon common in the ultra-high-frequency range 
is the superregenerative receiver. As a simple receiver, using a minimum 
number of tubes and having a high sensitivity, it is useful in that fre- 
quency range. Because it requires a detector that can be made to 
oscillate, however, it has not been very extensively used in the micro- 
wave region. Lighthouse tubes can be made to oscillate up to 3000 
Mc/sec and higher, but the noise figure that can be obtained as a super- 
regenerative detector does not appraoch that of the crystal mixer. 
Because the output level is high, and, therefore, little amplili cation is 
needed, a suixMTOgencrative receivcM* is useful for some applications where 
the noise figun^ and bandpass characiteristics arc of less importance than 
compac.tncss and small i)o\v(u- consumption. No attempt will be made 
in this vohiiiu^, how(^ve^, to describe circuits of this kind, and the i*eadcr 
who is intcM'Cistcjd in this suhjec.t is refcM-red to Vol. 23 where the develop- 
ments in superrcgcMierative receivers arc discussed. 

The siinpki reg<uierat.iv(^ detector has few advantages over the sup(U‘- 
regenorativ(^ detcMitor and is k^ss ndiablc and not so simple to operate. 
Consc<iu(uitly, <'4r(aiits of this type^ have received no serious attention as 
microwave detectors. 

An interesting possibility in connection with regenerative and super- 
regenerative ree.eivers for fr<‘-fiu(m(nes higher than about 3000 Mc/seo has 
very recently arisen in <u)iinee.tion with a development in crystal rectifier 
units. It has been diseovc^rod that a crystal ro<*tifier unit, designed 



[Sho. 1-16 

by H. Q. North at General Electric Company, which uses a very snoiall 
welded contact between a germanium-crystal element and a platinum- 
ruthenium ‘^cat whisker,” can be made to show a negative output con- 
ductance at the intermediate frequency when placed in a very special 
microwave circuit, with local-oscUlator power incident upon the rectifier 
unit. The crystal unit used in a superheterod 3 me converter could there- 
fore be made to oscillate and, consequently, could be used as a regenera- 
tive or supperregenerative frequency converter. Attempts to achieve, 
with this crystal, a better over-all receiver noise figure than can be 
produced with more conventional crystal mixers have not yet been 
successful. On the other hand, it may be that the rather large power 
gain that can be achieved will be of sufficient importance in reducing the 
required amount of i-f amplification to make some application of this kind 
worth while. Since this crystal unit is a relatively recent development, 
it may be that further work will make possible an improved noise figure, 
although the exploratory measurements showed that the noise figure 
obtained in the condition of negative i-f conductance was somewhat 
greater than that for the same crystal operating in the conventional 
fashion. The noise figure was not, however, so large as for a tube mixer 
at the same frequency (10,000 Mc/sec). In order to indicate the method 
in which this unit can be made to act as a regenerative converter, a 
discussion of frequency conversion by a local oscillator and crystal 
mixer must first be given. Further reference to this subject will be 
made in Chap. 2, following the linear-network representation of the 
crystal mixer. It will be seen that the special tuning conditions necessary 
in the microwave circuit may render the operation of such a regenerative 
converter impractical, or at least not worth the decrease obtained in the 
i-f gain required. Since the subject is in such a rudimentary state of 
development, no final conclusion can be made, except to say that at the 
present time there has been no indication of much to be gained with the 
present crystal units. 



Early in the development of radio communication, the crystal 
rectifier was used almost universally as a detector for radio signals. 
After the introduction of the three-element vacuum tube, receivers 
having crystal detectors were replaced by receivers using vacuum-tube 
r-f amplifiers, detectors, and audio amplifiers and, finally, by super- 
heterodyne receivers. The performance of receivers having vacuum 
tubes throughout was very much better than that achieved with the best 
crystal rectifiers then known. This fact, together with the need for 
frequent adjustment of the common galena ciystal detector led to the 
complete abandonment of the crystal for use in serious radio practice. 

With the extension of radio technicpies to higher and higher fre- 
quencies, however, complications due to electron transit time, lead 
inductance and distributed capacitance became apparent. As a result, 
the crystal ret^tilier, wliic‘.h can bo made in a very small package, has 
become reinstated. An important reason for the r(.^turn of the crystal, 
in addition to the great improvememts in it;S performance which have 
resulted from intensive research and <level()])ment during the war, is the 
fact that tlie (‘.rystal has been wide^ly used as the nonlinear element of a 
superheterodyne mix(n\ In this application, the <*-rystal rc^ctifier units 
now available give mixeu* noise figures that compare v(^ry fiivorably, even 
at 25,000 Mc/s(m^, with those of the best vacuiim-tiilx^ mixers and con- 
verters at low fre(iuen(d(\s. yervice in mixeu’ <‘irc.iiits places requirements 
on the charact(M-istic.s of the rectifier which dilhu* from the reciuirements 
imposed in low-l(^v(d-(lel.(x*.tor circuits. The major part of recent develop- 
ment has Ixurn dinxded toward th(^ produ(*4-i()n of units for superheter- 
odyne mixers; how(^ver, some units have beem desiginxl sp(H*.ifically for 
use as low-level det.(x*tors. Otlun* low-l(W(d (h^tex'-tors have been selected 
by appropriate tests from production-lots of mixer c.rystals. 

It is not the purp<)s<^ of Ibis volume to consider, in detail, the subject 
of crystal-re(d.ili(x* <l(‘sign but, in onhu* to clarify thc^ later mah^rial, 
the present ebaphu’ will Ix^ dcwotcxl to a bric^ disc.ussion of crystal- 
rectifier units. A rudiuKxitary discussion of t.he physi(‘.al mechanism 
of the units, and of f.he lim^ar-rudAvork tn^atrnemt of frecpienc-y conversion 
by the crystal mixer, will Ix^ given. This will Ix^ followed by sections 
giving characteristics and Army-Navy spe(*.ifi(^ations of the: units eoin- 




[Sec. 2*1 

mercially available at the time of writing. All of these subjects are 
treated in greater detail, and more rigorously, in Vol. 15 of this series. 

24. Physical Description of Rectification. — The electronic theory of 
matter, applied to crystalline structures, shows that the electrons asso- 
ciated with the atoms of the material possess energies in discrete levels, 
just as they do in single atoms. In a crystalline solid, however, the 
coupling among the various constituent atoms or molecules causes the 
energy levels corresponding to particular quantum numbers in each atom 
to be split, and a band of very closely spaced levels results. Some bands 
may overlap, but there are always regions of energy which may be 
occupied by electrons, and regions between these bands which are 
forbidden to electrons. In substances made up of moderately heavy 
atoms, the available energy levels associated with the most tightly 
bound electrons are completely filled. Above the uppermost completely 
occupied band there is a band of energy levels that may be either com- 
pletely empty or partially filled, depending upon the nature of the atoms 
making up the crystalline solid. For a monovalent alkali metal, for 

instance, all of the electron shells 

Outside energy 


Ywn'/m// )rmm rn m 


Partially full band 

Full band 

m ii mi mT/i fTin m 


2*1. — Electronic energy levels 

of a 

except the last are completely filled 
and the energy bands associated 
with these inner shells arc fully 
occupied when the atoms are in 
their lowest state. The band 
associated with the outermost shell, 
however, is occupied by only one 
electron per atom and an energy- 
level diagram for such a substance 
would be like that shown in Fig. 2-1. The energy difference between 
the maximum energy of an electron in the material and the energy of an 
electron outside is the work function for the material, or the minimum 
energy that must be imparted to an electron to cause it to escape from the 
material in the absence of thermal energy. 

Crystals in which the uppermost occupied bands are completely 
filled at 0°K and those in which these bands are only partially filled form 
two fundamentally different classes of materials. Those of the first class 
are insulators and those of the second, as shown in the diagram, ar(‘ 
metals or conductors. If the uppermost band is completely filled, 
the electrons are not free, and electric conduction cannot take place. 
Because of the forbidden region between the uppermost filled band and 
the next higher band, an electron, to become free, must ac^quire a con- 
siderable amount of energy. In a metal, electrons are easily excited into 
adjacent states within the band itself, where they act as free conduction 
electrons. Intrinsic semiconductors,” which can be used in crystal- 

Sec. 2*1] 



rectifier units, would be perfect insulators at absolute zero temperature, 
since at that temperature they possess only completely filled and com- 
pletely unfilled energy bands. At the temperatures at which they are 
used, however, the intrinsic semiconductors possess a few conduction 
electrons in an otherwise empty band. This situation exists because of 
thermal excitation of electrons from the highest filled band to the next 
higher band and, therefore, a condition for conduction of this kind is that 
the forbidden region between the bands have a \vidth not much larger 

Normally empty 

— Donators 
Acceptors — ^ 

Highest ^ 

normally full 

(a) (b) 

Fia. 2-2. — Energy-level diugram of two types of impurity semiconductors, (a) w-type. 

(b) p-type. 

than kT energy units, where k is Boltzmann’s constant and T is the 
absolute temperature. 

In order to facilitate the existence of a few conduction electrons, a 
semiconductor may contain a very small percentage of an impurity. 
In fact, this is very difficult to prevent. The impurity centers give rise to 
conduction, either because electrons normally associated with the 
impurity atoms, in levels just below the normally vacant ])and, are 
thermally excited into the vacant band, or because elec'.trons in the top 
levels of the highest normally full 
band are thermally excited into va- 
cant levels associated with the im- 
purity centers. In the latter 
instance, vacancies arc left in the 
uppermost occupied band and these 
can conduct. Semiconductors of 
both these types are called “im- 
purity semiconductors”; those in 
which the impurity acts as a donator, rcDreHontation of 

as shown in Fig. 2-2a, are often 

called “n-type,” whereas thosc^ in which it acts as an a(*,ceptor for elec.trons 
as shown in Fig. 2*26 are called ^'p-type.” 

A crystal rectifier usually consists of a small contact between a metal 
whisker and a semiconductor crystal. In view of the foregoing energy- 
level considerations, the junction between the metal and the semicon- 
ductor may be described in terms of the energy-level diagram of Fig. 2-3. 
The carriers of electric charge will flow from one material to the other 



[Sbc. 2-1 

until the energy levels are so altered that equal currents cross the junction, 
in the two directions. By this mechanism, a space charge is produced 
in the region of the contact. In the metal, this space charge resides in 
a very thin layer (about lO"* cm) at the boundary, but in the semi- 
conductor the space charge is distributed through a broader region, 
because the material has a much smaller number of available carriers of 
current. The thickness of the space-charge layer in the semiconductor 

can be calculated from a knowledge' 

Applied voltage 

Fio. 2*4. — Metal-tosemiconduotor oon- 
tact with applied voltage in high-resistance 

of the dielectric constant of thc^ 
semiconductor and the density of 
the carriers of current far from th<^ 
boundary. Such calculations show 
the width of this region in the semi- 
conductor to be of the order of 10“”*^ 
cm, or about a hundred times the 
width of that in the metal. A curve 
of the potential as a function of 
distance from the boundary has a very steep barrier on the metal side of 
the junction, in which narrow region the potential rises abruptly by 
amount <j)a which is the difference between the work functions of the two 
materials. There is a thin layer near the surface in the semiconductor 
in which a potential gradient exists because the curves of the potential is 
less steep. The diagram of Fig. 2*3 
applies to contacts for which the work 
function of the metal is greater than 
that of the semiconductor. 

The relative potentials of the levels 
in the metal and in the semiconductor, 
when equilibrium is established, can 
be shown to be such that the top of 
the filled region in the metal is at a 
potential approximately half way be- 
tween the donator level and the 
bottom of the vacant band in an 
n-type semiconductor. This is the 
type of contact to which Fig. 2*3 applies. 

If the equihbrium potentials are altered by tlie appl legation of u 
voltage between the metal and the semicondu(d,or, the shape of i.ho 
potential barrier is altered. When the semioonduc'itor is made positdvft 
with respect to the metal, the levels in the somieondiictor are depressed 
Avith respect to those in the metal, as shown in Fig. 2-4. The potential 
barrier, which may be considered as a thin layer having a high resistttuce 
because of a dearth of free electrons, is enhanced and, consequently, it has 

2*6.-“ T)ii'oc(,-cui ri*nt-- -voltage ri'flii- 
tion for (uyHtal c.ontiict. 

Sbo. 2-1] 



a still higher resistance to the j&ow of electric current. The amount of 
resistance rises if the applied voltage is increased. A limit to the rise is 
reached when electrons from the metal begin to tunnel through the 
barrier in a manner analogous to that of field emmission. A curve 
showing the current passed through the contact as a function of the 
applied voltage, with the semiconductor positive, is therefore, similar to 
the left half of Fig. 2-5. 

Application of a voltage of the other sign across the contact reduces 
the insulating effect of the potential barrier by raising the potentials 
in the semiconductor relative to those in the metal, as shown in Fig. 2*6. 
The effective resistance of the contact decreases until the voltage is 
reached for which the insulating layer no longer exists, as in Fig. 2*7. 
The resistance of a contact at this voltage and higher is primarily what is 
called the ^‘spreading resistance,’’ which is determined by the area of the 
contact and the bulk resistivity of the semiconductor. In the semi- 




Pig. 2*6. — Metal-to-somiconductor con- 
tact with applied voltage in direction of 
large current flow. 

Pig. 2*7. — Energy-level diagram with 
applied voltage corresponding to linear 
part of high-current characteristic. 

conductor, only a small cross-sectional area near the small contact is 
effective for caiTying the current, but inside the semiconductor the 
effective area rapidly increases with distance from the surface. The 
right-hand side of Fig. 2*5 shows the current as a function of an applied 
voltage of this sign (semiconductor negative). The steepest slope of the 
straight part of the curve is a measure of the spreading resistance. 

From this description it can be seen that a nonlinear current-voltage 
relationship exists for a metal-to-semiconductor contact. The device 
cannot be used as a rectifier unless a voltage can be applied across the 
contact. It might be argued that the second contact this requires 
would exhibit characteristics that are the reverse of those of the first 
contact and that the net effect would be a linear resistance. This would 
indeed be so if the two metals Vere the same, and if identical contact areas 
were used. The rectifying junction results when the connection to the 
back of the semiconductor is made through a very much larger area. 
This back contact could indeed be nonlinear in the reverse sense to the 
small contact, with respect to voltages applied to the unit, but, because 
the area is large, the resistance of the barrier layer is very small, even 


compared with the spreading resistance for the small contact. The d-c 
characteristics of a crystal rectifier unit, therefore, do resemble Fig. 2-6, 
and the effect of the back contact can be entirely neglected. 

In practice, the crystals used for microwave work are usually made of 
silicon in which has been dissolved a small amount of aluminum, which 
acts as the acceptor impurity for a p-type semiconductor. The back 
contact is made by soldering the piece of crystal into a cartridge unit, 
as sketched in Fig. 2-8, and the small metal contact is made by light 
pressure of a tungsten whisker, carefully prepared with a very small 
point. The research and development work that has 
been done toward the perfection of techniques for the 
production of these units is described in Vol. 15 of this 
series, to which reference has already been made. Con- 
siderable work has been done toward perfecting crystals 
with germanium semiconductors but these have not yet 
been widely used in microwave applications. The same 
principles are involved in the construction of microwave 
circuits for the use of such units and, in fact, the design 
of circuits for crystal units of any type could follow the 
if iQ — general methods to be outlined in the following chapters 
Typical crystal- of this book. Specific designs may have to be altered in 
rectifier unit. details for the best utilization of crystals of other types, 
but this can be done if the pertinent, characteristics of the units to 1)0 
used are known. 

2-2. High-frequency Effects in Crystal Rectifiers. — The deterioration 
of the performance of vacuum tubes at high frequencies is a result of their 
large physical size. The crystal rectifier can be made very much smaller 
because of its inherent simplicity and, therefore, proper design of the 
cartridge allows the effects of lead inductance and distributed capacitance 
to be neglected at very much higher frequencies than for any vacuum 
tubes so far constructed. Since only the barrier region in the semi- 
conductor is effective in producing the nonlinear characteristic, the device 
could theoretically be made microscopic in size. In practice, of course, 
considerable skill is required to assemble the small parts. Also, to 
achieve a whisker contact that has an appropriate area and that will 
remain stable, some spring action in the whisker is required. 

The quantity in the crystal-rectifier unit analogous to the inter- 
electrode spacings of a vacuum tube is the thickness of the barrier layer. 
The carriers of electric charge must be able to cross this barrier in a time 
short compared with a quarter cycle of the applied r-f voltage if the 
high-frequency behavior is to be simply related to the d-c characteristic 
shown in Fig. 2-5. Since this barrier thickness is of the order of 10“® cm^ 
it is obvious that transit-time effects may be neglected at very much 


higher frequencies than would be possible in. any device in which an 
interelectrode gap must be obtained by mechanical means. 

A simple equivalent circuit for the crystal-rectifier unit, exclusive of 
the transformation effects of the cartridge, may be used for illustrative 
purposes. Such a circuit, shown in Fig. 2-9, includes the nonlinear 
resistance R of the barrier, a linear resistance R^ equal to the spreading 
resistance, as measured by the linear part of the d-c characteristic, and a 
capacitance C shunted across the nonlinear resistance. This capacitance 
arises because the barrier layer, although it 
has very small conductivity, does have a 
considerable dielectric constant, and it can 
be shown that the effect on an applied r-f 
voltage is similar to that of a small con- 
denser shunted across the barrier region. Yia. 2-9.— Equivalent circuit for 
The magnitude of this capacitance is not crystal rectifier. 

independent of the applied voltage because the effective thickness 
of the barrier varies somewhat with the value of the applied voltage. 
For most purposes, however, the capacitance may be regarded as fixed. 

Because of the presence of the spreading resistance Rb, the capacitance 
of the contact cannot be resonated out by an external inductance and, 
consequently, this capacitance has a real effect upon the high-frequency 
behavior of the crystal rectifier. The capacitance acts as a shunt that 
lowers the effective impedance of the barrier at high frequencies. Since 
its presence has the greatest effect for the highest barrier resistance, the 
nonlinearity of the resistance, on which the usefulness of the crystal unit 
depends, is reduced. 

A voltage applied to the crystal in the direction of high resistan(‘.o is 
said to be applied in the ba(*,kward direction, and one in the low-resistanc^o 
direction is called a forward voltage. The ratio of the voltage to the 
current for a backward voltage is called the back resistance and for a 
forward voltage the front resistance. Because of the barrier (japacitance, 
the ratio of the back to front resistances is not so significant, as a measure 
of the quality of the crystal, as it would be if there were no capacitance 
present. Since the capacitance increases with in(*.reasing contact area, 
it is imporiant that the area of tlie contact be kept as small as is com- 
patible with other reciuirements. This is one of tlui n^asons for the care 
with which the whisker is prepared and brought into contact with the 
semiconductor. The small contact area used is produced by the flatten- 
ing of the whisker which occurs if a small forc,c is applied across the con- 
tact. Crystals designed for the highest frccpiencies usually liave a 
smaller force applied to the whisker and have, consequently, smtiller 
areas of contact than those designed for lower frequencies. By this 
means, it has been found possible to maintain about the same sensitivity 



[Sbc. 2-3 

over the microwave range, but the higher-frequency units are, con- 
sequently, mechanically and electrically less rugged. 

The back resistance of a microwave rectifier unit can be used as a 
measure of its quality, provided that a lower limit for the value of the 
back resistance of acceptable units of the same type is known. By 
statistical studies, it has been found that a lower limit to the back resis- 
tance of crystals of a given type, measured at a given applied voltage, 
can be set. Crystals of that type which have back resistances below this 
limit are probably damaged, wWeas those having resistances above the 
limit are almost certainly still acceptable. The measurement of the 
back resistance at the given voltage is a test by which it is possible to 
eliminate practically aU inferior units at the expense of losing some 
acceptable ones. In view of the difficulty of measuring, directly, the 
equality of a crystal, and in view of the large numbers of crystals available, 
such a loss has been considered a small price to pay for simplicity of 
•testing the crystals. 

The back resistance of a crystal unit that is in electrical use may 
become lower over a period of time. Such a change has more significance 
than the absolute value of the back resistance at any one time. Any 
change in the back resistance must mean a change in the contact or in the 
semiconductor and should, therefore, be looked upon with suspicion. 
In the past, a lack of realization of the significance of the back resistance 
or of a change in it has led to the continued use of damaged crystals in. 
receivers. Because of the simplicity of a back-resistance test the impor- 
tance of performing it at frequent intervals, if high-quality performance 
is to be maintained, cannot be overemphasized. Limiting values of the 
back resistance for crystals of various types are included in a table at the 
end of this chapter. 

2-3. Figure of Merit of Crystal-video Receivers. — In Secs. 1*5 to 1-7, 
a. discussion of the quality of a receiver with a low-level detector was 
given. For completeness, this discussion should include the definition 
and method of measurement of the “figure of merit,'" which is used as a 
measure of the quality of crystal detectors available commercially. In 
order to correlate the figure of merit with the minimum signal detectable 
by a receiver consisting of a low-level detector and an amplifier, it is 
necessary to have the definition include a parameter that takes into 
account the noise power arising in the amplifier. Two crystal detectors 
bhat are identical in performance when used with a noise-free amplifier 
do not necessarily make equally sensitive receivers when used with, 
practical amplifiers. Therefore, the figure of merit of a crystal detector 
is a quantity that is related to the quality of the over-all receiver, when a 
"typical video amplifier follows the detector. 

As stated in Sec. 1*6, a crystal upon which a signal is incident may be 



represented, at the output terminals, by a current generator i in shxint 
with a conductance equal to that measured between these output ter- 
minals. It has been found that the noise generated in a video amplifier 
can be represented as the noise of a resistance between the grid of a 
perfect amplifier and the input terminal, as shown in Fig. 2*10. Over a 
wide range of impedances across the input terminals, the noise power 
available at the output terminals of the amplifier, in excess of that arising 
from the circuit connected across the input terminals, can be considered 
as arising as Johnson noise in this series resistor. The entire circuit at the 
amplifier input terminals may then be represented by Fig. 2*11, where R 
is the resistance of the output terminals of the crystal detector and 72^ is 
the equivalent noise resistance of the amplifier tube. The relation 

Fig. 2*10. — Equivalent circuit of first ampli- 
fier tube ^th noise resistance. 

Fig. 2*11. — Modulation-frequency circuit 
of low-level detector. 

between the output voltage E of the amplifier, caused by an r-f signal, 
and the r-f signal power P is 

( 1 ) 

where b is the proportionality constant defined in Sec. 1*7 and A is the 
voltage gain of the amplifier. Since the rms output noise voltage of the 
amplifier now originates completely as Johnson noise in the two resistors 
R and Ra, its value is 

= A VAkTBiR + Rlj, (2) 

where B is the equivalent noise bandwidth of the receiver, as defined in 
Sec. 1*4, and the remaining symbols have the same significance as pre- 
viously stated. The signal-to-noise ratio at the output terminals of the 
receiver is thus given by the ratio of Eq. (1) to Eq. (2), 

N V'4/cT^ 

The right-hand side of Eq. (3) has been divided into two factors, tlu^ 
second of which includes the quantities descriptive of the detector. 
This quantity, 


b y/R -b Ha 



[Smc. 2-4 

is called the figure of merit of the video crystal and has been used to 
evaluate the acceptability of production crystal units intended for use 
as low-level detectors. 

Before the figure of merit may be evaluated from measurements of the 
quantities b and R for the crystal, the value of Ra must be known. This 
value is, of course, dependent upon the particular amplifier tube and 
varies somewhat among specimens of the same type and widely among 
different types. The amplifier tube most commonly used in video 
receivers that have crystal detectors is the 6AC7 tube in pentode con” 
nection. Tubes of this type have been shown by measurement to have 
equivalent noise generating resistances of 1000 to 1200 ohms. The 
Army-Navy specifications, under which the various types of video 
crystals have been produced and tested, are based on calculations for 
the figure of merit in which the value for Raj in Eq. (3a), is taken to be 
1200 ohms. 

At the end of this chapter is a list of the various types of crystals for 
which Army-Navy specifications existed at the time of writing. Included 
in the list are several types of low-level detector crystals, designed foi- 
specific frequency regions as indicated in the table. It will be obsei*ved 
that these so-called video crystals have, in addition to a specification of 
figure of merit, a definite minimum or maximum value of output resis- 
tance. The reastance of the crystal determines the bandwidth of the 
first circuit of the amplifier, because the capacitance of this circuit is 
largely outside the control of the designer. If the resistance becomes 
too great, the pass band of the amplifier becomes too narrow; therefore^ 
the receiver does not respond properly to signals of the typo for which it 
was designed. 

2*4. The Crystal Converter. — The crystal rectifier, when used as a 
frequency converter, is operated under conditions rather different from 
those in the low-level-detector application. For this reason, an entirely 
different set of parameters are used for the evalutaion of the quality of a 
unit intended for use as a frequency converter. This can be seen from 
a simplified consideration of the mechanism of rectification based on the 
d-c characteristic of Fig. 2*5. Although an analysis based upon the d-c 
characteristic gives a poor picture of the microwave behavior of the 
contact as a frequency converter, because of the barrier capacitance, 
it does serve as a qualitative description. 

In Fig. 2-12, a typical d-c characteristic is drawn. In addition, 
there is shown, as a function of time along the negative ordinate axis, a 
voltage corresponding to the superposition of the local-oscillator voltage 
upon a small signal voltage. The output terminals of a crystal mixer are 
so arranged that no microwave-frequency components of the current in 
the crystal appear at them. The output terminals carry only the direct- 

Sbc. 2-4J 



current and the beat-frequency components, as indicated by the curve 
representing this current as a function of time plotted along the right- 
hand part of the horizontal axis. The magnitude of the beat-frequency 
component in this current is related to the efficiency of the device as a 
frequency converter. From the diagram it is evident that the magnitude 
of this beat-frequency component depends primarily upon the ratio of the 
slopes of the d-c characteristic at 
the negative peak and at the posi- 
tive peak of the local-oscillator 
voltage. It is apparent that the 
curvature of the characteristic in 
the vicinity of the origin is of 
little direct importance compared 
with the ratio of what might be 
called the differential impedances 
at two points symmetrically 
chosen at some distance on either 
side of the axis. From this con- 
sideration, it would be expected that the crystal rectifiers that make the 
best low-level detectors do not necessarily make the best units for use as 

, Signal amplitude 
LO amplitude 

Fig. 2*12. — Graphical illustration of fre- 
quency conversion on basis of d-c charac- 
teristic of crystal. 

frequency converters, and vice versa. 

Another significant relationship that can be qualitatively determined 
from this simple analysis is the dependence of the conversion efficiency 
on the magnitude of the local-oscillator voltage applied. If the signal 
voltage is kept small compared with that of the local oscillator but 
of constant magnitude, and the amplitude of the local-oscillator voltage 

is varied, the magnitude of the modu- 
lation component in the linear super- 
position of the two voltages remains 
constant. Because of the curvature 
of the d-c characteristic, particularly 
on the positive side of zero voltage, the 
ratio of the differential impedances on 
the two sides diminishes with decreas- 
ing lo(5al-oscillator voltage and, as a 
result, the conversion efficiency of the 
device should be less with small local- 
oscillator amplitudes than with large amplitudes. The conversion effici- 
ency, plotted as a function of the local-oscillator power, may 1)0 expected to 
behave as in Fig. 2T3, where the abscissa is the local-oscillator power and 
the ordinate is the relative conversion efficiency. There is no longer 

Fki. 2-13. — Typical curve for con- 
veraion efficioucy va. local -owcillutor 

any significant increase if the local-oscillator power is increased beyond 
that which utilizes the straight portion of the d-c characteristic in the 



[Sbc. 2>4 

forward direction. At larger amplitudes, there may even be a decrease, 
because the differential back resistance may decrease. This situation has 
not been indicated, however, in either Fig. 2-12 or Fig. 2-13. 

The conversion eflSiciency is usually specified as the gain of the con- 
verter unit, considered as a network, between the signal input terminals 
and the i-f output terminals. This gain, as defined in Sec. 1-4, is the 
ratio of the available i-f output power to the available signal input power, 
and, for a crystal converter, it is almost certainly less than one. Con- 
sequently, it has become customary to use the reciprocal of the gain, 
called the ‘^oss’’ L of the converter and to express it in decibels. In 
order to specify completely the quality of the converter, it is necessary to 
know the value of the output noise power from the converter, considered 
as a network, as discussed in Sec. 1-4. From these two quantities, the 
effective over-all noise figure of a receiver in which such a converter is 
used in conjunction with an i-f amplifier of known effective noise figure 
may be estimated. The noise temperature ty as defined in Sec. 1-4, has 

been most commonly used as a measure of 
^ the noise. In order to specify the local- 
J ^ oscillator power for optimum effective 

I over-all noise figure, it is necessary to 

I 2 - ^y"^ know both the dependence of the noise 

^ ^y^ temperature of the crystal on the local- 

1 ^ LxT oscillator power and the noise figure of the 

Local-oscillator power i-f amplifier for a generator impedance 
Fig. 2* 14.— Typical curve of equal to the impedance of the output 

terminals of the crystal converter. This 
impedance also depends somewhat on the 
local-oscillator power, although it varies only slowly for local-oscillator 
drive suflScient to give a conversion gain near the maximum. 

The noise temperature of a crystal converter is found to be approxi- 
mately .linearly dependent upon the incident local-oscillator power, as 
indicated in Mg. 2*14. Equation (1-26) may be used to calculate the 
effective over-all noise figure if Ft, the effective noise figure of the i-f 
amplifier, is known for the range of output impedances possessed by the 
crystal converter. Since the over-all noise figure is usually expressed in 
decibels and since the loss L, also usually expressed in decibels, is used 
instead of the gain, this equation may be rewritten as 

^^*+2 db = Ldb + 10 logic (F* + ^ — 1), 

where t and F* are numerical ratios, not expressed in decibels. Figure 
2-15 shows a typical curve of the effective over-all noise figure of a receiver 
resulting from the combination of the three quantities in Eq. (4). It will 

Sbc. 2*6] 



^ I Optimu m 

Local-oscillator power 

Fig. 2*15. — Over-all noise figure vs. 
local-oscillator drive. 

be observed that the noise figure decreases in about the same way as the 

conversion efficiency increases, for small local-oscillator power. For 

high local-oscillator power, the conversion efficiency no longer increases 

so rapidly but the noise temperature 

continues to increase; therefore the ^ \ 

over-all noise figure goes through a ^ \ 

minimum value and then increases g> \ 

again. The noise figure does not vary S \ 

rapidly in the region of the minimum » - - " 

value and, therefore, a reasonably 

large deviation in local-oscillator g , 

power from the optimum value can be g , 

tolerated. The optimum local-oscil- % i 

lator power is usually about 0.5 mw ^ I 

into the crystal, which results in a g i 

continuous rectified crystal current of ^ | Optimum 

about 0.5 ma. More specific informa- Local-oscillator power 

tion about conversion losses and noise Fig. 2-15.— Over-aU noise figure vs. 

temperatures, as well as about i-f im- locai-osciiiator drive. 

pedances of typical units, will be given in later sections of this chapter. 

2«6. Linear-network Representation of the Crystal Converter. — The 
use of the terms loss and noise temperature, to describe the crystal 
frequency converter, suggests that the device may be considered as a 
network that possesses two pairs of terminals: one pair to which the signal 
is applied, and one pair from which the i-f signal is obtained. Although 
the converter depends for its action upon the nonlinear relationship 
between voltage and current in the crystal unit, a linear relationship 
exists between the i-f output voltage and the microwave input signal 
voltage, provided the signal amplitude is very small compared with that 
y ■ yA of the local oscillator. This is 

/L o because the voltage-to-current 

Signal I / Output relationships of the crystal, which 

terminals j/ terminals are effective f or the conversion from 

Fig. 2*16. — Symbolic ropresoiitation of crys- the signal frequency to the inter- 

tal cowvertor. mediate frequency, are differentials 

of the d-c and r-f characteristics, and these may be regarded as constant for 
very small signal amplitudes and for a given local-oscillator power. 
The converter may then be regarded as a box containing a pair of signal 
terminals and a pair of output terminals for the i-f voltages, as indicated 
in Fig. 2*16. A considerable number of relationships that help to 
clarify the complex behavior of crystal converter units can bo derived 
from this representation. 

It might be wondered what would result if the device were worked 





Fig. 2*16, — Symbolic ropresoiitation of crys- 
tal cowvertor. 



[Sec. 2*5 

backward. If an i-f voltage were impressed upon the i-f terminals, 
would an r-f signal be produced at the signal terminals? A return to a 
consideration of the d-c characteristic will help to answer this question. 
If, as in Pig. 2-17, the local-oscillator voltage is impressed upon tb'e 
crystal, in the absence of an r-f or an i-f signal, and a d-c bias is added in 
series with the crystal, then the operating point shifts, with the result 
that a different part of the characteristic determines the r-f impedance 
of the crystal. If the bias voltage is made to vary through zero sinus- 
oidally at the i-f frequency, the effect is to modulate the r-f impedance 
of the crystal at the i-f frequency or, in other words, to amplitude-modu- 
late the r-f current in the crystal. It is well known that an amplitude- 
modulated r-f current or voltage may be considered as equivalent to the 
immodulated current or voltage plus two other r-f components, one 
above the original frequency and one below it. These two added 

Fig. 2-17. — Graphical illustration of 
efffect of bias voltage on r-f admittance. 

components differ in frequency from 
I / the incident radio frequency by an 

/ amount equal to the modulation fre- 

L- quency. In the crystal converter. 

Local-oscillator where the modulating voltage is sup- 

L-5hift"dueto be at the intermediate 

^ j bias voltage frequency, one of these new radio 

I frequencies will correspond to the 

^ ^ * signal frequency and the other to 

Fig. 2-17. — Graphical illustration of ^ • j? 

efffect of bias voltage on r-f admittance, tne image frequency. \Vhen an 1— t 

voltage is applied to the i-f terminals 
of the converter of Fig. 2- 16, voltages of equal magnitude, at the signal 
and the image frequencies, appear at the r-f terminals. This assumes, 
of course, that there is contained in the box between the crystal and the 
input terminals nothing that is sufficiently selective with respect to 
frequency to favor one of these voltages over the other. 

To return to the use of the converter in the direction for which it was 
intended, the appHcation of a signal voltage to the input terminals gives 
nse to an i-f voltage at the output terminals. This voltage in turn 
produces, at the input terminals, a voltage at the signal frequency and 
one at the image frequency. The presence of the signal-frequency 
volt^e serves only to determine, in part, the signal-frequency impedance 
of the converter, but the image-frequency voltage has considerable 
ffl^ficance. It is clear that the behavior of the converter cannot be 
mdependent of the image-frequency impedance of the generator circuit 
connected to the mput terminals; a reflection of the image-frequency 
wave from the generator back into the converter unit will produce a 
voltage at the intermediate frequency. The phase and amplitude of this 
intermediate-frequency component, relative to the one produced directly 

Sec. 2-6] 



by the signal, is dependent on the phase and amplitude of the reflected 
image-frequency wave. The signal-frequency impedance, the output 
impedance and the conversion loss must all be dependent, to some 
degree, upon the impedance presented by the generator circuit to the 
image-frequency wave. 

Because the crystal is a nonlinear element, there must be developed, 
in addition to these voltages, many other higher-order components 
corresponding to harmonics and products, sums, and differences of these 
components. A rigorous analytical treatment of the device must include 
all of these components as well as the image voltage. In addition to the 
process just described, the image-frequency voltage may be developed 
as the difference frequency between the second harmonics of the local- 
oscillator frequency and the signal frequency. The effects of the higher- 
order frequencies, however, are smaller than those produced by alterations 
in the crystal impedance. They are, moreover, analytically and experi- 
mentally, very much more difficult to handle. To estimate the effects of 
these voltages, it is useful to consider the image frequency alone because 
it is probably of the greatest importance, and relatively simple experi- 
ments can be made to verify the analytical predictions. The effect of 
varying the impedances presented to the higher-order frequency com- 
ponents, such as the second harmonics, may be anticipated to be quali- 
tatively similar, but less pronounced. 

2*6. The Three-terininal-pair-networfc Representation. — ^Let us sup- 
pose that the only voltages of significance in the converter circuit arc 
those at the signal, image, and intermediate frequencies. Although the 
first two of these appear on the 
input terminals of Fig. 2TG, it is 
convenient to assume that there 
exist separate tencninals for them, 
as shown in Fig. 2T8. This could 

be achieved m practice by an 2-i8.-Syinboiic ropre»out«,tion of 

appropriate splitting network, com- oonvortor with separate signal- and image- 
posed of frequency-selective cir- froquoucy tomiinals. 
cuits, within the box. A threc-terminal-pair network, in which the 
voltages and currents are linearly related, as they are for small voltages in 
the crystal converter, may be described by a set of three transformation 
equations involving a total of nine independent coefficients characteristic 
of the network. Because of the symmetry between the signal- and image- 
frequency components in the converter, assuming the converter to have a 
low Q in terms of the frequency difference involved, the number of 
independent coefficients may be reduced to five, provided the equations 
take account of the phase relation between the signal- and image- 
frequency components. These equations may be written as. 



[Sac. 2-6 

yaa^ot "4“ yafi^P "I" VayPy^j 

ip = ypaea + yppep + ypa%*f ( 6 ) 

V* “ yay*^y 4“ 4“ 2/aa*®7*> 

where the subscripts «, /s, and ^ refer respectively to the signal, inter- 
mediate, and image frequencies, and the asterisks denote the conaplex 
conjugates. The i-f current due to the image-frequency voltage ey has a 
value that is the complex conjugate of that produced by the signal 
voltage. Therefore the complex conjugate of the term y^uCy is taken, 
in the second equation, to be the contribution of the image-frequency* 
voltage to the total i-f current. For this reason, the complex conjugate 
of the image voltage is used throughout, and the third equation gives the 
complex conjugate of the image-frequency current. 

If the image terminals are connected, independently of the signal 
terminals, to an external admittance yy, the relationship between the 
image-frequency current and voltage is 


i = -Vr ( 6 ) 

If this expression is substituted into Eqs. (6), and if and are elimi- 
nated between the resulting equations, the relations between the voltage 
and eurrents at the signal and intermediate frequencies become 


^ot — Ycea^a 4" 

ip = Ypefia 4" Yppepy 





Y _ y^ct Vay* 




Equations (7) show, through their dependence upon the image 
termination yy, that the behavior of the device as a converter from signal 
to image frequency cannot be specified independently of the treatment of 
me image-frequency component. Specifically, the conversion loss, the 
signal input admittance and the i-f output admittance can all be calcu- 
lated from Eqs. (7) in terms of E.,, and plus the signal- 

generator admittance y„ and the i-f load admittance at the output 
terminals, yp. 

Sbc. 2*61 



To find the signal input admittance ¥„ for an i-f load admittance 
yp, Eqs. (7) may be written as, 

{Y eta — Y e^^a + YapGp = 0 , 

Ypaea + (Ypp + yp)ep = 0, (12) 


Ya = y and = — -■ (13) 

€a Op 

To be consistent, the determinant of these equations must vanish, or, 

= Ya 


2/j3 + Ypp 


The i-f output admittance Yp, by analogous steps may be shown to 
depend upon the signal-generator admittance ya, as 

Yp = Ypp - 


Yaa y a 


These two relations, Eqs. (14) and (15), reveal a point about the design 
of crystal mixer circuits which must not be overlooked if the best possible 
performance from a given crystal unit is to be obtained. The choice of 
the r-f and i-f matching conditions cannot be considered to be independent 
or to be completely a property of the crystal alone. Because of the inter- 
dependence, the design of the input circuit of the i-f amplifier should 
take into account the effect on the i-f output characteristics of the signal- 
frequency and image-frequency admittances that are connected to the 
r-f terminals of the converter. In turn, the signal- frequency admittance 
of the converter is dependent both upon the i-f load admittance presented 
to the converter by the i-f amplifier and upon the admittance presented 
to the converter at the image frequency. If the image-frequency termi- 
nation is fixed, the coefficients of Eqs. (7) may be regarded as constants 
descriptive of a particular converter unit. There is, therefore, a great 
similarity between the converter and an ordinary piece of transmission 
line, with respect to the dependence on the signal-genei*ator and output- 
load admittances. In the representation of a transmission line by equa- 
tions analogous to Eqs. (7), it can bo shown that the transfer admittances 
analogous to Yap and Ypa must be equal. That this is also tiue for the 
network representing the crystal converter cannot be proved without 
making some restrictive assumptions. 

Dicke^ has shown that, if certain assumptions about the time depend- 
ence of the voltage across the barrier in a crystal rectifier unit are true, a 
relation between Yap and Ypa exists such that 

^ R. H. Dicke, "A Reciprocity Theorem and Its Application to Measurement of 
Gain of Microwave Crystal Mixers,” RL Report No. 300, Apr. 13, 1943. 



[Sdc. 2*6 

On the basis of this relation, the conversion loss of a crystal converter can 
be calculated from measured values of the signal or i-f admittances of 
the converter, for each of several different admittances connected to the 
other pair of terminals. Comparisons have been made between the 
values of the conversion loss found in this way and the values measured 
on the same imits by the standard method that involves the measurement 
of the ratio of the available input power to output power. It is found 
that the reciprocity condition holds very closely for silicon crystals, but 
that it does not hold for germanium crystals. If this condition is not 
obeyed, the eflBiciency of conversion of r-f power to i-f power is not the 
same as that from i-f power to r-f power. It has been found that units 
that do not obey the reciprocity condition are usually more ejSSicient as 
converters from low to high frequency than in the opposite sense. The 
agreement between the measured conversion loss and that calculated 
from the admittance data, for silicon units, is excellent confirmation 
of the usefulness of the linear-network representation of the crystal con- 
verter. Even for units that do not show reciprocity, the same qualitative 
interdependence of r-f and i-f admittances is found. 

The conversion loss of the converter in terms of the parameters of 
Eqs. (7) may be derived in the following way. The output power from 
the converter unit is the real part of — iipep*, whereas the power enter- 
ing the unit is the real part of therefore the loss is 

L - 

which, by Eq. (13), becomes 






Here, Ga and are the real parts, or conductance parts, of and y/j, 
respectively. If the second of Eqs. (12) is solved for \eje^\ and the 
solution substituted in Eq. (17), the expression for the loss becomes 

r ^ |F/3|3 + 


If the value of Ga from Eq. (14) is substituted in this expression, the loss 


where is the real part of F««. This may be written in the form 

Sdo. 2-6] 



+ (Bm + W’-^(B» + m]' (20) 

where the O’b and B’s are the real parts and imaginary parts of the y’s 
with the same subscripts. In addition, Ga» 0 a and are, respectively, 
the real and imaginary parts of Ya^Yfa- The gain of the network which 
appears in the expression for the effective over-all noise figure of a cascade 
of networks, is defined (see Sec. 1‘7) as the ratio of the signal power 
available from the network to that available from the signal generator 
connected to the input terminals of the network. The full power availa- 
ble from the converter is obtained when the load admittance yf is so 
chosen that the loss L is a minimum. There are two orthogonal quanti- 
ties, Qfi and hfi, in Eq. (20) which must be adjusted to make L a minimum. 
The quantity hp can be given any value from plus to minus infinity. The 
minimum of L will occur for a minimum of 

(Bpp -b hpy - (Bpp + bp), (21) 

which is obtained when 

Bpp + bp = (22) 

as is evident if the derivative of Eq. (21) with respect to {Bpp + bp) is set 
equal to zero. Thus Eq. (20) becomes 

^ + »’>■ - “ar <“*’ + ■"> - fe)']- 

If the partial doiivalivo of L with respect to gp is taken, the value of gp 
resulting in minimum loss can be found to bo 

where only the positive', root has physical significance. The optimum 
load admittance, from the combination of Ecis. (22) and (24), is 

Upon substitution of I'ki. (24) into E(i. (23), the expression for the 
minimum loss becomes 


By algebraic manipulation, Eq. (26) can be put into the form 

/ I + 

Vl - VT^e} 


where € is given by 

€ = 

^OaaGfifi — (Jai3/9a+ \Y apY fia\ 



The second factor in Eq. (27) may be called the impedance loss, because it 
can be evaluted from direct measurements of the impedance of one pair of 
terminals of the mixer for each of two different load conditions at the 
other pair. This loss and the actual minimum loss encountered in prac- 
tice are the same only if the first term in the expression is unity. This is 
true if the mixer obeys the reciprocity condition. 

If the mixer is worked backward, that is, caused to generate the signal 
frequency from an applied i-f voltage, the loss for this process may be 
calculated in a similar manner. The loss L' from low- to high-frequency 
power is found to be identical with Eq. (27) except that the reciprocal of 
first term appears; that is. 

L' = 

If the ratio of Eqs. (27) and (28) is taken, 






This ratio of the losses in the two directions reveals to what approximation 
reciprocity holds. Since, as mentioned earlier, the loss is usually greater 
in the direction from r-f to i-f power than in the other direction, when 
the reciprocity theorem is not obeyed the relation between Yob and Y^a 
can be stated to be, almost without exception, 

\YaA ^ \Ypa\. 


2*7. The Relation between the Input Admittance and the Load Admit- 
tance. — The representation of the mixer as a linear network makes it 
apparent that the input admittance cannot be independent of the load 
admittance, and, in fact, the relationship between them may be calcu- 
lated with the aid of Eq. (27). This is most easily done for certain simple 
cases from which the general interdependence may be discovered. For 
example, suppose that the i-f output terminals are connected to a pure 
susceptance which can be adjusted through all values between negative 
and positive infinity. Suppose, further, that the mixer includes r-f 
matching devices such that, under the condition of infinite load suscept- 

Sec. 2-7] 



ance, the signal admittance is real. From Eq. (14) it is evident that this 
may be written 


The load susceptance may then be adjusted to make the input admittance 
mismatched to Fbo by as large an amount as possible. This may be 
expressed, by use of Eq. (14), as 

1 oo “■ C}txa 

0 /S |3 + + h^) 


The mismatch between Yoo and Y»c^ may be expressed in terms of the 
absolute value of the reflection coefficient r of Yoo relative to Fao, which is 


To. - V«. 


+ GaPPa. + j^GaaiBpp + bp) ^ 


_ (Ga0fi„)“ + 

+ [^raa{B(i0 + bfi) — 


The maximum loss due to mismatch, corresponding to the maximum 
of [rl'-*, can be found by sotting the pai-tial derivative of \T\^ with respect to 
( 5 / 3/3 + bp) equal to 7An\). Tho. result of this is 

/iw + h = + 1“ (36) 

This exprcission is identical wii.h lOcp (22), \vhi(4i giv(\s the optimum load 
susceptance from tlu^ standpoint of (».onversion loss. If this susceptance 
value is used in JO(i. (32), tiu^ n^sult is 

\ ' / r 

-* <m f ti 


('till + J 



The r-f signal is ui)plic<l 1.<) a ini(in>\vii,v(( <!onv(ii-t.(u‘ throngh a coaxial 
line or a \vav(fgui<l('. 'I'lic position in this input lino at which the 
aignii.1 terminals of tluf (upiivahuit luitwork am located is, as yet, arbi- 
trary. It is conv<uii(uit to chooser th(is(! t(irininals to be at a point 
at which is n^jil. This is not iiuioinpatibhi with making T™ real, 
because, for instanc.e, tlu^ r-f matching in tlui mixer could bo such that 
Gaa is the c.haracl.(U'istic, aclmittiiiux^ of tlui transmission line. Then Y,„ 
would be mal at all [)oints along the in|)ut lin((. ('boosing the position of 
the input terminals to make n'al makes the. imaginary pai't of th(5 
second term of Mip (IK)) (upial to zero, or 

(I'llllliatlll,, — 

nflfit’^' ntlllu 


= 0. 




[Sec. 2*8 

This is satisfied if 

2Gaa Gpfi = Gafifiaj Or Ba^^a “ 0. (38) 

The first of the oonditions of Eq. (38) results in c greater than one and, 
therefore, it does not have real significance. The second of these condi- 
tions, however, results in 

V n Gafi$a /y 

oo — ~~py ““ woo* 



From Eqs. (31) and (39), 

Goo 1 _ Ggfifict 

Gao GctaGpfi 


Under these conditions, however, Eq. (28) for e may be used to show that 

Therefore Eq. (27) becomes 




It is now clear that the measurement of these two admittances at one 
pair of terminals of the converter, under each of two conditions at the 
other pair, constitutes, according to Eq. (42), a measurement of the 
mimimum conversion loss of the converter, except for the reciprocity 
factor. The result of this measurement, sometimes called the impedance 
lossij^, is given by 

1 y/Goo/Gno 

1 - VgMo 


This expression is identical with one which can be derived for the trans- 
mission loss of a piece of transmission line an integral number of half 
wavelengths long. For the transmission line. Goo is the conductance of 
the input terminals with the output terminals open-circuited and Gao is 
the conductance with the output terminals short-circuited. An experi- 
mental apparatus to be described in Chap. 8 has been designed and used 
to measu re the impedance loss of crystal mixers, by measurement of 
y/Goo/Gao- The results, for silicon crystals, have been in good agree- 
ment with those obtained by more direct methods. 

2*8. The Dependence of Input Admittance on the I-f Load Admittance. 
The ch aracte ristic admittance of a transmission line may be shown to be 
just y/GsoGoo. That the same expression holds for the converter may be 
verified by putting Eq. (24), for into Eq. (14), under the condition 

Sbo. 2-8] 



that the choice of the position of the input terminals is the same as 
before, and therefore is zero, as in Eq. (38). It is now posable 
to discover the range of input admittances which will be shown by the 
converter for all possible values of i-f load admittance, by use of Eq. 
(43). It is a general theorem for linear networks that a circle on an 
admittance dia gram is transformed by the network into another circle. 
It is known that, under the special conditions here assumed, two points 

of the admittance contour at the input terminals, resulting for output 
load admittances along the circle = jbii (a circle of infinite radius in a 
cartesian plot of conductance vs. susccptance, or the outside circle on 
a Smith chart) , fall upon the conductance axis. It has also been shown 
that Goo differs from G,o by the maximum amount for this range of load 
admittances and, therefore, it follows that the conductance axis is a 
diameter of the input-admittance circle. If, further, the r-f tuning is so 
chosen that -y/ G«,Goc corresponds to a matched input line, the circle will 
be centered, on a Smith chart, at Fo. Several such circles are shown in 



Fig. 2*19, corresponding to various values of Lz between 0 and 10 db. 
Under these conditions, only points inside the circle corresponding to 
the Lz of the converter in question can be produced as the input admit- 
tance to the converter by choice of the load admittance. The center 
point of the circle Fo is obtained when the load admittance has the opti- 
mum value, as given by Eq. (25). 

One of the important tasks in the design of converter and mixer cir- 
cuits is the adjustment of the tuning of the input circuit in such a way that 
minimum loss is obtained for the largest possible number of crystal units. 
In this connection it is important to realize the significance of the definition 
of the gain, and its reciprocal the loss, as it appears in the expression for 
the over-all noise figure for the cascaded converter and i-f amplifier. The 
input circuit of the i-f amplifier does not need to provide for the converter 
a load admittance such that the converter delivers noaximum power. The 
conversion loss of a given converter, therefore, is not necessarily nadni- 
mized by a tuning that matches the signal generator to the converter, 
with the converter connected to the i-f amplifier. The i-f input circuit 
is so chosen that the smallest possible noise figure compatible with the 
desired bandwidth and the amplifier tubes is achieved. As a result, 
the input admittance of the mixer lies nearer to the boundary of the region 
inside the appropriate circle of Fig. 2*19 than to the center. Never- 
theless, for minimum over-all noise figure, the mixer tuning should be 
such that the characteristic admittance of the mixer is matched to the 
admittance of the r-f signal generator, since this gives minimum conver- 
sion loss. Therefore, a load admittance having the value such that the 
mixer delivers maximum power should be used in experiments intended 
to establish optimum r-f tuning conditions for the mixer. 

For converters in which \Yccp\ ^ \Y^a\, and the actual loss therefore 
does not equal the impedance loss, the dependence of the input admittance 
upon the load admittance is greater than would be expected if reciprocity 
were assumed because of the relation of Eq. (30). With such units it is 
even more important that the input matching is achieved under the 
proper load conditions than for units of equivalent actual loss but for 
which reciprocity holds. 

Because the values of the parametric admittances, of Eqs. (7) are 
dependent, through Eqs. (8), (9), (10), and (11), upon the image- 
frequency termination yy, the characteristic signal input admittance as 
well as the loss are to some extent determined by this image-frequency 
termination. In a converter unit that is, in itself, insensitive to frequency 
but that is to be used with a high-Q resonator such as a TR switch, the 
measurement of the characteristic input admittance should be made with 
this resonator in place. The input admittance is less dependent on the 
image-frequency load admittance, however, than on the i-f load admit- 

Sbc. 2*9] 



tance. The nusmatch encountered if the tuning is made optimum 
without the resonator in place is not large because an increase in loss of 
only a few tenths of a decibel would result even if the mixer were matched 
to the signal generator with an incoiTect admittance connected to the 
i-f output terminals. A calculation of the magnitude of the interdepend- 
ence of the signal admittance and the image-frequency load admittance 
requires a knowledge of the values of the parametric admittances ynm of 
Eqs. (6). Although these can be measured, this subject will not be 
discussed here. 

2*9. Dependence of the I-f Admittance upon R-f Matching Condi- 
tions. — In a fashion exactly analogous to that of Sec. 2-8, the admittance 
of the i-f terminals of a converter may be shown to be dependent upon the 
signal-generator admittance. The symmetry of Eqs. (7) suggests that an 
expression similar to Eq. (43) could be written down immediately, where 
Goa and Gao refer respectively to the conductance of suitably chosen i-f 
terminals for the conditions of open-circuited signal terminals and short- 
circuited signal terminals. It is more convenient, however, to keep 
the previous choice of the position of the r-f signal terminals and the 
r-f matching conditions previously defined, to allow a single set of 
terminals to be used for the description of the converter in either direction. 
In practice, a special r-f circuit is required to allow variation of the admit- 
tance connected to the signal terminals independently of that connected 
to the image terminals. It will be assumed that this can be done, how- 
ever, and with this assumption a useful relation can be derived. 

The three conditions set up in the previous section wore: 

1. R-f matching such that Yaa is real, and equal to G««. 

2. Choice of the position of the r-f signal terminals such that (YapY^a) 
is real, and equal to Gap$a- 

3. Addition of a susccptance, to the i-f terminals, which resonates 
out the imaginary part of Y^p, This is the condition of Ecp (35), 
which was used to calcxilato the quantity denotcnl by 

By the use of these three conditions, the expression for the impedance 
loss may be calculated for measurements of the i-f admit!, an(*.(^ for short- 
circuited and open-circuited signal terminals. From Condition 3 and 
Eq. (15) the i-f admittance for short-circuited signal terminals may be 

Vhc« = G^/5 — (44) 

From Conditions I and 2, the i-f admittance for opcm-circuited r-f 
terminals may be written 

= a„,„. (45) 

The ratio Guoei/OH.'(x istlu^refore id(mt,ii^al with that givcui by h](\. (10), a?id 



[Sec. 2-9 

the impedance loss can be written in terms of this ratio in the same way as 
for the r-f terminals 

1 "S/Oooa/G 


1 — y/Goca/Gica 


This relation reveals a point that is important in the design of con- 
verters and i-f amplifiers. The i-f output admittance of the converter^ 
which plays an important role in determining the i-f amplifier noise 
figure and bandwidth, can fall anyv^here inside the appropriate circle on 
Fig. 2T9 depending upon the admittance of the signal generator con- 
nected to the input terminals of the converter. If a resonant circuit 
is included in the converter or in the line between the converter and the 
antenna, the i-f admittance may be expected to vary with the inter- 
mediate frequency. If the signal generator is matched to the crystal 
converter, the i-f admittance will be the characteristic admittance of the 
i-f terminals, which corresponds to the center point of Fig. 2T9 for that 
particular crystal, image-frequency termination, and harmonic-frequency 
termination. If the image-frequency termination is identical with that 
at the signal frequency, the i-f admittance of most crystals now available 
is between 2000 and 3000 micromhos. This value for the i-f conductance 
of the converter is valid only when the signal and image terminals are 
both connected to admittances matching the input admittance of the 

Since the converter is tuned for minimum conversion loss, the admit- 
tance of the signal generator is nearly matched to the characteristic 
admittance of the signal terminals of the converter. At the image 
frequency, however, the signal generator admittance may have a different 
value, and this, too, affects the i-f admittance of the converter. In 
circuits involving an r-f resonator, the image-frequency load admittance 
is usually very different from that at the signal frequency. A TR cavity 
having a loaded Q of 300 at a signal frequency of 3000 Mc/sec almost 
completely refiects the image-frequency wave if the intermediate fre- 
quency is 30 Mc/sec. Because of the symmetry, shown by Eq. (6), 
between the signal and image frequencies, an expression may be written 
which expresses the impedance loss of the converter in terms of the i-f 
conductances measured with the image-frequency terminals open- 
circuited and short-circuited. This expression is 

1 + 

1 — "s/OovJOZy 


The impedance loss Lz is the minimum loss that could be obtained if the 
roles of the signal and image terminals were interchanged. It is, there- 
fore, the same as the conversion loss between the signal and i-f terminals 

Sbg. 2-9] 



when the image-frequency terminals are connected to an admittance 
equal to the admittance of the signal generator. Again, Fig. 2-19 is 
applicable. The center point now corresponds to the admittance 
resulting if the image terminals are connected to an admittance equal 
to the optimum signal-generator admittance. Since the termination at 
the signal frequency will be near this value, a low-Q circuit would provide 
the same admittance at both signal and image frequencies. The i-f 
admittance would then correspond to the center of the chart and would 
be between 2000 and 3000 micromhos, as mentioned above. 

If the termination at the signal frequency is kept constant and the 
phase of a complete reflection of the image-frequency wave is varied, the 
resulting i-f admittance should move along a circle, such as the appro- 
priate one in Fig. 2T9. This could be done by varying the length of a 
transmission line, matched both ways at the signal frequency, connected 
between the converter and the TR cavity. An incomplete reflection of 
the image frequency would give rise to admittances on a smaller circle. 
It is thus apparent that any mixer or converter circuit, or any circuit 
preceding the converter, which reflects at the image frequency may be 
expected to give rise to an i-f admittance that varies with the operating 
frequency. For this reason it is advantageous to make the line length 
between the crystal and TR cavity, or other device reflecting the image 
frequency, as short as possible. The variations encountered in the i-f 
conductance are of suflflcient magnitude to affect seriously the bandpass 
characteristic of the input circuit, and the variations in capacitance can 
have a serious detuning effect on the i-f input circuit. In order to evalu- 
ate these variations it is convenient to put Fa{. (47) into a different foi-m. 
If Eq. (47) is multiplied through by -v/Oh «7 and then by (V GHcy+^/Gocy), 
the result is 

T — +a^y + 2V(Lyary 

JjZ — ~ ~ ^ 

'I’wi'y Vl'o.*7 

Since \^G^yGocy = Go (the center point of Fig. 2-19, or that value of the 
i-f admittance with an imagc-freciuency admittance eciiial to that at the 
signal frecpiency), it may be shown that, for losses greater than 5 db, 
the equation 

Gtmy Gtuty 4 

~Go “ 

holds, within about 10 per cent. Since 5 db is about the minimum loss 
found for available crystal units, the maximum variation of i-f con- 
ductance is from about one half to twice the mean vahic for open-cir- 
cuited and short-circuited image-frequency terminations, respectively. 
In a given r-f circuit, the variation with different crystal cartridges, at a 



[Sec. 2*9 

fixed frequency, is determined by the variation in Go from unit to unit 
and by the fact that the effective phase length, and so the position of the 
apparent terminals satisfying Condition 2, is not the same from cartridge 
to cartridge. A consideration of Fig. 2*19 shows that small variations 
in the phase of the reflection of the image frequency give rise, primarily, 
to changes in i-f susceptance, for lengths giving either minimum or 
maximum conductance. In the region between these values, small varia- 
tions give rise, primarily, to changes in conductance. The choice of the 
length of line used could, in part, be determined by which of these two 
kinds of variation has the less objectionable effect upon the receiver noise 
figure and bandpass characteristic. 

Because the complex conjugates of the image voltage and admittances 
appear in Eqs. (6), it can be shown that the i-f admittance resulting 
from given signal-frequency and image-frequency terminations is the 
complex conjugate of that resulting if the signal-frequency and image- 
frequency admittances are interchanged. For instance, if the signal 
terminals are connected to a signal generator of the admittance that 
gives minimum loss, and if the image terminals are connected to a 
variable length of line, short-circuited at its far end, the i-f admittance 
goes around a circle such as the appropriate one of Fig. 2*19, as the line 
length is varied. If the roles of the signal and image terminals are 
interchanged the same circle will result but it will be traversed in the 
opposite direction as the line length is varied. 

From this it can be shown that, if the signal and image terminations 
are kept equal to each other but are changed together, the i-f admittance 
will remain real provided Condition 3 is satisfied. The connection 
between the impedance loss and the limiting values of the i-f conduc- 
tance, for complete reflection of both signal and image voltages, for all 
phases, is 

Lz = 2 

Gmin/ Gna 
'V/G inin / Gm 

Experiments to measure conversion loss by means of this relation 
have been performed by R. H. Dicke. For silicon crystals, where reci- 
procity is found to hold, good agreement with the conversion losses 
measured by other methods was found. Instead of a complete reflection 
of the signal- and image-frequency waves. Dickers method made use of a 
post protruding into the input waveguide of the mixer, giving a known 
reflection coefficient less than unity, to allow transmission of the local- 
oscillator wave through the same waveguide. It is necessary in such an 
experiment to use such a low intermediate frequency that a reflection 
some distance back from the crystal in the input waveguide gives rise to 
identical load admittances at the mixer, at the signal and image fre- 



quencies. If the i-f wavelength is not very much longer than the distance 
in the waveguide between the crystal and the point at which the reflec- 
tion occurs, the phase lengths of the waveguide at the image and signal 
frequencies are different and the imaginary parts of the i-f currents 
excited by the reflected signal and image waves are not exactly equal 
in magnitude and opposite in phase. There will be, consequently, a 
variation of the imaginary part of the i-f admittance as the line length is 
varied. In Dickers apparatus the i-f frequency used was 60 cps and, 
therefore, this condition was well satisfied. However, with intermediate 
frequencies of 30 Mc/sec and line lengths of several feet, variation of the 
susceptance component is observed. 

In summary, it should be emphasized that the i-f admittance of a 
crystal converter is not a function of the crystal unit alone but is depend- 
ent to a . considerable degree upon the details of the design of the mixer 
circuit. The range of admittance values that are possible is determined 
by the crystal unit and by its minimum loss as a converter. However, a 
reasonably good crystal unit can be made to show conductances differing 
as much as a factor of 8, as can be seen from Eq. (48), the factor depending 
on the nature of the mixer circuit. In addition, the susceptance of the i-f 
terminals of the converter is not completely determined by the dis- 
tributed and lumped capacitances and inductances of the physical 
structure, since the susceptance can be affected to a considerable extent 
by the design of the r-f circuits. These effects become rapidly more 
pronounced as the c.rystal units are improved and, therefore, increasing 
care must be takcMi to obtain optimum performance from improved units. 
The input circuit of the i-f amplifier must be designed to give satisfactory 
performance with all values of the i-f output admittance of the mixer to 
be expected with different crystal units in the whole band of operating 
frequencies. It may be found advisable to restrict some receivers to the 
use of crystals having more than the minimum loss, just to gain the added 
independence in the r-f and i-f circuits such crystals would give. The 
effect would be similar to that of adding an attenuator to increase the 
total loss by the same amount, in cither the r-f or the i-f circuit. 

2*10. Dependence of Conversion Loss on Image-frequency Tennina- 
tion, — The minimum loss for a particular -image teimination, as defined 
by Eq. (27), depends upon the value of the image-frequency load, 
through E(is. (8), (9), (10), and (11). The magnitude of the variation 
in the minimum loss which can be produced by changes in the image- 
frequency load admittance depends upon the values of the parameters 
y«a, y«/3, y«T, y/3«, and y/s^ of 15(i. (5), and cannot be simply related to the 
minimum loss with a particular image-frequency load admittance. 
That there should be an cffecjt of this kind, however, can qualitatively be 
seen from simple arguments. 



[Sec. 2*10 

The most pronounced effect of the image-frequency admittance on the 
conversion efficiency might be expected to occur with crystals with the 
smallest loss. Suppose, for instance, one had a converter that had 
unity loss, with a dissipative load connected to the image terminals. The 
device is said to have unity loss if the signal voltage develops the same 
available i-f power as is available from the r-f signal generator. The 
existence of the i-f voltage across the i-f terminals, however, must give 
rise to an image-frequency voltage across the image terminals and, 
therefore, to some dissipation of power in the image-frequency load. 
The signal is thus responsible for the generation of more total power than 
is available from the signal generator and this is incompatible with the 
assumption that the converter can be represented by a linear passive 
network. A perfect converter, for which the passive network representa- 
tion is valid, has a loss of 3 db if the signal-generator and image-load 
admittances are equal and are matched to the characteristic input 
admittance of the converter. One half the available signal power is 
transferred to the image frequency and dissipated in the image-frequency 
load. If there is no isolation of the signal- and image-frequency waves 
by means of tuned circuits, the minimum loss which a crystal convei*ter 
representable by a linear passive network can have is 3 db. 

If, on the other hand, the image terminals are provided with a load 
having no conductance component, there will be some value of the 
susceptance of the load which will allow the converter to have no loss 
between the signal and i-f terminals. It can be sho\vn that this will occur, 
if the terminal positions are chosen in accordance with the conditions of 
Sec. 2*9, for the image terminals either open-circuited or short-circuited. 
The i-f admittance will be a pure conductance, if the signal generator is 
matched to the characteristic admittance of the signal terminals and if 
the conditions of Sec. 2*9 are fulfilled. 

Such a perfect converter has not so far been made, but the crystals 
now available for use as converters do give losses as small as 5 db. The 
dependence of the loss on the image-frequency load would not be expected 
to be so pronounced as in an ideal lossless converter. A reduction of less 
than 3 db in the conversion loss from the value obtained with an image- 
frequency admittance equal to the signal-frequency admittance, there- 
fore, could be obtained through the use of an image-frequency load 
reflecting in the optimum phase. The magnitude of the effect depends 
on other parameters of the crystal as well as on the loss measured under 
the matched condition of the image, and an analysis will not l^e given 
here. This subject is discussed in detail by H. C. Torrey in Vol. 15 of 
this series. This discussion shows several possibilities for the dependence 
of the loss on the image-frequency load admittance. A plot of the loss as 
a function of the image load admittance can be made in the form of a 



surface, where the height of the surface above a particular point in the 
complex half plane corresponding to positive image load conductances 
gives the loss associated with that particulai* value of the image termina- 
tion. For some crystal units, the loss is highest for open-circuited image 
terminals and falls to a minimum at large absolute values of the load 
admittance. For other possible crystals, the reverse might be true, 
and for still others a maximum loss, or a highest point of the surface, 
might occur for a load consisting of a pure conductance, with the mini- 
mum loss at open circuit. 

The determination of the best image-frequency load admittance for a 
crystal of a particular type must be done experimentally. There are 
two ways in which this can be done. One way is to measure certain 
differential coefficients descriptive of the crystal mixer. R. H. Dicke and 
S. Roberts^ have shown that the coefficients of the linear-network repre- 
sentation of the crystal converter can be expressed in terms of these 
differentials, which in turn can be found by measurement of the r-f 
admittance at the local-oscillator level and measurement of the d-c 
characteristics. Examples of differentials to which the description of the 
converter has been reduced are the rate of change of direct current with an 
applied d-c voltage, the rate of change of the direct current with the r-f 
power, the rate of change of r-f conductance with the applied d-c voltage, 
and the rate of change of r-f conductance with r-f power. It was possible 
to show that from these differentials, the coefficients of Eq. (5), descrip- 
tive of the converter in question, can be evaluated and therefore the 
conversion loss for any particular image-frequency load can be evaluated. 
Also from these measurements, the value of \ Yap\/\Yfia\ can be found and, 
therefore, the loss can he calculated for the conversion of an r-f signal 
to an i-f signal, or of an i-f signal to an r-f signal. This treatment has 
been extended by II. C. Torrey and is discussed in detail in Vol. 15 of 
this series. 

The magnitude of the variations in the minimum loss of a converter 
with ordinary crystal units, resulting for different image-frequency 
loads, has l)eeri found by calculation from the differential coefficients to be 
about 1.5 (lb. Thcj loss can usually be made cither greater or less than the 
value obtained with an image-frc<iuency load equal to the signal-generator 
admittance. The loss with equal signal and image loads is usually about 
midway betweem the two limits. Thus there might be a reduction of 
about if (lb in conversion loss to he gained by choice of the best phase of an 
image-frequency reflection in the convertor. Because the noise tem- 
perature of the converter may also be affected by the reflection of the 

1 R. H. Dicke and S. llobcrta, ‘'Theory of Radar Mixers,” RL Report No. 287, 
July 16, 1942. 



[Sec. 2-10 

image frequency, the effect of the image-frequency reflection on the over- 
all noise figure is not determined by the loss alone. 

Another measurement that can be made to determine the effect of the 
image-frequency load on the loss is the direct measurement of the loss 
for various values of the image-load admittance. Direct measurements 
of the available i-f power, for a particular value of available signal power, 
are difficult to make because the i-f output admittance and the signal 
admittance of the mixer depend on the image-load admittance. For 
each experimental value of the image admittance, the r-f matching must 
be adjusted for minimum loss, since otherwise the effect of a mismatch 
may give rise to a change in the measured loss, which obscures the effect 
under investigation. If the available i-f power is found by measurement 
of the power delivered to an i-f load, the admittance of the i-f load must 
be such that the load absorbs all the i-f power available, or the power lost 
because of mismatch must be known for each value of the admittance of 
the image-frequency load. 

Experiments of this sort have been carried out at the Radiation 
Laboratory and elsewhere, and the results were substantially in agree- 
ment with the predictions from the measurements of the differentials. 
In the experiments a variable length of line was used between the mixer 
unit and a resonant TR switch. The TR cavity provides almost a 
complete short circuit of the input line of the mixer at the image fre- 
quency, whereas it provides a matched generator at the signal frequency, 
when the signal generator is connected to the input side of the TR cavity. 
The r-f tuning of the mixer was such that when the TR cavity was not 
present and the image frequency was therefore not reflected to the mixer, 
the mixer represented a matched load on the waveguide. Under this 
condition, the signal admittance of the mixer with the TR cavity in 
place should fall on a circle of constant reflection coefficient for all lengths 
of the line between the TR cavity and the mixer. Variation of the length 
of this line, therefore, should not change the reflection loss on the r-f 
side of the mixer. The i-f load admittance was made equal to the complex 
conjugate of the i-f output admittance of the mixer when the TR cavity 
was removed and the input line was thus matched at both the signal and 
the image frequencies. With the TR cavity in place, the i-f output 
admittance measured relative to the i-f conductance with no TR cavity, 
should then fall, for all lengths of the line between the TR cavity and the 
mixer, on a circle about the center of a Smith chart. In this manner, the 
reflection loss on the i-f side is made to be independent of the r-f line 
length. With these precautions the results were still not considered to be 
very dependable, but no gross disagreement with the results of othei- 
methods was found. 

According to the calculations based on the differential coefficients, the 



Tninimiim and maximum values of the loss should occur when the suscep- 
tance has the same value as when the TR cavity is not present. This 
prediction was not verified, however, and therefore, measurements 
were made of the i-f output admittance as a function of the line length. 
Instead of a circle on a Smith chart, a curve reproduced in Fig. 2*20 
was found, where the expeiimental points are indicated by the crosses and 
the closed contour is a smooth curve drawn through them^ consistent 

Fig. 2*2().— LornH of Uio i-f julinitUun^o of u couvoi-Um- jis» ploust* of t.lio iintiKO rofloc.tion 

is vnrii'd. 

with the probable (^xperiiiuMital (‘rror. It will ho ()l)S(M’ve(l that there is a 
considerable departure from a (ureh^ in th<^ valiums of the suseeptance for 
conductances higher than th<^ (diara<d.(u-istic c.onduetanc.e. The values of 
the maximum and minimum c.ondiietaiK^es, how(W(u*, if jnit into ICq. (47), 
give a loss for tlu^ mixeu* whicdi agrcM^s wc^ll with a previous (linnet measure- 
ment of the conversion loss of the same crystid. A e.irc.h’t repn^senting the 
expected locus of the i-f admittance n.s a function of tlu^ r-f line length is 
also drawn in the figure for (comparison. In addition, the value of the 
conductance was nucasured with tho TR cavity nnnoved, and it was 
found to be exacdly tine g(M)metric m(‘an of th<‘ minimum and maximum 



[Sec. 2-11 

values, or V 6007/G807, as predicted from the linear-network representation. 
Thus the only disagreement is in the susceptance values of the i-f admit- 
tance, and no explanation for this has been found. A possibility is that a 
variation in a harmonic-frequency load is responsible, but, since the line 
length was changed by the use of a long split waveguide of variable 
width, it is improbable that the variation of the effective length of the line 
at harmonic frequencies would bear a simple relation to that at the 
fundamental frequency. Since the figure appears to be closed, such a 
relation would be necessary if a harmonic frequency were responsible 
for the distortion of the circle. 

2-11. Measurement, with an Admittance Bridge, of the Dependence 
of Conversion Loss on the Image Reflection. — Another measurement of 
the dependence of the conversion loss on the image-frequency load 
admittance was carried out for several crystal units by means of measure- 


Fig. 2*21. — Apparatus for measurement of effect of reflection of the iinage-froqucMK^y wave 

on conversion loss. 

ment of the impedance loss of a mixer with several different lengths of line 
between the crystal and the TR cavity. The apparatus with which this 
was done was an admittance bridge, which will be described in Chap. 8. 
The TR cavity and the variable length of line between it and the crystal 
were considered to be included in the circuit represented by a linear 
network. The resulting impedance loss therefore included the loss in the 
TR cavity. Figure 2'21 shows a block diagram of the convertor and 
variable i-f load circuit that were used. Since the shrmt admittance of 
tils i”f resonant circuit appears as a part of the converter cii’cuit and 
contributes to the loss, pains were taken to make it sufficiently small to 
contribute only a negligible amount to the loss. With the coil used, the 
shunt admittance was less than twenty micromhos and this is very much 
smaller than the several thousand micromhos usually encountered as the 
output admittance of a crystal converter. 

The procedure of the experiment was as follows. For a particular 
setting of the variable line length, the switch S was first set in position 
(1), giving an i-f load admittance equal to the complex conjugate of the 
i-f output admittance of a mixer with an average crystal and no TR 
cavity. Then the mixer tuner was so adjusted that a small signal at the 
signal frequency was not reflected from the TR cavity. At the same time 

Sec. 2-11] 



the coupling and frequency of the local oscillator were set to the correct 
values. This tuning serves to establish nearly the proper loading on the 
TR cavity. If a large standing- wave ratio existed in the line between the 
mixer and the TR cavity, the part of the total conversion loss contributed 
by the TR cavity would be large, and a variation in it might obscure the 
effect under investigation. 

Next, the switch 8 was put at position (2) and the tuner on the input 
side of the TR cavity was adjusted to make the small signal pass into the 
tuner and converter without reflection. This made Obo equal to the char- 
acteristic admittance of the waveguide. Next, the switch was put into 
position (3) and the variable condenser adjusted for maximum reflection 
of the small signal at the input terminals of the first tuner. Under these 
conditions, the ratio (jbc/s/Goo/s is equal to the voltage standing-wave ratio, 
and Eq. (43) may be written as 

i. _ (49) 

Vr — 1 

From this expression, the impedance loss was calculated for that partic- 

ular setting of the variable line 
length. The line length was ad- 
justed in units of about 16® of phase 
and the whole procedure was re- 
peated for each setting. Curves 
showing the impedance loss of the 
converter, including the loss of the 
TR cavity, as a function of the sot- 
ting of the variable line length, for 
three representative crystals, are 
shown in Fig. 2-22. Because the 
loss measured by this apparatus, 
with the TR cavity removed, agreed 
well with the calibration of the 
crystals by other methods, it was 
assumed that reciprocity hold and 

0 40 . 80 120 160 200 240 280 320 

Setting of the variable line length in arbitrary units 

Fia. 2-22. — Three roproHontativo eurvoH 
for the iinpodanoe Iohh of a (louvortor inelud- 
ing a TU cavity, au a function of the lonjiitli 
of the lino between the Til cavity and the 

the impedance loss was the same as the loss for conversion of the signal 
from radio to intermediate frequency. 

It will be observed that the curves do not show a cyclic variation of 
the loss as a function of line length, as would be expo(*.tod. One reason for 
this might be that, for each line length, the mixer tuner was adjusted to 
establish the proper load admittance for the TR switch and this adjust- 
ment has some effect on the phase length of the lino lietwcon the TR 
switch and the crystal. It is therefore possible that the a(*,tual phase 
length of the line was not a simple function of the setting of the line-length 


adjustment. Another possibility is that the harmonics and other 
high-order waves developed by the crystal, which would be reflected to a 
large extent by the TR cavity, are responsible for the irregularity. 
These higher-frequency components would be affected in various ways 
by the setting of the line-length adjustment. The line length was 
varied by means of a polystyrene wedge that could be slid from the side 
to the center of the waveguide. This explanation of the irregularity 
would be in agreement with some measurements made at the Bell Tele- 
phone Laboratories on the effect of the image-frequency load on the 
conversion loss by the direct measurement of output power. It was 
reported that, in these experiments too, very irregular results were 
obtained until harmonic chokes were installed in the mixer unit. These 
chokes prevented the transmission of the frequency components in the 
region of the second harmonic back into the adjustable line and so to the 
TR cavity, and the curves obtained for the loss as a function of line length 
with the chokes in place were simple and periodic. The peak-to-peak 
variations were about the same as in the curves of Fig. 2-22, although, 
since they did not apply to the same crystals, no exact comparison could 
be made. 

An attempt was made to discover which line length corresponded to 
minimum loss. For each point of the curves of Fig. 2-22, the setting of 
the i-f condenser which maximized the standing-wave ratio was observed 
and from this the imaginary part of the i-f admittance could be estimated. 
The nxaxima and minima all seemed to correspond to real i-f admittances, 
in accordance with predictions from the linear-network representation, 
and independent measurements of the admittances for some of these 
points showed that, in most cases, the minimum loss occurred for the 
minimum-conductance point of the i-f admittance contour. This, 
however, was not always true; that is, with some crystals the mgYimiim 
conductance point gave minimum loss. It thus appears that consider- 
®'bly more data must be obtained before it will be possible to include, in 
the design of converters, the image-frequency termination giving the 
m inimu m possible conversion loss. None of the designs to be described 
in later chapters includes this feature. Before it could definitely be stated 
that the converter should be designed for mim'miiTn loss in this way, the 
effect of the image-frequency load admittance on the noise temperature of 
the converter would have to be measured. Also, the fact that a low i-f 
conductance is usually associated with the best conversion efficiency 
makes the design of input circuits having a wide pass band difficult 
because the i-f capacitance of the output temoinals of the mixer unit 
cannot be correspondingly reduced. If, on the other hand, there is a 
further decrease in the conversion loss of available crystals, it will become 
more important to include the proper unage-frequency load in the 

Sbc. 2*12] 



converter. At present, it appears that with ordinary crystals only a 
fraction of a decibel is to be gained by the reflection of the image wave in 
the best phase. An experiment on the effect of image reflection on both 
the noise temperature and the conversion loss has been performed by 
E. R. Beringer, M. C. Waltz, and C. P. Gadsden. The apparatus used 
for this experiment is described in Chap. 8. The results show that 
the over-all noise figure can be definitely improved by the proper choice 
of the phase of the image reflection, because the noise temperature did not 
change to compensate for the decrease in conversion loss. Experiments 
similar to this should be done for large numbers of crystals to determine if 
a fixed image-frequency reflection could be used for all crystals and over a 
broad band of frequencies. 

242. The Effect of Reflection of the Second Harmonic. — ^As has 
already been stated, the crystal mixer contains frequency components 
at the second harmonic and at higher frequencies. The treatment of 
these harmonics is likely to have some effect on the i-f admittance, the 
loss, and the signal admittance. Some manifestations of these fre- 
quencies have already been mentioned ia Sec. 241 but a few remarks 
about some experiments that dealt independently with the higher- 
frequency components are in order. These experiments have been 
primarily concerned with the effect on the conversion loss of the load 
admittance at the frequency of the second harmonic. 

The first observation of an effect of waves having frequencies at the 
second harmonic of the local-oscillator or signal frequency was made at 
the Bell Telephone Laboratories in conjunction with experiments on a 
coaxial-line mixer designed l)y W. M. Sharpless^ for 3000 Mc/sec. One 
of the design parameters was the position of an abiupt change in the 
diameter of the center conductor of the coaxial line connecting to the 
crystal. The signal generator could be matched into the mixer, for any 
position of the step change in diameter, by two other adjustments. 
Data were taken of the conversion loss as a function of the position of the 
step, with the signal-generator admittance adjusted for minimum loss at 
each position. When these data were plotted it was found that the 
conversion loss varied cyclically, with a repetition occurring for a motion 
of about 2.5 cm. Any variation caused by changes of admittances at 
the fundamental frequency would have repeated at each half wavelength, 
or 5 cm, of motion. Therefore, the observed variation was attributed to 
second-harmonic components. The magnitude of the variation was 
between 0.5 and 0.75 db from minimum to maximum. The final mixer 
design was chosen with the step in the position of minimum loss, and this 

1 W. M. Sharploss, “The Influence of Plarmonics on 10-ccntimetor Performance of 
Silicon Crystal Converters,” mT Report MM-42-160-80, July 24, 1942. 



ISbc. 2-12 

mixer has since been used as the standard test mixer for acceptance tests 
of 1N21, 1N21A, and 1N21B crystals. 

In the process of establishing the crystal-test specifications, measure- 
ments were made of large numbers of crystals in mixers of many different 
designs. None of the other mixers had dimensions specifically chosen for 
optimum second-harmonic effect and yet no large disagreements were 
observed between the average values obtained with the various types as 
long as the signal-frequency matching was made to correspond to the 
same tuning condition. It might be that an effect due to the second 
harmonic is very frequency-sensitive, and also requires individual 
adjustment for each crystal unit because of variations in the effective 
phase length of the cartridges. It appears that equally good conversion 
losses are obtained on the average with 3000-Mc/sec mixers that have 
no provision for reflection of the harmonics in the best phase. If it were 
considered worth while to include adjustments m a mixer which would 
allow the best possible performance to be obtained from each individual 
crystal, it would perhaps be reasonable to include, m addition to adjust- 
ments for the signal matching, the local-oscillator injection, and the 
image-frequency termination, an adjustment to give the best load 
admittance at the frequency of the second harmonic. It is doubtful that 
the termination for the second harmonic could remain optimum over the 
wide band of frequencies in which most mixers are now designed to be 
used, A noixer that contained all these adjustments would probably be 
very difficult to tune, unless each of the adjustments could be made 
independently of the others. 

There have also been experiments in the 3-cm region (9000 to 10,000 
Mc/sec) for the purpose of finding the effect of second harmonics on the 
conversion loss. For one of these experiments, also made at the Bell 
Telephone Laboratories, a mechanism indicated in Fig. 2*23 was used. 
A common crystal mount in this frequency range has a crystal mounted 
across the waveguide, along the narrow dimension. The waveguide 
extends a short distance beyond the crystal and is then short-circuited by 
a plate or a sliding plunger. The distance to this short circuit determines, 
in part, the tuning of the mixer at the signal frequency. Instead of an 
ordinary plunger, the mixer of this experiment had a thin plate extending 
across the waveguide along the narrow dimension in the center of the 
wide dimension and continuing in this position a considerable distance 
back along the waveguide. Except for a small phase shift, this plate 
acts in the same way, at the fundamental frequency, as a short-circuiting 
plate or plunger filling the whole cross section of the guide, since the 
half-width waveguides on either side of the diaphragm are waveguides 
beyond cutoff for the fundamental-frequency waves. At the frequency 
of the second harmonic, however, these half-width guides are wide 

Sec. 2-12] 



enough to allow propagation. Short-circuiting strips in the small guides 
can be adjusted to control the admittance of the waveguide at the 
harmonic frequency. Observation of the output power from the con- 
verter, with fixed input power, revealed a cyclic variation which repeated 
with the proper distance of motion of the two side strips to correspond to a 
second-harmonic effect. The variation observed totaled about 0.5 db 
from minimum to maximum. When the two side strips were replaced by 
resistive cards, tapered to give small reflections, the observed output 

Fio. 2-23,--Back pliinRor, iiulopenilontly adjuHtiiblp for fuiirlamoiital and harmoiric 


power was about midway between the maximum and minimum values 
found for the metal strips. 

A similar experiment was undertaken in which the apparatus used for 
the measurement of conversion loss by the admittance method was used. 
This apparatus also operated at about 3.2 cm and contained waveguide of 
0.400 by 0.900 in. inside dimensions. A short-circuiting plate was used 
over the end of the waveguide behind the crystal mount. To detect an 
effect due to the harmonic admittance of this part of the mixer circuit, 
this plate was replaced with one in the center of which was inserted a 
waveguide of 0.170 by 0.420 in. inside dimensions, as shown in Fig. 2*24, 



[Sue. 2'12 

Because this waveguide was beyond cutoff for the fundamental fre- 
quency, the motion of a short-circuiting plunger in the small waveguide 
would not affect the fundamental waves but would be expected to affect 

the admittance to the second har- 
monic and higher frequencies. In 
the second experiment, the tuner 
for the harmonic couples to a har- 
monic wave in the dominant mode 
only, whereas the tuner in the first 
experiment couples to both the 
dominant and the second modes. 

A change in the conversion loss 
of the mixer, caused by a change in 
the position of the small plunger, 
would produce a change in the 
admittance measured with the i-f 
leads either short-circuited or open-circuited, or for both conditions- 
When this experiment was tried, with several representative 1N23A and 
1N23B crystals, however, it was found that the effect on the admittances 
of moving the plunger was much smaller than could be measiu'ed, for both 
conditions, although the apparatus 
had sufficient sensitivity to detect a 
change in conversion loss as small as 
0.05 db. The effect of harmonic 
frequencies would be expected to be 
larger for crystals designed to oper- 
ate at the frequency of the second 
harmonic. An adapter was made 
to try 1N26 crystals normally used 
in the 1.25-cm band and for these 
crystals also, a negative result was 

In an effort to make the timing 
of the load admittance at the har- 
monic frequency cover a wider 
range, a tuner illustrated in Fig. 

2-25 was tried. This tuner con- 2-25.— Hannonic-frcduoiH^y admits 

- . « . , taruio tuuor. 

sists 01 two small waveguides con- 
nected at right angles to the full-sized waveguide, about five-eighths of a 
harmonic wavelength apart. Sliding plungers in the small waveguides 
affect only the admittance at the harmonic frequencies because the wave- 
guides are too narrow to support waves at the fundamental frequency. 
The section of waveguide containing these side arms was placed in the line 

Fig. 2-24. — Hannonic-frequenoy “back- 
plunger” tuner. 

Sec. 2-131 



between the signal generator and the mixer. In this experiment no 
measurable effect of the position of the plungers on the value of the 
admittance of the converter at the signal frequency was found. In both 
these experiments, a slight change in the admittance of the mixer, which 
repeated at settings of the plungers corresponding to half-wavelengths 
at the second-harmonic frequency, was detected. The change was 
not large enough, however, to allow measurement of a change in the 
impedance loss. 

Unfortunately, a direct measurement of output power was not tried 
with these same harmonic tuning devices. It may be suggested, however, 
that the reflection of the second harmonic appears in the reciprocity term 
\Ya$\/\Ypa\9 in the expression for the conversion loss and therefore 
affects the actual conversion loss but not the impedance loss. This 
possibility may have further foundation in the fact that Dickers proof 
of the reciprocity theorem requires certain relations to hold between the 
phases of the harmonic and fundamental frequency components in order 
that a time zero can be chosen about which the potential across the 
barrier may be expressed as an even function of time. 

Like the image-frequency effects, the harmonic effects cannot be 
evaluated in terms of the possible improvements in the over-all noise 
figures of receivers without parallel experiments on the effect on the 
noise temperature of the convei*ter. No such experiments are known to 
the author. It appeal's, at the present time, that the image-frequency 
termination has a greater influence on the over-all performance than the 
harmonic-frequency termination. The effects of the load admittance at 
harmonic frequencies are small compared with the variations among 
crystals. Making a converter circuit that has a wide pass band and 
includes optimum terminations for the image and harmonic frequencies 
throughout this band is not a simple task. Whether a fixed setting of 
these terminations would give, even at a single frequency, optimum or 
nearly optimum performance with the majority of crystal units, cannot be 
decided until further data have been acjcumulated. These arc some of the 
questions that were not answered satisfactorily dui'ing the war l^ecausc 
they were of less importance to radar development than was the develop- 
ment of converters and mixers for new frequencies and types of service. 

2-13. The Welded-contact Germanium Crystal. — A recent develop- 
ment in crystal units, reported by II. Q. North of the General Electric 
Company, lias resulted in crystal rectifier units that behave very differ- 
ently from any others previously observed. A description of their 
behavior is most easily given by an account of the experiments that led 
to the discovery of the unusual properties. 

These crystal units wore originally intended for use at 25,000 M c/sec, 
and were developed as a part of a program of research on germanium 



[Sec. 2-13 

crystals. Very great care was taken in the preparation of the ger- 
manium and the cat whisker and these parts were assembled into a 
cartridge resembling that of the 1N26 crystal (to be described in a later 
section of this chapter) to allow their use in the standard r-f circuit. 
The whisker was supported on a glass bead which was sealed into the 
outside cylinder of the cartridge, and the contact was made with very 
light pressure. It has been observed with other germanium units that 
some improvement in the conversion characteristics could be obtained 
if the crystal was subjected to a rather large direct current for a short time 
before it was used. In making an experiment on this effect, North 
discovered that a current of several hundred milliamperes in the forward 
direction could be passed through the unit without apparent damage to its 
high-frequency characteristics. The result of this large current was that 
the tip of the platinum-ruthenium-alloy cat whisker became so hot that 
it fused and became welded to the germanium. That such a weld was 
produced was verified by measurement of the force required to pull the 
whisker away from the germanium. This force was found to be suflBcient 
to break the whisker itself. The crystal units resulting from this process 
seemed at first to be comparable, in their behavior at 25,000 Mc/sec, with 
silicon units of more conventional design. If for no other reason, 
welded crystals would have been interesting because of their great 
mechanical and electrical stability. 

Because these units did not have the same r-f characteristics as the 
1N26 units, it was thought probable that their conversion loss, as meas- 
ured in the test set for the 1N26, suffered considerably from reflection of 
the signal. As a consequence, they were tried at 3.2 cm. The 3.2-cm 
test set was equipped with a tunable crystal holder and it was found that, 
when the crystal holder was tuned for maximum delivered power, the 
losses of the welded units were as small as 3 db. An additional adjust- 
ment was used in the form of a d-c bias voltage in the forward direction. 
This bias voltage had a considerable effect on the minimum conversion 
loss obtainable and was retained as part of the converter circuit in all the 
subsequent experiments. Since the test set has the same load admit- 
tances at the signal and image frequencies, it was thought that these 
crystals were exhibiting the smallest loss compatible with the representa- 
tion as a passive network. Therefore, a few readings of a few tenths 
of a decibel less than 3-db loss were considered to indicate a small error in 
the absolute calibration of the test set. 

To verify the result obtained with the test set, the loss of a few of the 
best units was measured by the admittance-bridge method, described in 
Sec. 2-11. No resonant circuit was used to separate the image termina- 
tion from the signal-frequency termination, but the result of the experi- 
ment was that the reflection coefficient, for the open-circuit switch 

Sec. 2-13] 



position and optimum load susceptance, was as large as unity for some 
crystals. The impedance loss was therefore unity, indicating that the 
same power should be available from the i-f terminals of the converter as 
was available from the r-f signal generator. For some crystals, the 
reflected wave from the crystal seemed to be a little larger in amplitude 
than the incident wave, but this was thought to be an experimental error. 
In order to obtain the best results it was necessary to adjust the level of 


the local-oscillator power and the magnitude of the forward d-c bias 
voltage, and with each crys^l several tests were made in search of the 
optimum combination of these adjustments. The experiment definitely 
confirmed the result of the earlier one. 

In the experiment with the test set it had been found that the con- 
version efficiency was better if the 400-ohm i-f load resistance normally 
used was changed to 800 ohms. The test set measures the ratio of the 
available r-f power to the i-f power delivered to the load, and not the true 
conversion loss. Further experiments with this test set showed that 
still more i-f power was delivered to even larger i-f load resistances. The 



[Sec, 2-13 

loss factors became less than 3 db for many crystals and, for some, were 
even less than 0 db. This corresponds to an actual power gain, and it 
occurred without any isolation of the image terminals. An experiment 
was done to determine the i-f output admittance of a converter using 
these crystals, to discover the optimum load admittance. Since such a 
low loss must depend markedly on the r-f tuning, provision was made to 
include tuning of the r-f circuit by means of a sliding-screw standing-wave 
generator in the r-f-input waveguide. Local-oscillator power and a d-c 
bias voltage were provided. With the tuning screw inserted for a large 
reflection, the i-f (30 Mc/sec) admittance was measured for various 
positions of the screw along the waveguide. The result of this experiment 
is shown in Fig. 2-26, plotted on a Smith admittance chart. The signifi- 
cance of the extension of the contour outside the circle representing the 
ordinary complex half-plane, is that negative conductances were encoun- 
tered for some conditions of r-f tuning. The circle of zero conductance 
is the normal boundary of the Smith chart, but if negative conductances 
are included these become circles of larger diameter and, like the circles of 
constant positive conductance, have centers on the real axis and pass 
through the infinite-admittance point. 

The discovery of the negative i-f conductance of the welded-contact 
germanium crystals explained the experiments in which a conversion loss 
of less than unity was found, as well as the fact that this was obtained 
only under critical conditions of the r-f tuning. A device having a 
negative conductance can be made into an oscillator if it is loaded by a 
positive conductance of absolute value smaller than that of the negative 
conductance itself. The same device may be used as an amplifier with a 
true power gain if it 'is loaded with a conductance just too large to 
allow oscillation. The crystal, when used as a converter, delivered 
an increasing amount of power to the load as the load conductance 
was increased. When a resistance of several thousand ohms was used 
as the i-f load, a conversion gain of more than 10 db was obtained. 
The crystal was therefore acting as a regenerative converter. Further 
confirmation of the existence of the negative i-f conductance was 
obtained by connecting the converter to a shunt-resonant circuit, which 
had a shunt conductance smaller in absolute value than the measured 
negative conductance of the converter. Oscillation at the resonant 
frequency of the tuned circuit was obtained for all frequencies from 
6 to 45 Mc/sec, and a later experiment at the General Electric Company 
revealed oscillation near 10,000 Mc/sec, when the crystal was tried in a 
converter with a local oscillator at 25,000 Mc/sec. A negative i-f 
conductance has not been produced with crystals of other types. 

The d-c characteristic of the welded-contact units is also different 
from that of other units. A curve resembling the d-c characteristic of a 

Sec. 2-13] 



typical unit is shown in Fig. 2-27. The slope of the curve in the vicinity 
of the origin corresponds to a resistance of several megohms whereas the 
steepest part of the curve on the right side has a slope corresponding to 
a resistance of about 3 ohms. As 
mentioned previously, this part of 
the curve is a measure of the spread- 
ing resistance ■ of the crystal and, 
with ordinary silicon units, it is 
about 60 ohms. On linear scales, 
the d-c characteristic appears to 
have a sharp bend in the forward 
direction, but the position of this 
bend on the voltage axis depends 
upon the scale of the current coordi- 
nates. A formula deduced on theoretical grounds, which expresses the 
relation between current and voltage applied across the barrier of the 
crystal in the forward direction is 

I = - 1), (50) 

where e is the electronic charge, k is Boltzmann's constant, and T is 
the absolute temperature. The constant A is related to the density 
of current carriers in the semiconductor and the area of the contact, and 
V is the voltage across the rectifier unit minus the drop in the spreading 
resistance. The d-c characteristic of the welded-contact crystal has been 
measured carefully and it is found to follow this formula closely over a 
wide range of current. When the logarithm of the current is plotted 
against the applied voltage on a linear scale, the plot is a straight lino 
over six decades of current. Similar curves for other crystal units follow 
the formula over only two or three decades at most, and the slope does not 
agree closely Avith the formula. For the welded-contact crystal, H. C. 
Torrey has shown that the d-c characteristic can be used to calculate the 
value of the electronic charge. Using a more precise formula than Eq. 
(50), Torrey obtained a value for c agreeing with the accepted value 
within experimental error. The d-c characteristic of the welded-contact 
crystal thus agrees more closely with the theoretical prediction than do 
the d-c characteristics of the more common types. 

If the d-c characteristic of a welded-contact crystal is displayed on an 
oscilloscope when the crystal is mounted in a converter with local-oscil- 
lator power incident, the presence of the negative conductance can be 
observed. For ordinary crystal units, a cuive similar to that shown in 
Fig. 2-28 is obtained. The intercept with the current axis is the rectified 
current caused by the incident r-f power, and the plot shows the total 
current for bias voltages of both signs. The shape of the curve for a 

Fia. 2-27. — D-c characteristic of welded- 
contact germanium crystal. 



[Sbc. 2*13 

conventional crystal is not very much affected by the r-f tuning but, when 
the welded-contact units are tried, the situation is changed. Dependiag 
upon the r-f tuning, a variety of curves can be produced and among them 

are curves resembling those of Eig; 
2-29a and 6. The curve of Fig. 
2 •29a is not much different from 
the curve for an ordinary crystal, 
but that of Fig. 2*296 clearly demon- 
strates the negative conductance 
and the fact that it is most easily 
obtained with a small forward bias 
voltage applied to the crystal. 
Other effects on the d-c character- 
istic could be obtained by adjusting harmonic-frequency admittances in 
specially designed r-f circuits. 

A theory of the source of the negative i-f conductance of these crystals 
has been given by Torrey. He has shown that the i-f conductance of a 
crystal can be made negative under certain conditions of r-f tuning, if the 
variation of the barrier capacitance with the voltage applied across the 
barrier is taken into account. The negative conductance should show u.p 
only in units which have very small spreading resistances,, as have the 
welded-contact crystals, and for high-frequency local-oscillator voltages, 

Fig. 2*29. — D-c characteristic of welded germanium crystal for two conditions of r-f tuning. 

where the effect of the capacitance on the rectification efficiency is con- 
siderable. There is no possibility of producing the negative conductance 
in the absence of local-oscillator voltage, because it is from this source 
that the necessary energy associated with the negative conductance must 

If, because its conversion gain can be made large, a crystal of this 
type could be used to obtain a receiver having a smaller effective over-all 
noise figure than is obtained with conventional crystals, it would be of 
great importance as a converter for a microwave receiver. Experiments 
by E. R. Beringer, M. C. Waltz, and C. P. Gadsden, with an apparatus 

Fig. 2-28. — D-c characteristic of normal 
crystal with local-oscillator power incident 

Sbc. 2*14] 



similar to one described in Chap. 8, showed that the noise power available 
from the converter, when the converter is operated in the condition of 
negative i-f conductance, was also large. As a result, it was not found 
possible to obtain with these crystals, in any of the many tuning condi- 
tions tried, an effective over-all noise figure smaller than can be obtained 
with conventional crystals. The tuning conditions tried included the use 
of separate tuning of the signal-frequency and image-frequency circuits, 
but the only advantage of the converter over one using a conventional 
crystal was that the greater output power allowed the use of some- 
what reduced gain in the i-f amplifier. When operated in a tuning condi- 
tion in which a negative i-f conductance was obtained the over-all noise 
figure was not very much larger than that obtained with conventional 
crystals. The tuning is critical, however, and a receiver, the perform- 
ance of which depends on the large conversion gain, would be difficult to 
keep in proper adjustment. 

Some attempts to make regenerative and superregenerative converters 
were made but they were not carried very far, The use of germanium 
crystals for such converters may have importance in lightweight appara- 
tus, because the i-f amplification required could be considerably reduced. 
The noise power available from crystals of this type may be reduced by 
further research, and such a development would allow lower receiver 
noise figures to be obtained. The treatment of the image and harmonic 
frequencies in converters designed to operate with germanium crystals 
would be much more important than it is with the crystals in use at 
present. A more complete discussion of the welded-contact crystals, is 
given in Vol. 15 of this series. 

2- 14. The Converter Noise Temperature. — The noise temperature 
was defined in Chap. 1 and reference to it has been made in connection 
with the effect of the image load admittance on the loss'and in the discus- 
sion of the wcldod-contact germanium crystal. The magnitude of the 
effect of a given noisci temperature on the over-all noise figure of a receiver 
depends on the magnitude of the noise figure of the i-f amplifier. With an 
i-f amplifier having a noise figure of unity, a change in the noise tempera- 
ture of the converter by a given factor produces a change in the over-all 
noise figure by the sanie factor. Since amplifiers with noise figures 
smaller than two can now be made, it is important that the noise temperar 
ture of the converter he as small as possil)le. 

The noise teinpcu’ature of a crystal converter is never less than unity. 
By definition, it would be unity if no excess noise were developed in the 
crystal itself and the noise power available from the convei’ter were only 
the Johnson noise associated with the i-f output admittance. If the 
conversion loss of the unit were very small, the i-f admittance of the con- 
verter would have a temperature determined by the objects and the 



[Sec. 2-14 

a-bsorbing media in the field of view of the antenna. When the noise 
temperature of a converter is measured, however, the antenna is replaced 
by an r-f resistance at room temperature and, if no excess noise were 
developed in the converter, the noise power available from the converter 
would be kTBj where T is room temperature. 

As a result of the research on semiconductor crystals and on techniques 
of preparation and manufacture of rectifier units, the noise temperature of 
units now available has become considerably smaller than that of early 
units. The excess noise developed by the crystal unit is associated with 
the flow of current through the barrier; this current consists of a flow of 
discrete charges and, consequently, has a nonuniform character. The 
approximately linear relationship between the noise temperature of the 
converter and the crystal current, which is roughly proportional to 
the incident local-oscillator power, bears out the theory that the noise is 
similar to the shot-efifect noise in a diode. If there is no incident local- 

oscillator power, the crystal no longer acts as a frequency converter, and 
the available noise power is just Johnson noise. 

In order to specify the quality of a crystal as a converter, it is neces- 
sary to give the conversion loss and the noise temperature corresponding 
to same amount of local-oscillator power. The magnitude of local- 
oscillator drive should be chosen to be the magnitude for which optimum 
over-all noise figure is obtained in a receiver using the crystal as a con- 
verter. The optimum local-oscillator power depends on the noise figure 
of the i-f amplifier following the converter. The local-oscillator drive 
chosen for the specification of the loss and noise temperature is that which 
result in the minimum over-all noise figure in a receiver using an i-f 
amplifier with a noise figure typical of present production. If a receiver 
uses an x-f amplifier with a smaller noise figure, the optimum value of the 
over-all noise figure is. obtained with less local-osciUator drive For 
best results, the optimum local-oscillator level should be determined 
expei^entally Since the over-aJl noise figure does not vaiy rapidly 
jith local-osciUator drive m the region of the minimum, a small departure 

from the optimum local-oscillator drive does not entad a large increase in 
over-all noise figure. 

temperature of a crystal converter, 
T.T’" ^ independent of the intermediate fre^ 

qu^cy at wtech it is measured. In general, it is found to be lower at 

^ove a wtr *^*'“/* although at frequencies 

above a few me^cyeles per second the variation with frequency is not 

Sbc. 2-14] 



For some purposes it is desirable to have a receiver with an i-f ampli- 
fier at a frequency lower than this, or even to connect an audio-frequency 
amplifier to the output terminals of a frequency converter. It is easier 
to make an i-f amplifier having a very narrow pass band at low frequencies 
than at high frequencies, and for this reason a low intermediate frequency 
might be desired. An audio-frequency amplifier might be used, in an 
application such as c-w radar, where the reflected wave received differs 
from the transmitted frequency because of the doppler effect with a 
moving target. It is important to realize that the noise temperatures 
usually quoted for crystal converters apply at 30 Mc/sec and that the 
temperature at low frequencies is considerably higher. If a narrow pass 
band is desired, it is usually better to use a double i-f system, where the 
first amplifier stages operate at 30 Mc/sec or more, and a second fre- 
quency conversion is made to allow the use of a narrower, low-frequency 

Measurements, made at the University of Pennsylvania, of the noise 
temperature in the video- and audio-frequency range, show that the noise 
temperature of a crystal converter increases as 1// in this range. The 
values common at a low audio frequency are very large. At 100 cps, a 
noise temperature as large as 10® is common. The noise figure of a 
receiver using an audio-frequency amplifier would be correspondingly 
large. The minimum signal power detectable with such a receiver would 
be very much larger than that detectable with a receiver having the same 
bandwidth but a high intermediate frequency. This same limitation is 
encountered when crystals are used as rectifiers for experimental purposes 
and small changes in the rectified current are intended to show small 
changes in the incident r-f power. Because of the low-frequency noise, 
there are slow changes in the rectified current witli a fixed incident r-f 
power, and the fractional change in incident power which can be detected 
is therefore limited to a rather large value. 

Usually, the noise temperature of a crystal converter is raised if a 
backward bias voltage (one in the direction of high resistance) is applied 
to the crystal. For this reason, it is advisable to keep the resistance of 
the circuit through which the crystal current flows as low as possible. 
For the purpose of filtering, resistors have been used in series with the 
crystal-current leads but, because the flow of ciystal current through such 
resistors develops a backward bias voltage at the crystal unit, it is not 
advisable to use such resistors unless they are small or are shunted by i-f 
chokes of low d-c resistance. A total resistance of about 100 ohms can Ix^ 
tolerated in the crystal-current path without producing an apprcciabU^ 
deterioration in the over-all noise figure of the receiver. Since the crystal 
current is usually less than 1 ma, a backward bias voltage of loss than 0. 1 
volt can be tolerated. 



[Sec. 2-15 

Specific values and an outline of the method of measurement of the 
converter noise temperature of crystals of various available types are 
given in later sections of this chapter. It must be remembered, however, 
that since all the standard tests are made at 30 Mc/sec and at higher fre- 
quencies, the test specifications cannot be used to estimate the noise 
figure of receivers using intermediate frequencies much below this. 

2-16. Crystal Burnout. — In Chap. 1, the need to protect the sensitive 
part of a receiver was discussed in explaining the function of the duplexer 
common to all single-antenna radar systems. The amount of protection 
the duplexer must provide depends on the amount of power that can be 
dissipated in the input circuit of the receiver without damage. Since the 
best over-all noise figures are obtained with microwave receivers, using 
crystal converters as input circuits, the more power a crystal unit can be 
made to withstand without damage, the less protection is required from 
the duplexer. A considerable part of the work on the development of 
crystal rectifiers, therefore, has been directed toward increasing the 
amount of electrical shock they can withstand without damage. Great 
increases in the resistance of crystals to both mechanical and electrical 
shock have been made. In some instances, there have been simultaneous 
reductions in the loss and noise temperature. This improvement is 
valuable for crystals intended for use in isolated receivers because, 
although the danger of damage from a local transmitter may not exist, 
accidental mechanical and electrical shocks can occur. 

The crystal cartridges now available are all hermetically sealed by 
filling the region above the semiconductor and around the cat whisker 
with a wax having a low r-f loss factor. In addition to making the 
hermetic seal, the wax serves to support mechanically the fine wire cat 
whisker, and the contact is therefore made more stable against mochani- 
cal shock than it would be otherwise- There is no reason to believe that 
a crystal rectifier unit that was never subjected to electrical power greater 
than a few milliwatts, and that was never subjected to severe mechanical 
shock, would ever change in its characteristics. Nevertheless, the prob- 
lem of burnout of the crystal converter has been one of the greatest 
sources of trouble in a radar system, and, as a consecpience, a large amount 
of work has been done to reduce the frequency of occurrence of burnout. 
This work has been directed toward increasing the amount of protection 
and the lifetime of the TR switches, and toward increasing the resistance 
of the crystal units to damage by electrical shock. Rcsistan(‘,e to electri- 
cal shock could be increased relatively easily at a sacrifice in the noise 
figure of the receiver, but this sacrifice could not be tolerated. 

A crystal rectifier, to be useful at very high frequencies, must have a 
very small contact area. The barrier capacitance is partially determined 
by this contact area and, with a large contact area, the nonlinear resist- 

Sac. 2«161 



ance of the contact is effectively bypassed by the capacitance. When a 
large current is passed through a crystal rectifier, heat is generated in the 
very tip of the cat whisker and in the semiconductor just below it, because 
these are the regions of highest electrical resistance. The weld of the 
special germanium crystals was accomplished in just this way. Unfortu- 
nately, ordinary tungsten-whisker silicon crystal units do not react 
favorably to such heating. Instead, the contact is destroyed, or the area 
of contact is made so large, by the fusion of the tip of the whisker, that 
the crystal is no longer a good high-frequency rectifier. A crystal that 
has deteriorated because it has been subjected to excessive electrical 
power is said to be burned out. A bumed-out crystal may exhibit its 
deterioration as an increase in conversion loss, an increase in noise tem- 
perature, or both, if it is used as a frequency converter or, if it is used as a 
low-level detector, as a decrease in rectification efficiency. 

2'16. Correlation between TR Leakage Power and Crystal-burnout 
Power, — It has already been stated in Chap. 1 that the power that leaks 
through a TR switch consists of two 
components called the “ spike and 
the flat.'' The spike occurs at the 
beginning of the radar transmitting 
pulse and builds up with that pulse 
to an amplitude sufficient to initiate 
the arc in the TR switch. After the 
arc is initiated, the amplitude of the 
leakage signal falls abruptly to a smaller value, whore it remains until 
the end of the transmitting period. The envelope of the pulse trans- 
mitted through a TR switch can be observed with an r-f envelope viewer. 
This instrument consists of a crystal detector and a video-frequency 
amplifier, the output voltage of which is applied to the vertical-deflection 
plates of a cathode-ray tube. A sweep voltage, synchronized with the 
pulse rate of the radar transmitter, is applied to the horizontal-deflection 
plates of the tube. In Fig. 2-30 a sketch of a typical trace produced by 
the leakage power from a TR cavity, as viewed with an r-f envelope 
viewer, is shown. In this sketch, and on most of the viewing systems, 
the peak power of the spike appears to be about twice that of the flat. 
The average leakage power can be measured with bolometers and is 
usually found to correspond to an average power for the duration of the 
pulse of less than 50 mw. The power level at the peak of the spike cannot 
be found from the trace on the envelope viewer alone, because the band- 
width of the video amplifier is not sufficient to ensure that the r-f envelope 
viewer responds rapidly enough to show the true magnitude of the spike 
relative to the flat power. 

Measurements of the r-f pulse power, in l-Aisec pulses, reciuired to 

Fi(*. 2‘30. — Envelope of the r-f pulse 
leakage from a TH switch us viewed with 
an r-f envelope viewer. 



[Sec. 2-16 

damage crystal rectifiers have been made. This power was found to be 
considerably larger than the 60 mw of average power that passes through 
the TR switches during the transmission period. Yet crystal burnout 
was not at all uncommon in the radar systems in which such crystals and 
TR switches were used. Even after crystals that could withstand several 
watts of r-f pulse power had been developed and the apparent safety fac- 
tor was very large, the burnout problem persisted. Finally, techniques 
for the measurement and viewing of the spike were developed. One 
of these techniques consisted of a measurement of the total leakage power, 
by the bolometer method, and a measurement involving the calibration 
of the r-f envelope viewer as a power meter. Comparison of the results of 
these two measurements showed that the average leakage power, as 
indicated by the bolometric method, was considerably greater than that 
calculated from the height of the flat part of the leakage on the viewer, 
the pulse length, and the recurrence rate. Therefore, the actual peak 
amplitude of the spike part of thei leakage is much greater than indicated 
by the viewer and, consequently, the time duration of the spike must be 
very short compared with the response time of the viewer. This was 
confirmed by measurement with the other method, which was accom- 
plished with a transmission channel bypassing the TR switch and having 
the right phase and amplitude characteristics to produce destructive 
interference between the waves transmitted by this channel and by the 
TR switch during the time of the flat-power leakage. The subsidiary 
channel was adjusted until the flat power was completely canceled, and 


I flat 

Tia. 2-31. — Leakage of a TR switch with 
flat power canceled out. 

only the spike remained to be seen 
on the envelope viewer. The amp- 
litude of the spike is almost entirely 
unaffected by the addition of the 
interfering channel because the 
spike power is transmitted through 
the TR switch without much atten- 
uation, before the arc is initiated. 
The attenuation of the subsidiary channel is the same as that of the TR 
switch when it is firing, and the power transmitted by it is therefore small 
compared with the spike power at the time of transmission of the spike. 
A sketch of the trace on the r-f envelope viewer with the flat power 
canceled out is shown in Fig. 2-31. When the residual average power 
under these conditions was measured with a bolometer, it was found to 
correspond exactly to the discrepancy between the measurements by the 
first method. 

Because the duration of the spike was found to be so short (less than 
10 * sec), it was not yet substantiated whether such a short pulse could 
damage a crystal unit by heating, since the crystal unit must have a 

Sec. 2 - 16 ] 



nonzero thermal time constant. The time constant had in fact been 
estimated to be somewhat longer than the duration of the spike and^ 
therefore, it was suspected that the damaging effect of the spike might be 
measured by the energy content of a single spike, independent of its peak 
power. Tests of the burnout characteristics of crystal units with video- 
frequency pulses, shorter than 10"“® sec but of various durations, were 
made and it was found that the energy was the important parameter- 
The methods of measurement of the spike allowed the calculation of the 
energy per spike pulse, and it was found that there was a much smaller 
safety factor of protection against burnout by the spike than by the flat 
leakage power. In addition, the methods of measurement and of viewing 
of the spike energy revealed a great dependence of the spike energy on the 
functioning of the keep-alive electrode of the TR tube. Improvements 
in the design of the keep-alive electrode and of the circuit supplying 
the voltage for it considerably reduced the frequency of burnout of crys- 
tals in radar systems. Consequently, the research on the burnout 
characteristics of crystals was directed most strongly toward measure- 
ment and improvement of their resistance to bumout by very short pulses. 
It was found that the burnout of crystals by the r-f spike energy correlated 
reasonably well with the values obtained from experiments with video- 
frequency pulses. 

In some frequency bands, crystals of several different types, having 
different degrees of resistance to bumout, are now available In the 
3000-Mc/sec region, for instance, the 1N21A crystals are subjected to 
short pulses containing 0.3 erg of energy, whereas the 1N28 ciystals are 
subjected to pulses containing 5 ergs, before their loss and noise tempera- 
ture are tested. That the increase in resistance to burnout was not 
achieved at a sacrifice in noise figure is evident from the fact that the 
limits on the loss and noise temperature of the 1N28 crystals are lower 
than those of the 1N21A crystals. The 1N21B units, however, have a 
bumout test at lower energy than the 1N28 units, and a lower limit on 
the conversion loss. 

In addition to bumout of this instantaneous kind, it has been found 
that a slow deterioration with time occurs when crystals are subjected to 
pulses of considerable magnitude but containing insufficient power to 
cause a crystal to be burned out by a single pulse or by a small group of 
pulses. For instance, a crystal that might withstand several hundred 
pulses of 2 watts pulse power sometimes shows a serious deterioration 
over a period of operation of many days when subjected to pulses of a few 
hundred milliwatts pulse power recurring 1000 times per second. It is 
therefore advantageous to make the leakage power of the TR switch as 
small as possible and to make occasional checks of the crystal unit, even 
if no failure of the TR switch has occurred and no abrupt change in 



[Sbc. 2*16 

receiver sensitivity has been observed. At power levels of a few milli- 
watts, crystals appear to last indefinitely if handled with reasonable care. 

In this connection it should be pointed out that one of the most fre^ 
quent causes of damage to crystal units is the discharge through the crys- 
tal of the electrostatic charge commonly accumulated on the body. 
Discharging the body capacity to the apparatus before a crystal is inserted 
or removed precludes the possibility of burnout by this means. In this 
way one makes certain that no discharging current will flow through the 
crystal unit. It is confusing to have a crystal burned out during the 
time between its testing and its insertion in the apparatus. The energy 
stored in the charge on the capacity of the body, even for electrostatic 
potentials that would not normally be noticed, is suflS.cient to cause burn- 
out of some units. 

In addition to damage by electrical shock, the delicate contact of the 
crystal rectifier unit is subject to damage by mechanical shock. The 
wax filling cannot prevent motion of the whisker if extreme accelerations 
are encountered, and, hence, it is advisable to make checks before use on 
all crystals that are accidentally dropped. For this purpose and for 
checking for damage from electrical sources, the back-resistance meter, to 
which reference has already been made, is a very useful and simple test 
device. Information on the design and use of this device is given in Sec. 
2*20. In the table at the end of this chapter, a column giving limiting 
values of the back current at one volt, for crystals of the various types, 
is included. 


In the earliest days of the development of crystal rectifiers for use as 
microwave frequency converters, the only specification of the quality of 
the crystal was the effective over-all receiver noise figure resulting with 
its use. The noise figure was ascertained by measurement of the r-f 
input signal power required to give an output signal power equal to the 
output noise power. In addition, the width and shape of the pass band 
had to be measured in order to evaluate the equivalent noise bandwidth 
B of the receiver. The ratio of the required input signal power to kl'B 
is the effective over-all noise figure of the receiver. This was sufficient 
description of the particular receiver for which it was measured, but it did 
not allow computation of the expected noise figure for the same crystal 
with a different i-f amplifier. 

The conversion loss and the noise temperature of a crystal used as a 
frequency converter are, together, a measure of the quality of the crystal 
alone. They can be used to calculate the effective over-all noise figure .of 
a receiver using the crystal as a converter if the effective noise figure of 
the i-f amplifier, with a generator having an admittance equal to the i-f 

Sec. 2-171 



adimttance of the converter, is known. The first equipment for measure- 
ment of the loss and noise temperature of a crystal closely resembled an 
ordinary microwave superheterodyne receiver. The loss was measured 
by calibrating the i-f amplifier as an i-f power meter and comparing the 
i-f power delivered by the crystal converter with the r-f power available 
from the signal generator. The measurement of noise temperature was 
made by comparison between the values of the output noise from the 
receiver with the crystal in place and with the crystal replaced by an 
equivalent i-f resistance. From this comparison the noise temperature 
can be calculated, provided the effective noise figure of the i-f amplifier 
is known. The amplifier noise figure was measured in a standard manner 
by use of a temperature-limited noise diode. 

This method of measurement of the quality of a crystal was rather 
unreliable and difficult to carry out. Simpler apparatus was subse- 
quently developed for making the measurements of loss and noise tem- 
perature. Moreover, a burnout test was included in the specifications 
and a standard apparatus for this test was developed. The remaining 
sections of this chapter are devoted to a description of the principles of 
this test apparatus. It is not intended to give sufficient detail in this 
description to enable the reader to duplicate the apparatus but only to 
make clear the meaning of the test specifications. A table of some of the 
specifications and related data for crystals of the types now available is 
included at the end of the chapter. 

2-17, Conversion-loss Measurement. — To measure the conversion 
loss of a crystal by the direct method, an accurately loiown amount of r-f 
signal power, 1 /xw or less, must be available. Similarly, it must be possi- 
ble to measure accurately a smaller i-f power. The frequencies of the r-f 
signal and the local oscillator of the converter must be such that the out- 
put signal of the conveiter has the frequency of the i-f amplifier that is 
used as a power meter. Because the conversion loss is dependent on the 
load admittances at the image and harmonic frequencies, the loss meas- 
ured in this way can be different for the same crystal in different mixers, 
even if all the available signal power is matciied into the converter. 

To simplify the measurement of conversion loss, the modulation 
method” was developed. In this method, no signal generator, separate 
from the local oscillator, is used and the converter output power is meas- 
ured with a standard instrument. The crystal is plac.ed in an appropriate 
mount, either a waveguide or a coaxial line, depending on the frequency. 
This mount is adjusted, on the basis of statistical data on large numbers 
of representative crystals, in such a way that an average crystal has the 
minimum loss at this adjustment of the mount. Provision is made in the 
crystal mount to bring out the rectified crystal current and low-frequency 
voltages in the same way as in a conventional mixer. The manner in 



ISbc. 2-17 

which this is done will be made apparent in the following chapters. This 
crystal mount is placed at the end of a similar waveguide or coaxial line, 
from which the local-oscillator power is applied, through a matched 
dissipative attenuator, at an appropriate known level. Because of the 
matched attenuator the local oscillator, as a signal generator, has an 
admittance equal to the characteristic admittance of the line. A small 
amplitude modulation is then introduced on the local-oscillator signal 
and the magnitude of the voltage thus produced at the output side of the 
crystal, across a resistance equal to the optimum load resistance for an 
average crystal, is measured by means of a sensitive a-c voltmeter. The 
modulation frequency is low, usually 60 cps, and an ordmary amplifying 
voltmeter having a full-scale sensitivity of 0.01 volt can be used. For a 
full-scale deflection of such a voltmeter, an i-f power of 0.25 /xw is required 
if the load resistance is 400 ohms. If the conversion loss were 6 db, the 
modulation required for a full-scale deflection would be equivalent to an 
available signal power of 1 /xw. This is found to be a small enough signal 
to allow the converter to behave linearly. 

The amplitude-modulated local oscillator is equivalent to an unmodu- 
lated local oscillator and a signal at each of the sideband frequencies 
corresponding to the signal and image frequencies of a converter. This 
may be shown in the following way. If 27r times the local-oscillator 
frequency is co, and 27r times the modulation frequency is p, the instanta- 
neous local-oscillator voltage is 

E = Eoil + m cos pt) cos wi, (51) 

where m is the fractional modulation and Eq is the unmodulated ampli- 
tude. A trigonometric manipulation allows this to be written 

E = Eq cos oj^ + .^0 "2 [(oj + p)t] + jBo ^ cos [(co — iS)^]. ( 62 ) 

Thus, there is a signal at each sideband frequency, of amplitude Eq ~ ; or a 


Tn ^ 

power equal to JSTgFo -g- The incident local-oscillator power is 

Po = (53) 

Therefore, the signal power in one sideband may be written 

P. = Po~ (54) 

In the measurement of loss, the incident local-oscillator power can be 
measured directly with a thermistor, or a Wollaston wire, in a bolometer 

Sec. 2-17] 



bridge and, therefore, the equivalent signal power can be found, provided 
that the modulation percentage can be measured. In one form of the 
loss-measurement apparatus, the modulation is produced by an eccentric 
rotating disk made of carbon-coated Bakelite. The disk projects into 
the waveguide that supplies the local-oscillator power to the mixer. The 
disk is so proportioned that when it rotates at a constant speed, sinusoidal 
modulation of the amplitude of the local-oscillator signal at the crystal 
results. By rotating the disk slowly the modulation percentage can be 
measured. The value of the loss can be calculated from knowledge of Po 
and of the delivered output power as measured by the voltmeter. 

It is more common, however, to make the absolute calibration by what 
is known as the incremental method” for a few crystals which are then 
carefully preserved as standards. If these crystals are inserted in an 
apparatus using electronic amplitude modulation, the level of the local- 
oscillator power can be set to give the proper rectified crystal current, 
and the a-c output meter may be made to read correctly by setting 
the modulation level. The incremental d-c method may be regarded as 
an extrapolation of the modulation method to zero frequency. A sensi- 
tive current meter is so connected that it measures a small fractional 
change in the rectified current. This change in the rectified current is 
produced by a small, known, percentage change in the r-f power. If the 
change in current and the differential admittance of the crystal to DC are 
known, it is possible to calculate the output power that would be produced 
if the change in incident power were repeated sinusoidally. With a set of 
a few crystals calibrated as primary standards in this manner, any num- 
ber of crystals may be calibrated with a modulation-method apparatus 
for use as secondary standards at the many locations where modulation- 
method apparatus is used. The use of several standards is a protection 
against changes or damage in any one of them, since a change in a crystal 
will immediately be discovered because of disagreement with its calibra- 
tion when the instrument is adjusted to read correctly for the others. 

The loss, as measured in the test, is not exactly the loss that is used for 
the calculation of noise figures, except for some special cases, although 
the measured loss does not differ greatly from the loss appearing in the 
formula for the effective over-all noise figure of a receiver. The i-f load 
of the testing apparatus is fixed at a value equal to the i-f output admit- 
tance of an average crystal, and the power delivered to it — not the availa- 
ble i-f power — ^is measured. Under the conditions of measurement, the 
i-f output admittance of most crystals does not differ from the load admit- 
tance by an amount causing a loss, due to mismatch, of more than a few 
tenths of a decibel. Because the tuning of the crystal holder is fixed, 
crystals having signal admittances that differ from that of an average 
crystal are not tuned for minimum couytu’sion loss. Both of these 


factors tend to make the measured loss greater than that which could be 
obtained from a given crystal if both the i-f load admittance and the r-f 
tuning were adjusted to the optimum values. 

In the calibration of the apparatus, each sideband signal contributCH 
a component to the low-frequency output voltage. There is a phase 
relationship between the local-oscillator signal and each aidc^band su<ih 
that two modulation-frequency components at the output terminals of the 
crystal are in phase, because they arise from amplitude mo<lulation. 
The output voltage, therefore, is twice as great as it would f)c if there 
were only one signal having the same amplitude as one of the sided )antl 
signals. The loss, therefore, is computed assuming a signal amplitude 
twice that of a single sideband component, or a signal power twice that 
available in the two sideband signals. Ai^en the calibration is made 
in this way, the loss obtained is, except for the mismat(;h fac^tors, 
that which would result if conversion were made from a sirigh^ signal 
frequency to the intermediate frequency and if the r-f tuning at the signal 
frequency were identical with that at the image frc(iuoncy. As was 
shown in Sec. 2*10 the minimum loss that a convertor, roprosontahU^ ns a 
linear passive network, can possess under these conditions of tuning is 3 
db. This corresponds, in the modulation-method test, to convc^rsioxi of 
aU the available signal power in the two sideband signals into low-fre- 
quency power. A crystal for which this is true shows a 3-db loss ac.eorcl- 
ing to the calibration. Thus, a crystal that shows less than 3-db of loss 
in this apparatus, as do the welded-germanium units, delivers to the load 
resistor more power than is available in the input signal. Such a crysfail 
converter cannot be represented by a passive network, although it may 
still be linear, and the excess power must be derived from tlus local- 
oscillator wave, the bias supply, or both. 

In the specification tests of crystals there is no explicit m(^asur(*m(mt 
of the r-f admittance in a particular mount nor, except for one type* of 
crystal, of the i-f admittance. Because the loss measured is tile’s ratio of 
the equivalent available r-f power to the i-f power delivered to a loa<h 

not the ratio of this r-f power to the available i-f powei*, a limit is 
implicitly imposed on the range of admittances possible. Crystals having 
r-f or i-f admittances greatly different from the average must also possess a 
minimum conversion loss considerably below the specified limit t^) pass 
the loss test. Such crystals are not often found because the xippov limit 
on the loss is not very much greater than the average loss for crystals of a 
pven type. The fact that some reflection loss can occur at tlu^ singles 
frequency of the test does not allow much margin for frequcncy-scuisitivn 
behavior m a circuit that must operate in a wide band since reflection loss 
mcreases much more rapidly with the degree of mismatch after th(. first 
few decibels. If all of the mismatch loss were to occur on the output side 

Sx)C. 2 * 18 ] 



of the test converter, the possible scatter of the i-f admittances of many 
crystals, from this cause, combined with the effect of the image-frequency 
termination when a high-Q TR cavity is used, could pose a considerable 
problem to the designer of the i-f input circuit. Fortunately the i-f 
admittance seems to be fairly uniform from crystal to crystal under the 
conditions of the test. The loss caused by r-f mismatch is usually greater 
than that caused by i-f mismatch because the crystal cartridge represents 
a fairly sizable circuit element compared with the r-f wavelength and there- 
fore its r-f admittance is determined not only by the semiconductor and 
contact but by all of the discontinuities and dimensions of the cartridge. 
The i-f admittance is determined by these things only in so far as the r-f 
tuning affects the i-f admittance, which is very little because of the buffer- 
ing effect of the conversion loss. 

2*18. Noise-temperature Measurement. — Because the noise tem- 
perature is dependent upon frequency, it must be measured at the inter- 
mediate frequency to be used. For this reason the noise-temperature 
test equipment resembles a complete superheterodyne receiver much more 
closely than does the loss-test apparatus. As is also time for the appara- 
tus used to measure loss, the noise-temperature test equipment used at 
present is similar in principle for all microwave frequency ranges and 
differs primarily in having r-f circuits in a medium suitable to the particu- 
lar frequency. Thus the 3000-Mc/sec test sets for loss and noise-tem- 
perature measurements utilize principally small coaxial lines, and the 
crystal mounts are of a coaxial-line type. The test sets for 9280 Mc/sec 
and that for 25,000 Mc/sec, on the other hand, use appropriate wave- 
guide transmission lines and crystal mounts. 

A block diagram of the present form of the noise-temperature measure- 
ment apparatus is given in Fig. 2-32. The local-oscillator power enters 
the mixer through a filter cavity in order to minimize any spurious noise 
that might enter at either of the sensitive sideband frequencies. Attenu- 
ators are used on both sides of this filter, to ensure that the filter does not 
pull the oscillator frequency badly and to provide a matched line looking 
from the mixer back toward the local oscillator. The mixer is identical 
with the one used in the corresponding loss-measurement apparatus and 
the level of the incident local-oscillator power is set to be the same as 
in the loss apparatus. The input terminals of the i-f system can be 
switched from the output terminals of the mixer to a fixed dummy 
resistor for purposes of comparison. Between the output tcu’ininals of the 
mixer and the preamplifier is a lumped-constant circuit. This circuit 
transforms the input admittance of the i-f amplifier to a value ecpial to the 
complex conjugate of the output admittance of the mixer with an average 
crystal. In addition, the transformer has such characteristics that it is 
equivalent to a transmission line having a characteristic admittance equal 



[Sue. 2-18 

to the output admittance of the mixer with an average crystal and having a 
length equal to five-eighths of a wavelength at the intermediate frequency. 
The function of this circuit is to make the output noise of the receiver 

Fia. 2*32. — Block diagram of noise-temperature test apparatus. 

independent of the i-f admittance of the converter provided that it is 
real and has a noise temperature of unity. It is this circuit that makes 

the apparatus better suited to the 
measurement of noise temperature 
than an ordinary receiver. 

The output noise of an amplifier 
miay be regarded as arising primarily 
in the input stage of that amplifier 
and ahead of it, provided the input 
stage has sufficient gain to make the 
contribution to the total output noise 
from other stages negligible. In the 
apparatus under discussion, this con- 
dition is fulfilled, and if the only 
sources of noise are Johnson noise 
and noise arising in the tube, the cir- 

f,g. 2-33.-Eqmyaient oirouil of i-f input. W be represented by Fig. 2-33, 

amplifier. to an approximation sufficient for the 

present purposes. The grid of the 
tube is considered to have no admittance, and the noise generated in the 
tube is considered to be caused by the Johnson noise in the resistance Rn 

Sec. 2 - 18 ] 



at room temperature. The impedance Zinpat, or its reciprocal the input 
admittance, may be considered to be made up of the input admittance to 
the tube plus all admittances associated with the circuit connected to the 
input terminals of the amplifier. In the case in question, however, the 
input circuit includes the i-f admittance of the mixer, transformed by 
the special circuit between the mixer and the amplifier, and a conductance 
added from grid to ground. The total effective circuit may be repre- 
sented by the equivalent circuit shown in Fig. 2*34. The i-f admittance 
of the mixer is made real by an added susceptance and, for a crystal 
having the average i-f admittance, the transformation effect of the input 
circuit is such that the admittance at the output terminals of this circuit 
is equal to gfo. Thus the only elements appearing in the circuit of Fig. 
2-34 are the transformed i-f conductance g of the mixer with its associated 
noise-current generator i, the conductance ^o, made up of the input 

Fbu. 2*34. — Equivalent circuit of inixor, five-oighth-waveleiiKth lino and input uiniilifier. 

conductance of the tube and an added resistor with its associated noise- 
current generator h, and the equivalent noise-generating resistance for the 
tube with its associated noise-voltage generator e^. Each of the noise 
generators generates a noise current or voltage given by the thermal- 
agitation equation. The temperature of the i-f conductance of the mixer 
is t times room temperature, and the temperature of the other resistors is 
room temperature. 

The admittance of the output terminals of the transmission-line sec- 
tion may be obtained from the general transmission-line equation, which 
for a line having no loss is 

y _ Y + il'o tan pi 
^ ^ Fo +lYt tan pi 


where Pv&%r/\ for a distributed-parameter line, I is the line length and 
Yi is the admittance of the pair of terminals at one end when an admit- 
tance Ft is connected to those at the other end. In the present case, the 
admittance of the output terminals of the five-eighth-wavelength line is 

Y i ^ go 

g + jgo 
go + jg 

_ ^ ^ggo + Kgl - g^) 

( 66 ) 



I81SC. 2-18 

A. 116 W GQuivslcni/ circuit ncEy now be dr&wnj climiimtin^ tbc ti nnsniissioxi 
line as in Fig. 2-35. The magnitude of the noise current associated with 
the mixer is found from the fact that the noise powei available at the 
output terminals of the line is the same as that from the mixor, since the 

line is lossless. The mean square |io|® of the noise cumint induced in 
the input conductance go, in a narrow frequency band dv, is 

where |fi| * and |is| * have the values shown in Fig. 2-3.'>. ''|■'h('! noise voltage 

developed across the conductance go is 



( 68 ) 

The substitution, from Eq. (66), for Yi and the insertion of tlie valucH of 
|fip and l? 2 f* in terms of the conductances, rediuu^s I0(i. (58) to 

<*'[!+» ( 50 ) 

The mean square of the total input noise voltage is the sum of this voltages 
and the voltage arising from the noise resistance of tlie tube, or 

R"* = R* + = 4 fc 7 ’ ji [1 + (< - 1 ) J + A>„ j ( 00 ) 

where the ratio g/go has been written as a. The admittance transforma- 
tion of the input circuit is used to make the value of l/2(/i, (somparablts 
with that of R„, which, for a typical pentode 30-Mc/sec amplifier tubes, 
is about 2500 ohms 

Equation (60) describes the behavior of the tesst s(st. First, let hh 
suppose that the mixer has a noise temperature of unity, or that a rc'siator 

Sec. 2 - 18 ] 



at room temperature is substituted for the mixer at the input terminals of 
the coupling network. The term that depends on the conductance at 
the mixer terminals is then zero and the output noise power of the ampli- 
fier is independent of the conductance, provided that the noise examined 
is only that contained in a narrow frequency band, in which the trans- 
formation effect of the input circuit may be considered to be independent 
of frequency. In practice, a fairly narrow-band communications receiver 
is used, follo^ving a preamplifier. If the noise temperature of the mixer 
is not unity, the contribution is a maxi- 
mum if a is equal to unity. The contri- 
bution falls to 80 per cent of the maximum 
value, for the same value of if a is as 
much as a factor of 2 larger or smaller 
than unity. The increase in the output 
noise power from the amplifier with a 
crystal in the mixer, over that with the 
amplifier connected to the resistor, is 
proportional to ^ — 1. 

To calibrate the apparatus, the value 
of Rjyr could be measured and an output 
meter measuring noise power at the output 
terminals of the amplifier could be used. 

Instead, the apparatus is calibrated in 
such a manner that the value of 'Rn need 
not be kno^^Tl, and a meter having any law 
of response can be used at the output 
terminals of the amplifier. For this pui^ 
pose the noise diode is included in the 
circuit. This diode is a specially con- 
structed tube having a tungsten filament 
and short leads. The magnitude of the 
plate current of the diode is controlled by 
tlie temperature of tins filament, and a 
plate voltage sufficient to ensure saturar- 
tion curniiit f(jr all filament temperatures is applied, ''rhus, space- 
charge smoothing of the plate cun*ent is eliminated. Under theses 
conditions, the mcaix-s<iuare fluctuation components of the plate current, 
in a given frequency band, caused by the shot effect can bo calculated. 
Diodes that are used for the measurement of amplifier noise figures in 
this way are called temperature-limited diodes. Figure 2-36 shows a 
possible circuit for utilization of such a noise diode, where Hi is the i-f 
resistance of the mixer, equal to 1/gy and Ih is the resistor included for 
comparison purposes. 

To preamplifier 

Fio. 2*30. — PosHible circuit for 
utilization of tiuiHc diodo. 

C « bypass condenser (1000 
Aijufd at 30 Me /hoc). 

JiJi'C = int’eri!iodiat.o-freiciuency 

R — Hlainunt rhoostut. 


The noise diode may be considered as a noise generator with a 
mean-square noise current given by 

= 2el dv, (61) 

where I is the diode plate current, e is the electronic charge, and dv is the 
narrow band of frequencies being examined. If a resistor of conductance 
g is put into the mixer in place of the crystal, the mean-square thermal 
noise current in this resistor is 

KP = 4 dv. 

( 62 ) 

Therefore, the total mean-square noise current in the resistor is 

= 2el dp + 4kTg dp. (63) 

The resistor may be regarded as having a noise temperature t given by 

_W_.. . 2el 

li;p ikTg 

( 64 ) 

The standard temperature for purposes of such calibrations is taken as 
that which makes e/kT equal to 40 per volt and corresponds to a tem- 
perature just less than 20®C. Thus Eq. (64) becomes, 

< = 1 + 20 (65) 

The calibration of the noise-temperature measurement apparatus 
can thus be made by observing the output meter at several values of 

diode current with each of several 
resistors having different conduct- 
ances in place of crystals in the mixer. 
A typical calibration curve for an 
output meter giving readings pro- 
portional to power is shown in Fig. 
2*37, where the ordinate is the out- 
put-meter reading on a linear scale 
and the abscissa is the value of a on 
a logarithmic scale. 

In practice, the input transformer 
is a lumped-constant 7r-network. 
This circuit contains several variable 
condensers which must be tuned properly. When the condensers are 
correctly adjusted, the output-meter reading is independent of the con- 
ductance of the resistor placed in the mixer and is the same for the switch 
in the position that coimects the dummy resistor to the amplifier input 






t = 3 



0.5 0.75 

1 1.5 2 

a — ► 

I’la. 2-37. — Typical calibration curves 
for noise-temperature measurement set, 
with special input circuit. 

Sbc. 2*19] 



Unfortunately, this special input circuit does not work so well for the 
measurement of the noise temperature of a mixer that has a reflection 
of the image-frequency wave. It has been shown in Sec. 2-11 that such a 
reflection can give rise to a susceptance component in the i-f admittance 
of the mixer and such a component would upset the adjustment of the 
special input circuit. 

For mixers not having reflections at the image frequency, the noise- 
temperature measurement apparatus can be used to measure the i-f 
conductance as well as the noise temperature, by use of the temperature- 
limited diode. The diode plate current required to cause a given deflec- 
tion of the output meter is dependent on the magnitude of the conduct- 
ance at the output terminals of the mixer. A calibration can be obtained 
using resistors in the mixer. Then a measurement of the diode current 
needed to produce a given deflection on the meter with a crystal in the 
mixer constitutes a measurement of the i-f conductance of the mixer, 
if a square-law (power) meter is used. 

2-19. Bumout-test Apparatus. — ^To simulate the spike energy as a 
cause of crystal burnout, the apparatus used to test crystals for suscep- 
tibility to burnout subjects a crystal to a very short video pulse. The 
specifications for most types of crystals require all units to be subjected 
to a pulse of this sort before they are tested for loss and noise temperature. 
Crystals intended for use as low-level detectors, on the other hand, 
because they are not commonly used in systems having duplexers, are 
rarely subjected to spike’' pulses but are more frequently burned out 
through the presence of powerful radar transmitters in the immediate 
vicinity. Therefore, the pulses to which such a crystal might be sub- 
jected would more likely be ordinary radar pulses of about l-/isec 
duration. Less attention is paid to the burnout characteristics of such 
crystals, as a consequence. 

The apparatus developed by H. C. Torrey for the burnout test of 
mixer crystals consists of a short piece of coaxial line, connected at one 
end through a high resistance to a source of d-c voltage which charges the 
line to that d-c voltage. The crystal to be treated with a burnout 
pulse is insei-ted into a holder at the other end of the line but not put 
into contact with the center conductor. A sudden contact of the center 
conductor with the pin end of the crystal cartridge is made by dropping 
the center conductor a short distance onto the cartridge tip. This 
discharges the line in a single pulse through the crystal in a time approxi- 
mately equal to 2l/c where I is the length of the line and c is the velocity 
of light. The length of the line is made such that the pulse length is 
about 6 X 10"® sec. This time is so short that the burnout of the crystal 
depends upon the pulse energy and not upon the pulse power. The 
energy delivered to the crystal is just the energy stored in the capacitan<*.e 



[Sbo. 2-19 

of the line and this is easily calculable from the size of the line and the 
voltage. In this way a single pulse of uniform energy is delivered to each 
crystal before it is tested for loss and noise temperature. If it has 
been damaged appreciably by this pulse it will not pass these later tests 
and therefore no electrically fragile crystals should find their way into 
service. The correlation between burnout by a video pulse of this Irinrl 
and burnout by an actual r-f spike pulse has been found to be good and, 
therefore, this simple technique has been adopted in preference to an r-f 
burnout test. 

The value of the energy of the pulse used depends on the t 3 q)e of 
crystal being tested, as will be evident from the table at the end of this 
chapter. The lower-frequency units can, in general, stand a larger 
amount of energy before burnout occurs because the area of the contact 
of the cat whisker and the semiconductor is larger. Also there are 
available, in some frequency ranges, units that have high burnout 
resistance and high loss, as well as units that have the lowest possible 
loss and reduced burnout resistance. This is not obvious from the 
table, however, because some tsrpes with high loss and noise-temperature 
limits but with small burnout energy, or no specification of burnout at aU, 
are also listed. These are obsolete or obsolescent types having character- 
istics inferior to the more recently designed types designated by the 
same code number followed by a letter A, B, or C. The lower limits on 
the loss and noise temperature as well as the higher resistance to burnout 
of later t 3 q)es are illustrative of the progress made in the design of crystal 
units through the intensive research that was caniod on during the war. 

For the burnout test of crystals for which the burnout specification is 
given in terms of watts of pulse power in a l-^xsec pulse, a video pulse 
is also used, but the pulse is formed by a lumped-constant pulse-forming 
network which is discharged through the crystal unit. The pulse power 
delivered depends upon the admittance of the crystal unit at this level 
relative to the characteristic admittance of the network. The specifica- 
tion is the available power, but this power is dissipated by the crystal 
only if the crystal admittance matches that of the n(<twoi-k. The 
network admittance is chosen to be approximately eciiial to the crystal 
admittance at this power level and, therefore, the available power is not 
greatly different from the power actually delivered. 

The burnout specifications, like the other specifications, were deter- 
mined on the basis of tests of representative units, rather than being 
arbitrarily set up as minimum acceptable requirements. When research 
and improved manufacturing techniques indicated that it wjis easy to 
produce large numbers of crystals passing existing specifications without 
large “shrinkage,” a new set of specifications was written for a crystal 

Sec. 2-20] 



with a different type number, usually the old number with the added 
A or B. In this way the improvements found possible on a laboratory 
scale were quickly reflected in improved production types. The result 
is that the crystals available at present represent a great advance in 
both burnout and noise-figure characteristics relative to those available 
only on a laboratory scale in 1942. 

2-20. The D-c Crystal Checker. — ^The fact that there has been shown 
to be a reasonably good, if not perfect, correlation between the back 
resistance of crystal units of one type and their noise-figure character- 
istics has been mentioned earlier. The correlation is suflSlciently good to 
enable it to be said that a crystal of a particular type, passing more than a 
given back current at a given applied voltage, has probably been burned 
out. Perhaps more important is the fact that a unit passing less than 
this given current has almost certainly not been damaged severely. 
Without a check as simple as this, the service problem of microwave 
receivers under field conditions is 
rendered very difficult because there 
are miuiy possible sources of trouble 
other than the crystal. By this test 
the condition of the crystal can be 
(juickly determined; if the crystal is 
not at fault, another source of trouble 
may be investigated. In addition, a 
simple check makes possible periodic 
cheeks of operating crystals, allowing 
slow deterioration whicli might otherwise go unobserved to be watched 
and not allowed to proceed far enough for it to be detrimental to the 
p(^rforinance of the receiver. 

The limiting back current is known, for most of the available crystal 
units, for 1 volt of potential difference across the unit. A circuit 
diagram of a test unit that can be used to make this check is given in 
Fig. 2*38. A switch Si is used to turn the unit on and off, and a second 
switch S>i enables the single meter to be used, with the switch in the upper 
position, to adjust the potential across the test crystal to 1 volt. In 
the lower position the current through the crystal is read on the meter. 
The position in the circuit of the meter and of a resistance iZ, eciual to 
the meter resistance, are interchanged by the switch and, therefore, 
the current through the crystal is the same for either switch position. 

The value of tlie maximum back current at 1 volt for a relatively 
undamaged crystal, has been found to be dependent upon the crystal type 
only, and not upon the manufacturer, with one exception. For the 
1N20 crystal, it was found that the limit on the current was sufficiently 



[Sbc. 2-21 

different for crsrstals of the two manufacturers to warrant the use of a 
value for each. These values as well as the single ones for the other types, 
where known, are included in the table of speciffcations at the end of this 
chapter although they are not to be considered as specifications. It is 
possible that the safe curre/its will change for crystals produced in the 
future imder the same specifications, because there is nothing included in 
the specifications which relates directly to them. If it is desired to 
guard against any amount of deterioration no matter how small, it is 
perhaps best to keep a record of the back current at 1 volt for each 
er3rBtal, from the time it is first used and to be suspicious of the crystal if it 
shows any tendency to pass greater current with use. If a nximber of 
crystals show such a change upon insertion into an operating miYcr it ig 
to be taken as evidence that the TR switch or some other part of the 
circuit is allowing the crystal to be damaged by excessive electrical power. 
It is worth while to repeat the caution about static charge on the body 
when handling crystals, and the importance, therefore, of grounding the 
body to the apparatus through a path other than the crystal while it is 
being inserted or removed. Care should be taken to be sure that the 
apparatus is electrically grounded. A considerable a-c voltage with 
respect to ground may be present, especially if the apparatus contains a 
filter in the arC line. Many crystals have become damaged because of 
this, and it is advisable to take appropriate precautions to eliminate such a 

2-21. Specifications and Relevant Information on Available Types. — 
Table 2-1, to which reference has been made many times throughout the 
chapter, follows. The table gives the specifications as well as other 
information on the various types of crystals currently available for use as 
detectors and mixers in the microwave region. There are two general 
types of cartridge, and the one applying to each crystal is indicated in 
the first column of the table as A or B. These symbols refer, respectively, 
to cartridges like those shown in Figs. 2-39 and 2-40. An outline of the 
physical dimensions, with tolerances, is given for each of these cartridges. 
This is an important factor in the design of mixer and detector mounts 
since considerable nuisance is encountered if the mount is designed on 
the basis of the dimensions of only a few units. The largo ceramic unit 
was originally used at 3000 Me/ sec in a coaxial-line mount where it is 
small compared with the dimensions of a convenient line, or compared 
with the wavelength. Later, crystals for the 3-cm region were built in 
the same cartridge. In this region the cartridge is still not large com- 
pared with the dimensions of conventional rectangular waveguides in 
which it is mounted. For 25,000 Mc/sec, this unit is excessively large 
compared with either the waveguide dimensions or the largest single-mode 



coaxial liae at that frequency. Consequently, the coaxial type of cart- 
ridge of Fig. 2-40 was developed by Bell Telephone Laboratories. It has 
much smaller internal dimensions in accordance with the use at shorter 
wavelengths. There has been some use of this same cartridge for units 
recently designed for lower frequencies because of the shie lding of the 
sensitive contact from stray radiation and because of the amnllAr physical 
dimensions. There is, in addition, less probability of damage through 

I'lij. — Coramic crystal cartridge. 

Note 1. Eccentricity ijctwocu tip and base shall not exceed 0.0075. 

Note 2. Metal parts shall bo silver-plated min. 20 mg/in* or gold-plated min. 10 mg/in*. 

Note 3, Used for types; 1N21, 1N21A, 1N21B, 1N23, 1N23A, 1N23B, 1N27, 1N28, 

This drawing is taken from BuSliips Dwg. RE 38A192. 

static discliarge from the body, since the mount is so constructed that 
contact to the outside cylinder will almost certainly occur before the 
discharge (^an go through the crystal. 

The table gives, next, the use for which the crystal is intended, either 
as a low-level “video'’ detector or as a mixer unit. The next column is 
the fre(iuen(‘,y of the specification tests. For mixer crystals, the local- 
oscillator power level to which the loss and noise specifications refer is 
given, then the minimum rectified current, measured by a meter of 100- 
ohms resistance, and then the maximum acceptable values of loss and 
noise temperature. For some crystals the i-f resistance under the con- 
ditions of operation in the test set is specified, and, if so, it is given in 


[Seo. 2-21 

the next column. For most crystals this is not specified and, for these, the 
value of the load resistance used in the loss test is indicated by the 

- 0.003 

U- 0 , 218 ^ 

r I j 

1 1 

(T) 0.032 

\ Note 7 

Alternate shape for end 
of pin 0.012 " radius @ 

Fig. 2*40. — Shielded coaxial cryatal c.artridKO. 

Note 1. Finisli: plate with 0.00002 tin over niokol fliiali or O.OOOl pold or .silvor. 

Note 2. OD dimension applies to length indicated. 

Note 3. Axis of center conductor not to deviate from axis of (t<)ndu<'t.(>r reftMTod 
to its outside diameter more than 0.004. 

Note 4. The polarity is such that sleeve is positive when (uirrcml. IIowh in tlu' jnins 
(forward) direction. 

Note 5. Crimp permissible but adjacent surface shall not bo bulged h<\von<l nmxiniuin 

Note 6. This edge to be sharp and free from buri-s. 

Note 7. Slight chamfer permitted. 

Type test following: F, H, notes 1 and 4, 6, and 7. 

Design test following: 5, D, J, K, 0. 

Production test all other dimensions and notes. 

This drawing is taken from BuShips Dwg. RE 38A208. 

numbers accompanied by TL for “test load.” The “vidcM)” output 
resistance is given in this same colunm for low-level (l('t(‘et<)rs un<l tlui 
next column gives the figure of merit/. Following this comes a column 



limit at 1 
volt, ma 








0.11 WE 
0.23 SEP 

noise fig. 
5-db am- 
plifier, db 

50 cq r-I |>! rjH CO lO * CO • 

1— IrHrHT— rH • tH> . 



0.3 erg 

2.0 erg 

2.0 erg 

0.3 erg 

1.0 erg 

0.3 erg 

6 . 5 watt 

0 . 1 erg 

5 . 0 erg 

0.3 erg 

0 . 02 watt 

fig. of 




I-f or 

300 TL 
400 TL 
400 TL 
300 TL 
300 TL 
300 TL 
200 TL 
300 TL 





Max. noise 




1 .5 










>0 lO »o o o »o o »o o • 

oofc^50»ooo65do6 00 • • 
























« r S 

8 g"" 

H £ UH 















iJaJSjoQjSajaJ cJ -g % 

.a .a .a .a .a .a .a .a .a s ^ g § 
<\ ^ ^ 

p p p 

Type of 

<< ..ti -tt pq -tJ pq 

Type of 














1N32 A Detector! 3295 | ... 5000- 100 0.36 watt 

I 20,000 design 



[Sec. 2'21 

giving the pulse energy of the burnout test, or the peak power where 
appropriate. For some types the number in this column is labeled 
“design.” This means that the test is made only on a few sample units 
and the number then represents only the approximate power that imits of 
this type may be expected to withstand. Next comes a column of over-all 
noise figures for a receiver using mixer crystals that just pass both 
the loss and noise-temperature tests and having an r-f amplifier with a 
noise figure of 6 db. This is by no means to be considered as the best 
noise figure possible with that type of crystal since some units show 
losses as much as 2db less than the maximum values, and noise temper- 
atures effectively equal to unity. Moreover, the 5-db i-f-amplifier noise 
figure is by no means the lowest obtainable; values as low as 1.5 db have 
been obtained with some recent circuits. A combination of such an 
amplifier with the best 1N21B crystal at 3000 Mc/sec would give an 
over-all noise figure of about 6.5 db. At 10,000 Mc/sec such noise 
figures are also possible with the 1N23B and at 25,000 Mc/sec over-all 
noise figures of about 7.5 db have been observed. Finally a column 
of maximum back current at one volt, as discussed in Sec. 2-20, is given. 
For the 1N26 crystal, two numbers are given, one followed by SEP 
standing for Sylvania Electronic Products Company, and the other by 
WE for Western Electric Company, the two manufacturers produemg 
these units at present. 

The region of frequencies near the test frequency is not the only region 
in which a unit may be used. In general, however, the units would be 
expected to show greater conversion loss at higher frequencies, although 
an increase of frequency of 10 or 20 per cent would not produce a serious 
effect. The use of the units at lower frequencies mil certainly not 
result in a greater loss and can, in fact, result in slightly lower loss, 
especially for the high-bumout units having relatively high loss at the high 
frequency. Because the units are not tested at these lower freciuencies, 
however, there is no implicit control over the r-f admittaiKio cliaractor- 
istics. Therefore, the admittances of the various units would not neces- 
sarily be very uniform or have any relationship to that of units designed 
for this frequency. 

In addition to the development of microwave crystal rrictifiers, there 
has been considerable work done on units for special purposes at lower 
frequencies. As an example, there are units for use as diodes in such 
applications as second detectors in superheterodyne receivers and as d-c 
restorers in special circuits where their characteristics and small j)hysical 
size make them more desirable than ordinary diodes. This subject is not 
within the scope of this volume and for details of the propertic^s of such 
crystals the reader is referred to Vol. 15 of this series. 



Some of the devices which have come to be known as “mixers'' 
or “converters" in the microwave range perform the function of con- 
verting a received signal at a microwave frequency into one at a lower 
intermediate frequency, in addition to several other secondary functions 
which are special requirements of their application in microwave radar. 
Some of these additional functions will be described in later chapters; the 
purpose of the present chapter is to discuss in some detail the considera- 
tions involved in the design of crystal mixers that perform, in conjunction 
with the local oscillator, the single function of frequency conversion of a 
microwave signal. 

There are many possible variations in the design of a mixer for a 
particular frequency region and it will not be possible to give details of 
each of the types in current use. The examples cited will usually be those 
of designs evolved at the Radiation Laboratory and these cannot be 
considered as the only possible ones. It has been the attempt, in design- 
ing these circuits, to make a single unit as a basic design for each frequency 
range for which a particular type of transmission medium is used in order 
to avoid the much greater labor involved in designing a particular 
unit for each piece of equipment and to allow as wide a tuning range in the 
equipment as possible. 

The problem of the design of crystal-mixer circuits cannot be treated 
with any degree of finality because the details of the mixer best suited to a 
particular task depend, to a larger degree than do other microwave 
circuits, on things outside of the control of the designer. The design 
must, for instance, be influenced primarily by the physical and electrical 
characteristic.s of the available crystal units. Since there is reason to 
believe that iinprovc^ments may lead to units considerably different from 
those available^ at present, one may expect that mixer designs for such 
future units will be (jorrespondingly changed. I'he frequency ranges 
covered by dc^signs for radar use are by no means the only important ones; 
hence, for many purpcjses, the details of these designs are not of general 
interest. Unlike the inindy microwave circuits, the mixer cannot be 
adapted from one frcupiency Imnd to another by a simple scaling process 
because th(^ crystal unit, which plays such a dominating role in the 
operation of the circuit, will neither have the same charac.tcu’istics in 
the scaled circuit nor be scalable in itself. The detaiUjd dc^signs that will 




be given as examples, therefore, will probably be of less general interest 
than would warrant the inclusion of a large number of them. More 
emphasis will be put on the general methods and ideas that have been used 
in the design of the mixers, in the belief that analogous courses may be 
taken for frequency bands and uses other than those encountered in the 
Radiation Laboratory experience. 

3«1. The Basic Mixer Circuit. — One of the simplest possible circuits 
that a mixer can have is that of Fig. 3-1. In this circuit, the antenna or 
signal generator is represented by the current generator delivering a 
current 4 and having an internal admittance Ya, and the local oscillator 
by the current generator producing a current and having an internal 
admittance These two generators are connected in parallel through 

I-f load 

the crystal unit to the i-f output terminals which, in use, would be 
connected to the input circuit of the i-f amplifier. In the diagram, 
a load circuit presenting an i-f load admittance F^g, and a low-rcsistance 
d-c circuit are shown. As shown in Chap. 2, the r-f tuning of the mixer 
should be set with a matched i-f load admittance in place. 

The functions of the various parts of the circuit arc the following. 
The magnitude of the local-oscillator current establishes, in conjunction 
with the i-f load admittance, the input admittance of the mixer to the 
small signal from the signal generator. The r-f choke on the one side 
of the crystal unit and the i-f choke on the other provide a low-rcsistance 
path to the rectified current. The crystal, therefore, docs not become 
appreciably biased by the rectification of the local-oscillator signal. In 
order that the r-f voltages of both the signal and the local oscillator may 
be impressed primarily across the crystal unit, an r-f bypass condenser is 
provided across the i-f output terminals. For maximum power delivered 
to the i-f load, this capacitance must either have a negligible susccptance 

Sec. 3-1] 



at the intermediate frequency or be resonated with an opposite suscep- 
tance component in the i-f load admittance. 

The basic mixer is most easily understood when the conversion loss of 
the crystal is large. Under this condition the r-f and i-f aspects of the 
mixer circuit may be considered separately because the effect of the load 

Signal generator Local oscillator 

I Crystal 

R-f choke 

** R-f bypass 

R-f admittance of 
i-f load circuit 

Fig. 3*5. — Simplifiod representation of r-f aspect of high-loss mixer. 

admittance on one pair of terminals is negligible at the other pair. Thus, 
both the signal admittance and the i-f admittance are dependent only 
on the crystal unit and the amount of its local-oscillator drive. The 
r-f circuit and the i-f circuit may be considered separately as illustrated in 
Figs. 3-2 and 3*3, respectively. The i-f load circuit influences the r-f 
conditions only in so far as, in combination with the r-f bypass circuit, it 
develops an r-f voltage drop. Similarly, the r-f circuit influences the i-f 
admittance only in so far as, in combination 
with the i-f bypass circuit, it produces an i-f 
voltage drop and so detracts from the i-f volt- 
age appearing at the output terminals. 

The best performance of a mixer of this 
kind, as a frequency converter, is obtained 
when the signal power is caused to develop 
the maximum possible voltage across the crys- 
tal unit. This condition is satisfied if the 
signal-generator admittance is made eciual to 
the complex conjugate of the input admit- 
tance to the crystal mixer, and if no r-f signal power is dissipated 
in the admittance of the local oscillator or of the i-f load. To siitisfy 
this last condition, the local-oscillator admittaiuu^ must be zero and 
the admittance of the bypass circuit must be infinite. In practice, it 
is necessary only to make the local-oscillator admittance so small, and 
the admittance of the r-f bypass circuit so large, compare<i with the signal 
admittance of the crystal, that the amount of signal power that is dissi- 
pated in them is a negligible fraction of the available signal power. The 

Fia. 3-3. — I-f flrouit of Iiigh- 
loaa inixor. 



Hppign of the r-f portion of a high-loss mixer, therefore, reduces to three 
parts which are: 

1. Design of a signal-coupling mechanism to match all available 
signal power into the crystal unit. 

2. Design of a local-oscillator-coupling mechanism that has negligible 
effect on the signal admittance. 

3. Design of an r-f bypass circuit for the i-f output terminals that will 
not allow the r-f power to couple to the i-f load circ-uit. 

Usually, the aignal generator to which the mixer should he matched is 
the antenna of the receiving system. The antenna, in turn, is so made 
that its radiation admittance terminates a transmission line in its char- 
acteristic admittance. The desirable signal-input circuit, therefore, 
would be a transmission line of the same type, with the mi,ver so arranged 
that the crystal provides a matched load to this transmission line, 
whether it be a coaxial line or a waveguide. In addition, thoi-c must be 
terminals to supply local-oscillator power, across which only a negligible 
part of the available signal power appears, and there must he terminals 
for the i-f output voltage. Experimentally, the admittancii of a high-loss 
crystal unit for the small signal in the presence of the local-oscillator 
drive, is found to be approximately the same as for a signal of the same 
magnitude as the local-oscillator signal in the absence of tlui local- 
oscillator drive. It is possible, therefore, to begin the task of mixer 
design by designing a crystal mormt that contains only tlm (uystal unit 
and the i-f output circuit without incorporating the LO c.ouj)ling circuit. 
The mount is so adjusted that a signal at the lo(‘.al-<)S(!illat(»r level is 
matched into the crystal unit. Moderate corrections may he reciuired, 
for low-loss crystals, to obtain minimum, conversion loss from tlu^ crystal 
mount, when finally operated as a mker. By such a proccMlurc^ the task is 
made strai^tforward even if there is no previous information as to the 
input admittance of a particular crystal in the desired mount and fre- 
quency range. 

3-2. The Design of a Crystal Mount.— The physical form of tho 
mount for the crystals in ceramic cartridges is ari)ii,rary. 'I’lie only 
features that all such mounts have in common are contacting (‘hunents for 
both ends of the cartridge unit. The unit can he made to he a part of a 
coaxi^ Ime, or it can be mounted in a waveguides or in a re^sonator. 
Nothing m the basic mixer circuit requires or excliules fnuiuency sehictiv- 
rty in the r-f circuit, except for the separation of i-f, d-c, and r-f voltages. 

ence, any form of the mount will operate equally well at th<( fniciuencies 
for which the fflgna,l-input-line admittance matches the antenna-lino 
admittance. Historically, resonant mixers were at first (lonsidcred 
necessary but only because admittance transformation was obtained 
through their use. The more recent designs of mixers use nonresonant 

Sec. 3*2] 



coaxial-line and waveguide mounts for the crystal. Any r-f preselection, 
or separation of signal- and image-frequency terminals, has been accom- 
plished through the use of a resonant TR cavity or of a resonator added 
between the crystal mount and the input terminals. 

The crystal is mounted in either waveguide or coaxial line, in such 
a way that it does not represent a large mismatch as a termination of the 
line when r-f power at the local-oscillator level is incident in the line. 
If, with an experimental crystal mount, a large mismatch is found, a 
measurement of the apparent admittance of the crystal allows a correcting 
change to be made. If the mismatch is not large, tuning elements, such 
as sliding-screw tuners, stub tuners, plungers, and sliding quarter-wave- 
length transformers, may be added to cause the crystal to match the line. 
An investigation of the admittance characteristics of a large number of 
representative, crystals will show whether all units can, by means of the 
tuning elements, be made to match the line. 

The tuning of most recently designed crystal mounts has been fixed. 
Fixed tuning is possible because the ciystal units are made to pass the 
conversion-loss test in a mixer having fixed tuning. As a consequence, 
it should be expected that the crystal units should behave identically 
in the receiver mixer, provided its tuning is fi.\ed at the same point as that 
of the test mixer. A crystal mount identical with the one used in the 
mixer of the crystal test set would be properly tuned only for the fre- 
quency of operation of the test set and with a circuit in which the image- 
frequency wave is not reflected to the mixer. If fixed timing is desired at 
a single frequency of operation different from that of the tost set, it may be 
achieved through fixing the tuning adjustments of the mixer on the basis 
of best results with a large number of representative crystals. On the 
other hand, if the mixer is required to operate over a wide band of fre- 
quencies, the same tuning may not be adequate, and tuning elements 
might be required for a mixer intended for use in a broad band if not for 
use at a single frequency. 

If fixed tuning over as wide a frequency range as possible is desired, 
the crystal mount itself should come as close as possible to a matched 
termination of the input line. Any additional transformer is then 
required to give only a small transformation efiect and it is, conseciuently, 
relatively insensitive to frcciuency. As a gc^neral rule, the larger the 
transformation effect of a simple microwave admittance transformer, 
the more sensitive to frequency it becomes. This ciTec.t is obvious for a 
transformer employing a quarter-wavelength section of transmission line. 
There is, of course, in addition to the frcciuency-sensitivc character of the 
admittance-matching circuit, frequency dependence of the admittance of 
the crystal unit itself, although it is difficult to separate the two effects. 
It is often possible to combine a mismatched crystal and mount with a 



matching circuit in such a way that the frequency sensitivity of the two 
tend to compensate each other. The match can then be held over a 
wider band than would be possible for a mount that was perfectly matched 
at the center frequency of the band. With a mount that is perfectly 
matched at a given frequency, it is often possible to add a resonant 
circuit that, at the resonant frequency, has a transformation effect of 
unity, and hence no effect, but that compensates for the frequency 
dependence of the crystal admittance at other frequencies. 

It shotild be noted here that the only difference between a crystal 
mount designed for a mixer and one designed for a low-level detector is 
in the level of the input signal for which the admittance measurements 
are made. For a low-level detector, these measurements must be made 
at a signal level of 1 /xw or less, and the resultant admittance of a partic- 
ular mount is consequently different from that at the local-oscillator 

(a) Coaxial-lino crystal mount for 10-cm band. (&) Crystal mount for 3-om band. 

Fig, 3*4. — Cartridge-crystal mount, 

level of signal. The design of a low-level detector, however, is completed 
when a satisfactory mount has been achieved for the small signal level, 
because there is no need for a local-oscillator circuit, and the eflEiciency is 
so small that the load admittance does not affect the r-f match. A mount 
for use in a mixer must ultimately be checked as a mixer with the local- 
oscillator injection operating and with an appropriate i-f load admit- 
tance and d-c circuit as well as any preselecting resonant circuits in place, 
because all of these things have some effect on the resultant small-signal 
admittance. The preliminary admittance measurements with the single 
signal at local-oscillator level must be made with a low-resistance path 
for the rectified ciystal current, in order to avoid the generation of a 
backward bias voltage across the crystal. That the level of power 
actually being dissipated in the crystal unit is about the same as the 
recommended local-oscillator level can be assured by use of a milliam- 
meter in this d-c circuit. The incident power may be appropriately 
increased if the mount has a large reflection loss. 

3-3. Crystal Mounts for the 3-cm and the 10-cm Bands — Two 
crystal mounts commonly used for crystals in ceramic cartridges are 

Sec. 3 * 3 ] 



illustrated in Fig. 3*4a and b. The first is a coaxial-line mount used in 
the range from 4000 to 2500 Mc/sec and the second is a waveguide mount, 
in rectangular waveguide 1 by -a- in. OD by 50-mil wall, used in the range 
from 9600 to 8500 Mc/sec. The diagrams are only symbolic of the r-f 
characteristics of the mount, for they show no provision for bringing 

out the low-frequency voltage or rectified current. The mounts in 
which this provision is included are shown in Figs. 3’5 and 3*6. In the 
coaxial-line mount it is necessary to have a path of low d-c resistance to 
and of low i-f impedance between the center and the outer conductors of 
the coaxial line, to correspond to the r-f choke of Fig. 3*1. Provision 
for this return path has not shown because its nature is dependent 


upon the rest of the mixer. In some mixers the return path is provided 
by a loop that excites the coaxial line. If there is no such loop a quarter- 
wavelength side stub, which is also useful for supporting the center 
conductor, can provide this d-c return The diameter and characteristic 
admittance of the coaxial line shown in Fig. 34a arc such that the line 
fits over the cartridge unit conveniently, and connects without serious 
mismatch to the standard type-JV coaxial-line fittings used for low-level 
cables The crystal admittance resulting with a line of this size and no 
transformers is not greatly different, at 3000 Mc/sec, from the line 

Fig. 3*6. — Waveguide crystal mount for 3-oin blind. 

admittance. If this had not been true, a line havinji; some other clmr- 
acteristic admittance would have been preferable. Inhere an^ s(^v(*nil 
parameters in the mount for 9000 Mc/sec which can be (*.hos(^n to nuik(‘ 
the average representative crystal unit terminate the line in its (‘.harac.ttir- 
istic admittance. The position of the crystal unit, both relative to th<‘. 
center of the broad dimension of the waveguide, and axially along the 
narrow dimension, may be adjusted to control the resultant admittance. 
The distance along the waveguide from the axis of the crystal (partridge to 
the short circuit at the back end of the unit is also such a parameter. 
None of these parameters afford strictly independent adjustment of the 
resultant admittance. It is found, however, that if the admittance 
determined from the measurement of the standing-v^^uv(‘ ratio in the 

Sejc. 3«3] 



waveguide leading to the crystal is referred to the plane of the axis of 
the crystal cartridge, the adjustment of the length of waveguide beyond 
the crystal unit results essentially in variation of the susceptance com- 
ponent of the crystal admittance. At a length about equal to one half of 
the wavelength in the waveguide, the crystal unit is completely short- 
circuited by the reflected short circuit at the end of the waveguide and 
the reflection coeflBicient of the mount is unity. The crystal current 
becomes zero for this length, since no voltage is built up across the 
crystal barrier. 

It is not advisable to achieve a match with the waveguide crystal 
mount by using a length, between the short circuit and the crystal, near 
to a half wavelength, since the susceptance introduced by the back part 
of the waveguide is then large. The susceptance varies very rapidly 
with frequency and the crystal mount is correspondingly sensitive to 
frequency. The adjustment of the length of waveguide beyond the 
crystal is the design parameter most easily determined, because a sliding 
short-circuiting plunger in the waveguide can be used. If the suscep- 
tance component of the crystal admittance can be tuned out only with a 
length nearly equal to the length for which the crystal is short-circuited, 
it is preferable to change the mount in some way to allow the use of a 
length more nearly equal to one-quarter wavelength in the waveguide. 
It has been found that a change of the position of the crystal along the 
line through its axis also causes a change primarily in the susceptance 
component of the crystal admittance. The position may be so chosen 
that the crystal mount has only a small susceptance with a shoii; circuit a 
quarter-wavelength beyond the crystal. The effect of moving the crystal 
cartridge across the waveguide in the plane perpendicular to the wave- 
guide axis is primarily to vary the conductance component of the 
admittance. This variation occurs because the voltage (integrated field 
intensity) between the top and bottom of the waveguide is a sinusoidal 
function of the crosswise position, with a maximum at the center and 
zeros at each side. Correspondingly, the presence of the crystal unit 
has the greatest effect on the electric field when the crystal is at the center, 
and has less influence when the crystal is moved toward the side of 
the waveguide. The conductance of the crystal mount thus falls from 
a maximum value with the crystal at the center to a minimum with the 
crystal at either side. 

In this way it has been found possible to make a (srystal mount for the 
9000-Mc/sec frequency region which has an admittance, with a crystal 
representing an average with respect to the admittance scatter of all 
units, equal to the characteristic admittance of the waveguide at the 
level of signal equal to the optimum local -oscillator drive. The crystal 
units used in this region are the IN23, 1N23A, and 1N23B types, all of 



which show approximately the same spread of admittance since they are 
tested, in production, in identical mixers. 

It is more difficult to make the desired adjustments of admittance in 
the coaxial-line mount than in the waveguide mount. Although the 
wavelengths for which the coaxial-line mount is used are longer compared 
with the dimensions of the crystal, the crystal cannot be treated as a 
lumped-circuit element because it appears as part of the center conductor 
of the coaxial line. It is largely fortuitous that a coaxial line of a con- 
venient size and characteristic admittance can be used as a crystal mount 
in the 3000-Mc/sec region, since the early crystal mixers used for pro- 
duction testing were not at all similar to the present mount. An r-f 
impedance of 40 to 60 ohms in the coaxial-line mount must be derived 
from the effect of the barrier capacitance and from the transforming 
effects of the various parts of the cartridge. At a frequency as low as the 
intermediate frequency, the crystal unit would exhibit an impedance to a 
small signal of the same order as the i-f output impedance. The i-f 
output impedance is usually several hundred ohms, and a crystal having 
an r-f impedance this high would be difficult to match to a 50-ohm line. 
At 9000 Mc/sec, the aspect of the crystal in the waveguide mount is 
such that it can be considered approximately as a lumped admittance 
connected across the waveguide. 

3*4, The Filter in the I-f Output Lead. — The r-f bypass at the low- 
frequency (i-f, video-, or audio-frequency or direct-current) output 
terminals is, in neither of the mounts under discussion, completely 
accomplished through the use of a simple lumped capacitance, as would 
be inferred from the basic equivalent circuit. The function of this 
circuit may be considered as twofold: (1) it provides a path of high r-f 
admittance, compared with that of the crystal, with the result that the 
loading of the transmission line is the same as if the ciystal were short- 
circuited to the line at this point ; (2) it prevents leakage of any appreci- 
able amount of r-f power — primarily local-oscillator power, since its 
level is so much higher than that of the signal — ^into the input circuit of 
the i-f amplifier. The requirements set on the effectiveness of the filter 
circuit by the first of these functions might at first appear to be much 
smaller than those of the second. Since the r-f admittance of the input 
circuit of the i-f amplifier to which the mixer is to be connected is arbi- 
trary, the effectiveness of the filter circuit could be reduced considerably 
if a resonance were to occur when the two were connected together. 
Consequently, to avoid such effects, a large capacitance or a more 
complex filter is required. It is felt that the circuit of the filter type 
is more effective, per unit of capacitance introduced at the i-f terminals, 
than the lumped capacitance, in a restricted band of radio frequencies. 
Since most applications of microwave mixers have been in receivers 

Sec. 3-4] 



having wide i-f pass bands, the i-f capacitance of the mixer is important 
in determining the maximum pass band of the input circuit of the ampli- 
fier. The lower this capacitance, the wider the input circuit can be made. 

The operation of the filter is similar to that of many filters used as 
joints for r-f lines. In the filter used with the 3000-Mc/sec crystal 
mount, a spring-metal contact is used to make connection to the large 
end of the crystal cartridge. The spring contact is mounted by a rivet 
on the base of a cylindrical metal cup that has an open end toward the 
i-f outlet. The center conductor of the i-f line extends into this cup and 
terminates at the solid end of it. The inside of the cup, which is filled 
with a polystyrene dielectric, is thus a concentric line short-circuited 
at one end and a quarter wavelength long, in the dielectric. The open 
end, therefore, has a vanishingly small admittance. A wave progressing 
along the coaxial line formed by the outside conductor and the outer part 
of this cup induces currents in the outer wall of the cup, and, in order 
for the wave to travel out the i-f line beyond the open end of the cup, 
the current of the inner conductor must pass through the sroall admit- 
tance of the cup. Thus, unless the r-f admittance of the i-f output line 
seen at the open end of the cup is also veiy small, the major part of the 
voltage drop at this point appears across the end of the cup or choke. 
The r-f current in the i-f output line is kept small, because of the small 
admittance of the choke and, therefore, the r-f power getting into the 
i-f circuit is kept small. In order that the choke system be equivalent 
to an r-f bypass at the base of the crystal, the length of the coaxial line 
formed by the outer conductor and the outside surface of the cup or 
choke is made equivalent to a cjuartcr wavelength. Because this line is 
terminated in an admittancie at least as small as the admittance of the 
choke, a large r-f admittance results between the base of the crystal 
and the outer conductor of the crystal mount. 

In the waveguide crystal mount used at 9000 Mc/sec, the r-f filter 
on the i-f output lead operates in much the same way, except that the 
addition of a small lumped capacitance just beyond the quarter-wave- 
length choke gives further assurance that the r-f admittance of the i-f 
output lino is large at this point. The choke occurs, for mechanical 
reasons, in the outer conductor of the coaxial i-f output line. The point 
at which the choke appears in series with the output line, however, is a 
quarter wavelength along the lino from the point at which the large 
bypass admittance is desired, in this case between the pin end of the 
crystal cartridge and the bottom wall of the waveguide. The reasons 
governing the choice of a (urcuit containing both a distributed-parameter 
filter and a lumped capacitance are largely mechanical, since the center 
conductor of the output line must be supported. The capacitance of 
the lumped condenser is not large compared with the distributed capaci- 



tance of the output lead. The total i-f capacitance, conseque 
could not be reduced greatly by elimination of the condenser, an 
inclusion makes the tolerances on the dimensions of the choke filte: 
rigid. The filter action is also less frequency-sensitive than it woxi 
without the condenser. 

A choke joint or a filter of this kind is most effective over a 
frequency range if the characteristic impedance of the coaxial 
for min g the choke is as high as possible, and if that of the line formin, 
quarter-wavelength transformer is as low as possible. At the frequ 
for which the effective lengths of the choke and of the transforme; 
exactly one-quarter wavelength the filter is perfect, since the imped 
at the open end of the choke is infinite. The impedance betweer 
crystal and the outer conductor of the crystal mount is therefore ze: 
dissipation in the filter itself is neglected. At a frequency differing : 
this by a small amount, however, the impedance at the open end o: 
choke is a large reactance. The larger this reactance is, compared 
the characteristic impedance of the transformer section and comp 
Avith the r-f impedance of the i-f line, the smaller are the leakage c 
power into the i-f circuit and the impedance between the end of 
crystal and the outer conductor of the crystal mount. The reactan* 
the choke is proportional to the characteristic impedance of the 
forming the choke. 

In the coaxial-line mount, therefore, the ratio of the diameters oj 
outer and inner conductors of the line forming the choke is made relati 
large and the ratio of the diameters of the outer and inner conduc 
of the line forming the quarter-wavelength transformer is made sr 
The maximum usable line size for the 9000-Mc/sec crystal mour 
one in which the mean circumference of the inner and outer conducto 
nearly 3 cm, for other modes than the principal mode may be propag 
in a larger line. The characteristic impedance of the choke, therei 
cannot be made very high and, consequently, the addition of the 
denser across the i-f line helps to reduce the leakage of r-f power 
wide band of frequencies. 

The only effect of the filter on the i-f characteristics of the crj 
mount is to produce a capacitance, provided the section is short comp 
with a quarter wavelength at the intermediate frequency. Since 
is true, the i-f capacitance is just the static capacitance between 
inner and outer conductors of the output line. In the coaxial cry 
mount the capacitance is contributed primarily by the quarter-wj 
length section of the cup and increases with decreasing character! 
impedance of this transformer. The desire for a small i-f capacita 
in the mixer sets the limit on the diameter ratio of this section of line, 
the bandwidth of the choke is therefore restricted. Each of the cry 


nxoiuits illustrated has an i-f capacitance of about 11 The effective- 
ness of the chokes in eli min ating leakage power can be measured by 
inserting the crystal moimt, with a crystal in place, between a signal 
generator at the local-oscillator level and an output indicator such as a 
spectrum analyzer. By comparison of the leakage power with the power 
available directly from the signal generator, the insertion loss of the 
crystal and filter is found, and if it is also known that the crystal mount 
approximately matches the signal-generator impedance, it may be 
concluded that the incident power is almost completely delivered to the 
crystal, if the insertion loss is large. Just how large this insertion loss 
must be is difficult to determine, but with the mounts described it is 
greater than 30 db in the frequency bands for which they are intended 
and with a matched coaxial-hne r-f load at the i-f output connectors. 
Two cups differing in length but other- 
\vise identical have been used in filters 
in the coaxial-line mount. One of 
these cups has an outside length of f 
in. and gives maximum insertion loss 
at a wavelength of about 10.7 cm. 

The other has a length of i in. and 
gives a maximum effect at about 8.8 
cm. The longer cup is used between 
9.5 and 12 cm and the shorter one 
between 7.5 and 9.5 cm. A cuiwe 
typical of the ratio of the power inci- 
dent on the crystal to that leaking into 
an r-f load matching the line admittance on the i-f output connector is 
shown in Fig. 3*7. The ordinate is the power ratio in decibels and the 
abscissa is the wavelength expressed in units of the resonant wavelength 
of the choke. 

3-6. Tunable Crystal Moxmts . — K technique commonly used in the 
9000-Mc/sec band to make the crystal mount tunable, after it has been 
designed to give an approximate match, is illustrated in Fig. 3-8. The 
position of the', short circuit behind the crystal is made adjustable through 
the use of a plunger of the choke type and, thus, the effective susceptance 
of the c.rystal is controlled. Two tuning screws, one situated three 
eighths of a wav(dength and the other five eighths of a wavelength ahead 
of the center line of the crystal are provided. These screws allow adjust- 
ment primarily of the conductance component of the admittance referred 
to the center lin<^ of the crystal. The admittance of the crystal itself 
is, of course, not changed by the insertion of the screw but the admittance 
at a point an integral number of half wavelengths toward the generator 
from the center line of the crystal is changed, primarily in the conductance 

Fig. 3 * 7 . — li-f leakage of choke vs. 



component, for a small insertion. That this is true can be seen with the 
aid of an admittance diagram, with the knowledge that the effect of the 
tuning screw is to add a capacitive susceptance in shunt at the center line 
of the screw. Thus, if the crystal were matched to the waveguide, a 
small insertion of the screw three eighths of a wavelength from the 
crystal would make the crystal appear to have a conductance larger than 
unity. A small insertion of the other screw would decrease the apparent 
crystal conductance. Only one screw is used at a time, the choice of 
screw depending upon whether the apparent conductance must be 
increased or decreased. The adjustments of the screw and of the plunger 

are completely independent only for very small insertions of either 
screw. A large range of tuning is available from the adjustment of the 
plunger and one screw. If, however, the crystal is severely mismatched 
to the waveguide with no insertion of the screw and with the plunger set a 
quarter wavelength from the crystal, some dissipative loss may result 
in the tuning screw and in the plunger when they are used to match the 
crystal mount to the waveguide. In addition, the frequency sensitivity 
of the resulting admittance is large. Both the plunger and the tuning 
screws have choke systems similar to that of the i-f output lead, to 
prevent leakage and to decrease contact losses. Only a small current 
flows at the points where metal-to-metal contact occurs and the design 
considerations of these choke systems are similar to those of the filter. 
The best operation over a wide band is obtained for a high characteristic 
impedance in the line forming the choke and a low characteristic imped- 
ance in the quarter-wavelength transformer section. Attempts have been 

Sbg. 3 * 5 ] 



made to design plungers and screws that actually make contact and thus 
have not the constructional complication of the chokes, but no designs 
have been found which are as satisfactory under service conditions as 
those using chokes. This is particularly true of the tuning screws, if 
smooth continuous operation is desired. For experimental purposes, an 
ordinary screw can be put into a threaded hole in the top wall of the 
waveguide and looked by forcing a nut on the screw above the waveguide 
against the top wall. This simple screw^ however, cannot be adjusted 
continuously because it depends for contact on the clamping effect of the 

The only tunable crystal mounts of the coaxial-line variety that have 
been built have used standard coaxial-line tuning elements. One of these 
mounts contained, in the line ahead of the crystal, a pair of polystyrene 
cylinders filling the space between the inner and outer conductors of the 
coaxial line. The length of each of the cylinders was one quarter of the 
wavelength in the dielectric. The cylinders could be slid together along 
the line, and the spacing between them could be varied from zero to 
one-half wavelength. This device constitutes what has been called a 
double slug” tuner. Since the characteristic admittance of the section 
of line in which one of these dielectric cylinders appears is \/Fo times the 
normal line admittance, where ko is the dielectric constant of the cylinder 
material, it is apparent from an admittance chart that the maximum 
transformation effect occurs for a spacing between the cylinders of 
one-quarter wavelength. An admittance corresponding to a voltage 
standing-wave ratio equal to kl can be made to match the line. With 
the cylinders together or one-half wavelength apart, there is no trans- 
formation effect because a half-wavelength section of transmission line is a 
one-to-one transformer. Therefore, any transformation from unity to 
kl can be achieved. The phase angle can be controlled by the position 
of the pair relative to the crystal mount and, in this way, any voltage 
standing-wave ratio loss than kl can be matched out. 

Under special conditions, tuners having tuning ranges smaller than 
this have been used. This is true, for instance, for some crystal mounts 
for low-level detectors, where the same basic mount was used but where 
measurements of the admittance of the mount with large numbers of 
representative crystals showed that it was possible to bring all of the 
crystals sufficiently close to a match over the required 10 per cent band of 
frequencies with a singU^ sliding metallic slug. Such devices can be 
designed only ])y ineasuremcmt of the admittances to be matched to the 
line. Thus, if the required tuning range is known, a satisfactory tuning 
device can be found. 

One frequent source of trouble in crystal mounts that have had 
several changes of crystals is in the contact to the pin end of the crystal 



cartridge. Experience has shown that contacting fingers such as those 
shown in Fig. 3-5 have been the most satisfactory ones tried, especially 
when made of tempered beryllium copper. Similar contacting fingers 
have consequently been used in all mounts used for crystals in ceramic 
cartridges, in both the 3-cm and the 10-cm regions. Saw cuts 0.020 
in. by 0.375 in. were found to give a good compromise between large 
contact pressure and ability to withstand reasonable deflections without 
becoming bent through distortion beyond the elastic limit. Although 
the specifications of the crystal cartridge call for a rounded end on the 
pin, it has been found well worth while to include an internal bevel in 
the end of the contacting fingers to assist in the centering of the pin 
during insertion of a crystal in the mount. 

3-6. Admittance Scatter in a Mount of Fixed Tuning. — Because of the 
desire to make crystal mixers that are fixed in tuning, a large part of the 
design of the crystal mount is concerned with finding the best fixed 
adjustment for all crystal units that are expected to be used. This can 
be done by measurement of the admittances of very large numbers of 
crystal units representative of those which will be used in the mount, and 
by adjustment of the mount in such a way that the scatter of admit- 
tances, when plotted on a Smith admittance chart, covers an area centered 
at the characteristic admittance of the input line. In order to reduce the 
labor involved in making these measurements, a special procedure of 
crystal selection has been used. 

To ensure that the crystals to be used in the tests were representative 
of those to be encountered in service, crystals were chosen at random from 
stocks of the various types made by each of the several manufacturers. 
A total of one or two hundred crystals was used and the r-f admittance 
of each was measured in a crystal mount that was found to be reasonably 
well matched for a few randomly chosen crystals. Then these admit- 
tances were plotted as points on an admttance chart and from this the 
area and, therefore, the proper timing of the mount could be determined. 
Once this had been done it was not considered necessary to use the large 
nuinber of crystals in further work for this frequency band, since the 
entire admittance region could be represented by a few crystals having 
admittances on the boundary of the region and by one or two having 
admittances in the center of the region. It was found that 10 per cent 
changes in frequency or small changes in the mount affected the admit- 
tances of all the crystal units in about the same way. Their positions 
on the margins or in the center of the admittance spread were conse- 
quently preserved, even though the whole region was transformed to 
another part of the admittance chart. These representative crystals were 
preserved for use in tests of many kinds and such tests could then be 
regarded as showing the results to be obtained with crystals of almost any 

Sbo. 3-6] 



characteristics to be encountered among production units. Since the 
crystal units of one type number but different sufiSxed letters (1N21, 
1N21A, 1N21B) were usually used interchangeably, the origiaal selection 
included samples of all such types. There was, usually, less difference 
found among the different types than among crystals of the same types 
but from different manufacturers. Almost all of the design considera- 
tions of the fixed-tuned mixer are dependent upon this admittance 

Fio. 3-0. — Irnpodiinco hcmiKku- of 1N21A and 1N21B crystals in a coaxial-line mount at 

8.6 cm. 

Spread. The borderline crystals, therefore, were used in many tests 
besides the admittance measurement of the mixer. 

In Fig. 3*9 a typical spread of impedances for a coaxial-line 8.5-cra 
mount is shown with the borderline crystals selected as representative 
marked with circles. An admittance scatter at 3.3 cm in a mount 
resembling the standard one of Fig. 3*G is shown in Fig. 3.10. The 
outlines of the spread at 3.13 cm and at 3.53 cm are also shown, with 
the positions for the representative crystals at these wavelengths indi- 
cated by the circles on these contours. It will be obseiwed that the 
admittance change occurs almost entirely in the susceptance component 
aiid i^ in the direction which would be found if the crystal unit were 



representable as a shunt-resonant circuit connected across the waveguide 
at the position of the centerline of the crystal unit. 

Fig. 3*10. — Admittance scatter of 1N23, 1N23A, and 1N23B crystals at 3.13, 3.33, and 

3.53 cm. 

3-7. Local-oscillator Coupling Mechanisms. — As discussed in Sec. 31, 
the prime requirement of the method of coupling the local-oscillator signal 
to the crystal is that it does not cause a significant loss of recicivod signal 

power. In the equivalent mixer cir- 
cuit of Fig. 3*1 this was shown to 
require that the shunt admittance of 
the local-oscillator circuit measured 
in the mixer be small compared with 
the signal-generator and crystal 
admittances. For this to be possi- 
ble the power available from the local 
oscillator must be much larger than that which is actually transmitted to 
the crystal, because a large mismatch exists between the local oscillator 
and the mixer circuit. In Fig. 3*11, an equivalent circuit illustrating this 
rituation is given. The signal-generator admittance has been assumed 

Fig. 3*11. — Simplified equivalent circuit 
of a mixer. 

Seo. 3-7] 



to be pure teal and the crystal admittance gc has also been assumed to be 
pure real. If the local-oscillator admittance were zero, Tna,ximuTn power 
would be delivered to the crystal if g, were equal to g^. The simplest 
case to analyze is the one in which these admittances are the same at the 
signal and local-oscillator frequencies, and the mixer may therefore be 
considered to have a low Q. It is easily shown that the fraction of the 
signal-generator power that is delivered to the crystal when the local- 
oscillator coupling is added is 

T„ = 4^^A(g. + ffc + giY + b?], (D 

where gi and bi are the real and imaginary parts of the admittance of the 
local-oscillator circuit as measured at a point in the mixer liue. Cor- 
respondingly, the fraction of the available local-oscillator power which is 
delivered to the crystal is 

Tie — 4giflre/[(g, -h fife + flfl)* + bf]. (2) 

The fraction of the signal which is lost through the introduction of the 
local-oscillator circuit is 

which is 

T.i = 

4g.g. _ m 

(gs + goY 

m _ 4flf,g„(2„.gt -b 2g^i + gj + bf) 

^ " (g. + g.)n(g. + gc + giY + b?] 



Under the condition that g, = go this is 

To, = H- g? + bf 

(g. + go + gi)* + b? 


If the admittance of the local-oscillator circuit is small compared with gf,, 
the last two terms in the numerator may be neglected and the equation 
then is identical with Eq. (2) . This means that, for small local-oscillator 
coupling, the fraction of signal power which is lost because of the presence 
of the local-oscillator circuit is approximately equal to the fraction of the 
available local-oscillator power which is delivered to the crystal. If, 
therefore, it is desircxl that not more than 5 per cent of the sipal 
power be lost because of the local-oscillator circuit, 20 times the required 
local-oscillator drive for the crystal must be available from the local- 
oscillator circuit in the mixer. Since the local oscillator is often coupled 
through a circuit that has loss, for reasons that will be discussed in a later 
section, the local oscillator must be capable of delivering more power than 
this, and the design of the LO coupling circuit is not so simple as it might 
appear. Even if the local oscillator can deliver 100 times as inuch power 
as is required to drive the crystal, precautions against deterioration in 



mixer noise figure caused by interaction between the signal circuit and the 
local-oscillator circuit must be taken. 

An additional complication to the problem of the design of an LO cou- 
pling circuit is that the output power available from different os(iillator 
tubes of the same type can differ by large factors. Usually, the tube 
specifications set a lower limit to this output power but many tubes can 
be found which give two or three times as much power as this minimum. 
When this variation is added to the variation encountered as tlie tube its 
tuned through a wide band and to the variation in the amount of coupling' 
with crystal admittance, the total variation of local-oscillator power 
delivered to the crystal under all conditions of operation is more than can 
be tolerated if the mixer is to operate within a few tenths of a deciihel of 
optimum noise figure. It has therefore been considered necessary to 
have an adjustable local-osciUator coupling in order that the optimum 
local-oscillator power at the nodxer crystal may always be ol)taine(l. In 
so-called fijced-tuned mixers this adjustment is retained and is the only 
adjustment required for operation with any crystal of the proper type 
and with any local-oscillator tube in the specified band of frequencies. 
If the amount of local-oscillator power delivered to the crystal is varied 
by adjustment of the coupling circuit, the values of gi and bi in lOcps. (2) 
and (5) vary. Equation (5) applies if the tuning of the (uystal mount is 
optimum in the absence of the LO coupling circuit. For a fixed amount of 
coupling, the tuning of the crystal mount could be mvh that th(^ sus- 
ceptance component of the admittance of the local oscillator was can(‘.oled 
by a susceptance of equal magnitude and opposite sign in tlu^ (‘.rystal 
admittance. The conductance of the crystal mount c.ould be made 
equal to + gi to obtain maximum signal power in th(‘. pr(\s(mc.('. of tlu^ 
LO coupling circuit. If this were done the percentage of tlu^ available 
local-oscillator power delivered to the crystal would be exaedly (Mpial to 
the percentage of available signal power lost because of the prescuuu'. of the 
local-oscillator circuit. A practical LO coupling circuit must Ix^ a<ljust- 
able and the correction in the tu n ing of the crystal mount cannot Ix^ made. 
The signal loss is therefore increased because of reflection. 

The simplest LO coupling circuits are inefficient because^ th(^ ad<le<l 
susceptance h is large compared with the conductance gi. Because^ of 
this, the signal power lost by reflection is larger at a given elTcMri.ivt^ (cou- 
pling than it would be if the admittance of the local oscjillator w(^r(i k(q)t 
real at all adjustments. 

Most of the mixer circuits that have been designed for radur service* 
have been operated with a TR cavity preceding the mixer in tlie signal 
line. ^ The most commonly used TR cavities are highly rcsotiant, ami the 
circuit representing the local-oscillator coupling is not the same ii,.s f.iiat for 
the signal. Many TR cavities have sufficiently high Q’s t.) he l,r<>ated ns 

Sec. 3-7] 



completely reflecting circuits at the local-oscillator frequency, when 
resonant at the signal frequency. If such a TR cavity is used the local- 
oscillator injection can be made at a point in the mixer line, between the 
TR cavity and the crystal, where the admittance of the line terminated 
by the cavity is almost zero. In a waveguide, for instance, the TR cavity 
appears as though it were a short circuit, at frequencies sufficiently 
removed from resonance and, therefore, the admittance of the line ter- 
minated by the TR cavity is very small at a point a quarter of a wave- 
guide wavelength toward the crystal. If the local-oscillator signal is 
injected at such a point, as a signal from a generator having a small admit- 
tance, the fraction of the available local-oscillator power delivered to the 
crystal is 

rp - 

“ (gc + gj)® + ^ 

( 6 ) 

Therefore, the effective coupling is greater by a factor of about four 
than the coupling obtained without the TR cavity for the same gi and 
bi, if g, is equal to g^ and if gi and h are small compared with g,. This can 
be explained in another way by supposing the local oscillator to excite a 
wave that travels in both directions from the injection point in the mixer 
line. Without the TR cavity the wave that travels toward the signal- 
input end of the mixer is lost, but with the TR cavity present, it is 
reflected. The choice of the injection point at a quarter of a wavelength 
from the position of the short circuit that is equivalent to the TR cavity 
at the local-oscillator frequency corresponds to a position such that the 
wave reflected by the TR cavity has the same phase as that traveling 
toward the crystal. Hence the total amplitude of the wave traveling 
toward the crystal is twice as great as it would be without the TR cavity. 
Therefore, four times as much local-oscillator power arrives at the crystal. 

Besides giving greater local-oscillator coupling for a given amount of 
interaction of the local-oscillator circuit and the signal circuit, the addi- 
tion of the TR cavity causes another change in the operation of the mixer 
•circuit. For a small coupling without the TR cavity, the power delivered 
to the crystal by the local-oscillator circuit is a stationary function of the 
crystal admittance when the crystal is matched to the signal generator. 
Only the ordinary reflection losses are involved when the crystal a,dmit- 
tance is different from this value, because the reflected local-oscillator 
wave is almost entirely dissipated in the signal-generator admittance. 
When the TR cavity is used, however, the local -oscillator power delivered 
to the crystal becomes very strongly dependent on the crystal admittance. 
If gi is small compai'cd with ge, the power delivered by the local oscillator 
to the crystal is propoi'tional to 1 /(/<:• This niciuires that the available 
range of adjustment of the local-oscillator coupling be much greater than 



without the TR cavity, to allow the optimum local-oscillator power to be 
delivered to cr3rstals of all admittances occurring in the representative 
scatter. Two crsrstals having conductances differing by a factor of four 
would require adjustment of the local-osciUator coupling by almost 
this factor for the same power delivered to the crystal. It is, therefore, 
even less satisfactory to use a £xed LO coupling adjustment in a miYsr 
having a resonant TR cavity in the signal line than in one having a com- 
pletely nonselective circuit. Thus, althou^ in the crystal test sets a 
fixed LO coupling adjustment is used with a single oscillator tube at a 
single frequency of operation, it is impractical to attempt fixed adjustment 
in a mixer for use with a TR cavity. 

3*8. Capadtive Local-oscillator Coupling in Coaxial-line Mixers. — 
At 10 cm, where the small coaxial-line crystal mount is used, the common 
LO coupling circuit is a small capacitive probe, terminating a coaxial line 

Input line To crystal 

Fig. 3-12. — Adjustable local-oscillator 
coupler for a coaxial-line mixer. 

that is coupled to the local oscillator 
and projecting into the main coaxial 
line of the crystal mount. One 
form of such a coupling mechanism 
is shown in Fig. 3-12. This device 
allows adjustment of the probe in- 
sertion without movement of the 
local-oscillator line, which is a con- 
venience when frequent adjust- 
ments must be made. It is simpler 
to construct a coupling probe that 
is adjusted by sliding or screwing 
the whole coaxial line of the local- 
oscillator circuit in a sleeve 

mounted on the mixer line. An 

adjustment of this type has been used in mixers such as those used 

for crystal testing. In the mixer for testing, however, the level of the 
local-oscillator signal is changed only if the local oscillator is changed; 
otherwise the coupling adjustment is locked. It is important that good 
electrical contact be made through the screw threads or in tlie sliding 
section; therefore, a clamping arrangement or a lock nut is usually pro- 
vided. In a circuit like that shown in Fig. 3-12, the center conductor of 
the side arm ending in the probe makes a sliding contact with the center 
conductor of the LO input line, and the spring used for this contact has 
been somewhat troublesome. The spring, which has slotted “fingers” 
at each end to contact the rod sliding in it, must be carefully soldered so 
that the temper is not lost. Beryllium copper is a very satisfactory 
material for a spring of this sort because it can be hardened after the 
soldering is done. The length of the stub line supporting the center 

Sbc. 3*81 



conductor changes with adjustment of the probe insertion, but, since 
the probe represents a severe mismatch at the end of the line, the small 
reflection due to this stub is not serious. 

In order that the local-oscillator tube will oscillate with this probe as its 
load, it is necessary to arrange that the actual load admittance presented to 
the oscillator is compatible with the characteristics of the oscillator. One 
way in which this can be assured is to use such a length of line, between 
the oscillator and the probe, that the admittance presented to the oscil- 
lator at the other end of the line lightly loads the oscillator. If this is done 
and if the system is to be continuoudy tunable, the line must be so short 
that the phase length of the line does not change appreciably in the 
required tuning range. If the equivalent electrical length of the line 
does change by a quarter wavelength, the loading will be very heavy and 
the oscillator may not operate satisfactorily. Another way of avoiding 
load admittances which upset the operation of the oscillator tube is to use 
lossy cable to couple the oscillator to the mixer circuit, to attenuate the 
wave reflected from the probe. 

Thus, the range of admittances that 
arc presented to the tube as the 
phase length of the line changes 
with frequency is reduced and can 
be made small enough for the tube 
to operate satisfactorily. In view 
of the difficulty in getting sufficient 
local-oscillator drive without suffer- 
ing from signal loss, however, this 
can be done only if a large excess of 
power is available from the tube. 

For operation with a 2K28 tube and 
with a nonresonant mixer circuit, 6 db of attenuation can be used but 
there is very little extra coupling available, with the most powerful tubes, 
before interaction and signal loss become serious. 

A third way in which the load admittance of tlie local oscillator can be 
maintained at a reasonable value over a wide frequency range and with a 
long coupling line is illustrated in Fig. 3T3. Here a ‘‘resistor disk” 
which is a disk of Bakelite, coated with a carbon resistance material, and 
having silvered inside and outside rings for contacts, is put into the line. 
The resistance between the contact rings of this disk is the characteristic 
impedance of the coaxial line, 50 ohms in the local-oscillator circuit. The 
disk would be a reflectionloss termination for the line if its r-f character- 
istics were su(‘.h that it loaded the line with a resistance alone and if the 
admittanc'.e of the remainder of the line beyond the disk were zero. In 
practice there is a capacitive siisceptance due to the large dielectric con- 

Fio. 3*13. — ^Local-OHcillator coupler with 
rosistor-disk termination. 



stant of theBakelite base of the resistor disk, as well as the conductance, in 
shunt with line in the plane of the disk. The line may still be terminated 
by the disk, however, if it is placed in a position where the admittance of 
the line beyond it contains an inductive susceptance of the same magni- 
tude as the capacitive susceptance of the disk. Thus, the susceptance 
is resonated out and the load terminating the local-oscillator line has the 
conductance of the disk plus a small conductance caused by the small 
power transfer from the probe to the crystal-mixer line. The small 
capacitive susceptance of the probe and of the disk makes the resonant line 
length between the probe and the disk somewhat less than a half wave- 
length. A resistor disk has been provided in all coaxial-line mixeis of 
recent design to secure a reasonable load admittance for the local oscil- 
lator. This circuit is less wasteful of local-oscillator power than that 
using attenuating cable. The local-oscillator power available at the 
mixer is reduced by a factor of approximately 2 (it cannot be specified 
exactly because the oscillator is not a linear generator) but the line may be 
made very nearly matched. In the design of Fig. 3T3, the admittance 
of the line between the probe and the disk varies as the probe is adjusted. 
Consequently, the termination is also varied but the voltage standing- 
wave ratio is less than about two for all adjustments and over a plus 
or minus 10 per cent band in the region of 10 cm. Since the half-wave- 
length section of line beyond the disk is frequency-dependent, the 
bandwidth is correspondingly restricted. The useful bandwidth is 
determined by the excursion in admittance that can be tolerated by the 
oscillator tube. At 10 cm, where the capacitive susceptances of the 
probe and the disk are small, the admittance of tlic tei*mination is 
given approximately by 

Yt « Yo(l +itan^"y 

For small deviations from Xo, the resonant wavelength, the admittance is 
Yt ^ F(j j^l ~ 

From this the wavelengths on each side of Xo for which a given reflection 
coeflB-cient would be encountered can be calculated to estimate tlui usable 
bandwidth. For a voltage standing-wave ratio of 1.5, a reflection 
coefficient of absolute value 0.2 is required and the wavelengths for 
which this standing-wave ratio would be encountered are approximately 
Xo i 0.12Xo; hence, a bandwidth of plus or minus 12 per cent is possible 
with that tolerance in the standing-wave ratio. 

3.9. A Local-oscillator Coupling Circuit for Coaxial-line Mixers. — 
A very useful LO coupling circuit for coaxial-line mixers in which rigid 

Sec. 3-9] 



connections between the local oscillator and the mixer can be used is 
illustrated in Fig. 3-14. This circuit has some very great advantages 
over the capacitive-probe coupling circuit, especially if the LO output 
power is low. A direct connection is made between the mixer line and a 
coaxial line terminating in the pickup loop of the local oscillator. This 
line includes a movable section, with spring contacts in both the inner 
and outer conductors, so that the orientation of the loop with respect 
to the mixer can be adjusted and then clamped. For decoupling of the 
signal from the local oscillator, the resonant nature of the local-oscillator 
cavity is utilized. Because the local oscillator is tuned to a frequency 
differing from the signal frequency by the intermediate frequency, the 
local-oscillator cavity is not resonant 
at the signal frequency. A signal 
wave traveling down the local-oscil- 
lator line is therefore almost com- 
pletely reflected at the loop. So far 
as the signal frequency is concerned, 
the local-oscillator line is just a stub, 
and if it is made the right length it 
has practically no effect on the 
signal-frequency wave. The line is 
approximately of nonrefiecting 
length if the distance from the inside 
wall of the outer conductor of the 
mixer line to the end of the loop, 
including the perimeter of the loop, 
is an odd number of free-space quar- 
ter wavelengths. A single quarter 
wavelength would allow a reflection in the mixer line producing a 
voltage standing-wave ratio of less than 1.2 over a band of plus or minus 
10 per cent. 

The load presented to the local-oscillator line is nearly matched in this 
circuit. If powesr enters the mixer through a resonant cavity or a TJR 
cavity, the reflection of power at the local-oscillator frequency by this 
cavity must reinforce the local-oscillator wave traveling toward the 
crystal, just as it does in the capacitive-probe coupling cheuit. In other 
words, the scic-tion of line from the junction to the cavity must behave as a 
quarter-waveUuigth stub. The local-oscillator line is terminated by 
the crystal and is usually not seriously mismatched. 

If no resonant cavity is used, the mixer line is matched in both 
directions — at one end by the crystal and at the other by the antenna. 
The local -oscillator line might be made to have a characteristic admit- 
tance twice that of the mixer line and the standing-wave ratio in it might 

From To crystal 

input line mount 

Fig. 3*14. — Adjustable local-oscillator 
coupling circuit in which the resonance of 
the LO cavity is utilized for decoupling 
the LO circuit from tho signal. 



therefore be nearly unity. With a line only one-quarter wavelength long, 
however, this would not be necessary, since the load presented to the 
oscillator would change very slowly with frequency, although the voltage 
standing-wave ratio would be about two. 

The coupling of the local oscillator is adjusted by rotating the loop 
in the local-oscillator cavity. A range in coupling from zero to full 
coupling is achieved for a rotation of 90® from a position with the loop in 
the plane of the magnetic field to a position perpendicular to the magnetic 
field in the local-oscillator cavity. The great advantage of this circuit 
is that full coupling between the local oscillator and crystal can be 
obtained without danger of interaction with the signal circuit of the 
mixer, provided the intermediate frequency is high compared with 
vo/Ql, where Ql is the loaded Q of the osciQator cavity and pq is the radio 
frequency. Thus the local-oscillator power required is reduced from 25 
or more milliwatts to about one milliwatt. For mixers that have no 
resonant cavity in the input circuit, this coupling circuit is especially 
useful, since the capacitive-probe type does require large oscillator power 
in that case. It is also simpler tha n the probe coupling circuit when 
it is necessary to include a resistor disk for maintaining a matched 
local-oscillator line. 

340. Local-oscillator Coupling in Waveguide Mixers. — In wave- 
guide mixers for the wavelength region for which the previously discussed 
waveguide crystal mount is used, the LO coupling problem is similar 
to the coaxial-line problem, but is complicated by the fact that the local 
oscillators commonly used. (723A/B, 2K25, and 2K45) have coaxial-line 
output leads of a very special type. These output lines end in a small 
dielectric-encased antenna which is supposed to couple as a probe to the 
waveguide. In many early mixers that were built and put into service, 
this antenna was used to couple local-oscillator power directly to the 
mixer by allowing the antenna to project by an adjustable amount into 
the mixer waveguide at an appropriate place. The adjustment of the 
probe insertion was made by using a tube mount, on the broad side of 
the rectangular waveguide of the crystal mount and mixer, which could 
be adjusted in spacing from the waveguide. In this way the antenna 
at the end of the coaxial line projecting from the base of the tube was 
made to extend into the waveguide by a variable amount. Local- 
oscillator coupling of this kind has recently been completely abandoned 
because it does not afford a controllable load admittance at the oscillator 
tube. Only enough coupling is needed to ensure that a few per cent of the 
available local-oscillator power is coupled into the waveguide of the 
mixer, in accordance with the preceding discussion. Decoupling of 
the signal from the local-oscillator circuit is thus assured but, because 
only a small percentage of the available local-oscillator power is coupled 

Sec. 3-10] 



out of the LO output line into the waveguide, a large standing-wave ratio 
can exist in the output line. Since the line has a physical length of about 
3 in., it is electrically about 2.5 wavelengths long and the electrical length 
is strongly dependent on the oscillator wavelength. Thus, the load 
admittance presented by this output line to the oscillator cavity varies 
rapidly with wavelength. Wavelengths are found, consequently, at 
which the oscillator operates very erratically or not at all. If the same 

Insulating material 

Fid. 3-16. — ToBt mount for a 2K26. 

tube is used in a circuit in which the tube is operated into a reasonable 
lulmittance, it can be timed smoothly through these same wavelength 
regions. The fault, therefore, can definitely be attributed to the load 

With a given tube, a coupling circuit of this type operates satisfac- 
torily at some wavelengths, and its simplicity would recon^end it for a 
simple mixer even if the tuning range were restricted. It is found, how- 
ever, that the wavelengths of satisfactory operation are not the same for 



various tubes of the same type, because the electrical length of the 
output coupling line is not controlled. Thus, many other w so satis- 
factory tubes must be discarded in favor of others which have output 
lines of different electrical lengths,, when the tube is coupled to the mixer 
in this way. 

As a result of the difficulties of this kind which have been encoimtered, 
a definite circuit for coupling these oscillators to a waveguide has been 
made a part of the oscillator specifications. With this circuit, almost the 
full power available from the oscillator is coupled to a matc.hed load 
terminating the waveguide. Continuous tuning of the oscillator over its 
specified tuning range results if the waveguide has a nonreflecting 
termination. To be certain that this is true, the specifications require 
that each tube be tested or this property in the specified mount, and 
the tube must pass a test for minimum output power in the same moimt. 

A mixer that is to use one of these tubes as a local oscillator must 
present to the tube the same admittance as is presented to it in this test 
moimt if continuous tuning and reasonable output power are to be asstired. 
Thus, the tube must be mounted with the same probe position, as regards 
insertion and position laterally and longitudinally on the waveguide, and 
the waveguide must be approximately matched at its load end. Figure 
3-15 shows the important features of the test mount or the 2K25 tube. 
In some mixers to be described in later sections, the tube mount is not 
identical with this in all details because it could not easily bo madc^ so. 
In these mixers, extensive tests with large numbers of tubes \v(U‘o made 
to ensure that the mixers would operate satisfactorily over the reciuirc^d 
tuning range with the great majority of tubes. 

3-11. A Directional Coupler for Coupling the Local Oscillator to the 
Mixer . — K simple mixer for the 3-cm region can be coupled to the loc'-al 
oscillator in a variety of ways. In view of the requirement that the local 
oscillator operate into a special circuit it seems advisable that, two 
separate waveguides be used, one for the mixer proper, and one for the 
local oscillator and load circuit, mth a coupling circuit botwc^cui these 
waveguides which transmits the required amount of local-osc.illatoi* power 
from the local-oscillator waveguide into the mixer wavc^guich'i. This 
suggests that a “directional coupler” would be the ideal circ.uit to us(\ 
A directional coupler is a special network having four pairs of tcu-minals 
and having the property that power sent into one pair of t('i*minals is 
almost completely transmitted to a matched load on the opposite*, pair. 
A small fraction of the power is coupled into a third pair of t(U’minals 
and none to the fourth. The symmetry is such that if the diroc-tion of 
power flow is reversed the small amount of power is available from tlu^ 
fourth pair of terminals and none from the third. At microwiive fre- 
quencies, the directional coupler can be realized by a strii(d.ui*e such as 

Sbc. 3-11] 



that shown in Fig. 3-16. The details of the design of circuits of this 
kind will be found in Vol. 11, Chap. 14, but a qualitative description 
of the operation of the directional coupler is given here to facilitate the 
discussion of its use as an LO coupling circuit. 

Two waveguides running parallel to one another are coupled together 
by two channels of the same width as the waveguides but of amnlloT- 
narrow dimension and one-quarter wavelength long. These filifttinola are 
spaced one-quarter wavelength apart, as indicated in Fig. 3-16. Both of 
these dimensions are only equivalent electrical dimensions because 
corrections must be made to compensate for end effects. The operation 
as a directional coupler depends on the fact that each ntm-nnAl excites 
a wave in one waveguide when a wave is sent through the other. The 
excited wave propagates only in the same direction as the exciting wave 
because destructive interference takes place between the two components 
traveling in the other direction. As a wave that is sent into the structure 

Kill. 3*16. — Wavoguido directional coupler. 

at A passes the channels, a small percentage of the energy is sent down 
each channel. If the coupling is small, the amplitudes of the waves in the 
two channels are almost the same. Each of these waves excites waves 
propagating in both directions in the lower waveguide but the com- 
ponent traveling toward C arriving at 3 by way of the path through 
2 and 4 is opposite in phase to that excited by way of the path through 
I and 3 because it has traveled one-half wavelength farther. Hence, the 
two waves traveling toward C interfere destructively. The two waves 
traveling toward D are in phase with each other and, consequently, a 
wave of twice the amplitude, or four times the power, of that which would 
result with a single channel is propagated toward D. Because of the 
symmetry of the device it can be seen that a vrave sent into B propagates 
primarily to A with a small part sent to C and none to D, and similarly 
for the other branches. 

The amount of power that is coupled from the one waveguide to the 
other is dependent on the width of the channels. The characteristic 
impedance for rectangular waveguides of the same broad dimension is 
proportional to the narrow dimension b. The junction formed between a 
channel and the main waveguide may be considered as e(][uivalent to a 



series connection and, therefore, the impedance loading one of the channel 
waveguides is twice the characteristic impedance of the main waveguides 
if both ends of the loading waveguide are matched. In units of the 
characteristic impedance of the channel waveguide the load impedance is 
26/6', where 6 is the narrow dimension of the main waveguide and 6' is 
that of the channel. At the other end of this channel, because the channel 
is one-quarter wavelength long, the impedance is the reciprocal, or 
6'/26. Returning to units of the characteristic impedance of the main 
waveguide, the impedance at the input end of the channel is (6')V2(6)*. 
This impedance may be considered as appearing in ser es with the load 
impedance in the waveguide on the side of the channel opposite to the 
side connected to a signal generator. If all four waveguides are matched, 
a fraction, approximately equal to (6') V2(6)*, of the power available from 
a signal generator on one waveguide would be coupled by a single channel 
into the other waveguide. With two channels, a fraction of the power 
approximately equal to (6')V(1>)^ is coupled into a matched load at one 
end of the other waveguide. 

To be used as an LO coupling circuit, the directional coupler of Pig. 
3-16 would be excited by the local oscillator at A and by the received 
signal at C, and it would be terminated by a matched dummy load at B 
and by a crystal mount at D, and a complete mixer results. The fraction 
of the received signal power which is lost by transmission to the dummy 
load at 5 is the same as the fraction of the total local-oscillator output 
power which is transmitted to the mixer crystal. One disadvantage of 
the directional coupler in this application is that it is veiy difficult to 
provide an adjustable coupling for it. Thus the only way of achieving an 
adjustable local-oscillator drive is to use a dissipative attenuator between 
the local oscillator and the coupling channels. If this is done, the 
coupling must be designed to give the required local-oscillator drive under 
the most adverse conditions of oscillator output power and crystal admit- 
tance. The signal power lost into the local-oscillator circuit is independ- 
ent of the attenuator adjustment and, therefore, is always that associated 
with the amount of coupling and is not reduced when a high-power 
oscillator ^d a good crystal are used. This is not a serious disadvantage 
but its existence should be realized. Many other forms of directional 
couplers can be made and it would not be worth while to go into the 
details of all of these here. Any directional coupler, however, with an 
approprmte coupling factor would be satisfactory. With a 2K25 tube, 
the minimum output power is specified as 15 mw and the local-oscillator 
drive desired for crystals of the 1N23 type is about 1 mw. A directional 
coupler for this combination should couple, from the local oscillator to 
the crystal, tV of the available power. Such a coupler is sometimes called 
an ll.S-db coupler. 

Sec. 3-11] 


It should be pointed out that there is a smaller loss of signal caused 
by the local-oscillator circuit with a directional coupler than tluuro us wit i 
a coupler of the simpler nondirectional type discussed in coiuitteiiou \Nit i 
Eqs. (2) and (5) for the mixer circuit without a resonator, h^* sinuliii ity 
between Eqs. (2) and (5) was stated to show that the fra< 5 ti<>n ol 
power lost could not be made smaller than the fraction of avaiinhh* loml- 
oscillator power delivered to the crystal, which is the saints coiulition that 
exists for the directional-coupler circuit. There is a differtuun^ hosv(^v(T, 
in that, in the former example, the available power was that in tlu^ nuxc^, 
and if a matched load such as a resistor disk is provided, only about half 
the power actually available from the oscillator is available in th<i inixor. 
With a directional coupler it is the total power available from the oscil- 
lator which enters into the reciprocity relation. Couse:<iu<‘ntly, th<^ 
directional coupler results in only half as large a signal losH as the nimphu’ 
coupling, if the full coupling is being used. The fact that tht^ signal loss 
does not decrease with more favorable conditions, howevc^r, nu'ans that 
this advantage is lost when attenuation must be \iscsd btdAvccui tli<‘ 
oscillator tube and the directional coupler. 

With the mixer preceded by a resonant circuit wiK‘h as a ’‘IMl (^avity, 
there is no such advantage from the use of a directional c.ouphu* over tlu% 
nondirectional circuits. It was shown that the fractional loss of signal 
power with a simple coupling circuit can be as small as om*! (juarttu’ of 
the fraction of the local-oscillator power available in the mixer (l(‘liv<T(‘<I 
to the crystal. With a matched load, such as the rc^sistor-disk cinunt 
discussed in Sec. 3-8, provided for the local oscillator, tiu’i loenl-oscillator 
power available in the mixer is one-half that available from tlu^ tube 
alone. The fractional loss in signal power, therefore^, <*.an b(* a.s .small 
as one-half the fraction of the local-oscillator power available from th(*s 
tube delivered to the crystal. Thus the signal loss with n clirt^et.iouul 
coupler is twice the minimum loss possible with th<^ simple* riivtiit if a 
resonant signal circuit is used ahead of the mixer. Ihu'.jmsc* the <*oui)ling 
with the directional coupler is independent of thc’i admittancM* ni the 
signal-input terminals of the mixer, the position of the*. e.ouph*r in t lu» litur 
between the resonant circuit and the crystal is not. im porta ut. If Uu* 
resonator were separated from the mixer by such a long l(*ngt h of line t hni 
the admittance looking toward the resonator at th<^ inj<*<*tion point- of 
the local-oscillator power varied rapidly with the fixMpKuur v, a <lire<dionul 
coupler would be superior to the simple coupling e.irc.uit.. Anolli(*r point, 
of great importance when no resonant circuit is uHcd b<>tAveen t ho antenna 
and the mixer is that the only source of signal ra<liat.<Ml fr<»in the mix<»r 
would be reflection, of local-oscillator power, by* crystal, if the 
directional coupler is used. With the simple einaiit, fbi* amount of 
local-oscillator power radiated under these conditions would l»e the .same 



as the amount delivered to the crystal. Directional couplers have not 
been used extensively in microwave mixer circuits, chiefly because it is 
difficult to make them adjustable and because they have not been 
mechanically convenient for most applications. It will be shown later 
that in circuits operating with a resonant TR cavity, it is desirable that 
the length of line between the TR cavity and the crystal be kept short. 
Most directional couplers transmit the coupled wave in the same direction 
as the original wave, as does the one of Pig. 3-16, and this requires that 
the local-oscillator tube be located at some distance from the crystal. 
This requirement has not been compatible with the desire for short 
line length between the TR cavity and the crystal with the duplexer 
circuits used and, consequently, other circuits have been found more 
adaptable to the service. The design of a mixer, whether a coaxial-line 
or waveguide type, using a directional coupler for the local-oscillator 
injection is straightforward and any of the directional-couplers that are of 
convement shape and have the required amount of coupling may be used. 

3«12. A Sin^e C hann el for Local-oscillator Coupling. — A simple 
nondirectional circuit for coupling the local oscillator to a waveguide 
mixer, which is s i mila r to the directional coupler of Fig. 3TG in principle 

but contains only one coupling 




Fig. 3-17, — Nondirectional coupling circuit. 

channel, can be used. Such a 
coupling circuit is illustrated in 
Fig. 3’17. Following the qualita- 
tive argument given for the] chan- 
nel width of the directional coupler, 
the power coupled from one wave- 

guide to the other, with all four pairs of terminals matched is approxi- 
mately (h')V2(i>)*. K this circuit is used as the LO coupling circuit 
for a mixer, the oscillator output power can be sent into A or Ji and 
a matched dummy load placed on the other end of this waveguide. 
The signal would be incident at C and the crystal mount would be at D. 
Since the coupled power is the total power taken out of the local-oscillator 
waveguide, with a termination in the mixer waveguide at each oml which 
is matched at the local-oscillator frequency, the power transmitted to 
the crystal is just half the power coupled from one guide to tho other, or 
h the mixer has a resonant filter such as a TR cavity 
in the signal line, the coupling depends upon the admittance presented by 
^ circmt, at the lo^-oscillator frequency, at the coupling channel. 
Because the junction is a series connection, the largest coupling occurs 

* , ^ coupling is then approxi- 

mately (& ) /(b) . All of the power taken out of the local-oscillator 
waveguide is transmitted to the crystal and this power is twice the amount 
Without the resonator smee the impedance terminating the cross-coupling 

SBC. 3-12] 



channel is 1 instead of 2 in units of the characteristic impedance of the 
main waveguide. 

The amount of the coupling for the single channel can be made 
variable by the addition of an adjustable susceptance element in the 
channel. In Fig. 3*18 the effect of adding a capacitive susceptance in the 
coupling channel at a point midway between the two waveguides is 
illustrated on an admittance chart. The load admittance in imits of the 
characteristic admittance of the channel was taken as 0.25 at point (1). 

Fia. 3-18.— Admittanc.o diwain illustrating effect of adjustablo HUH<?oiJtaii (!0 for coupling. 

Without the susceptance, the admittance at the input end of the channel 
corresponds to the point (2a) or a conductance of 4 in units of the char- 
acteristic admittance of the channel. Since this conductance is added 
in a series circuit in the local-oscillator waveguide, the impedance is more 
significant, and this is 0.25 in units of the characteristic impedance of the 
channel or 0.125 in units of the main-waveguide impedance. Hence, the 
power coupled from the local-oscillator waveguide to the other would be 
about 12.5 per cent of the power delivered by the local oscillator to the 
dummy load. Only one half of this power goes into the crystal. With a 
capacitive susceptance of 0.5, in units of the admittance of the channel, 



added at the midpoint of the channel, the admittance at the input end of 
the channel is that of the point (26). The corresponding impedance is 
that of the coordinates at (2c) or 0.16 + ^‘0.22 in units of the character- 
istic impedance of the channel. In units of the characteristic impedance 
of the main waveguide this is 0.08 + iO.ll. Therefore, 8 per cent of the 
power delivered by the local oscillator to the load is transmitted into the 
mixer waveguide and the delivered power is slightly changed because of 
the appearance of the reactive term. 

It might be thought that to avoid the reactive term the susceptance 
should be added at a point such as (3), where the circles of constant 
conductance are approximately orthogonal to the circles of constant 
standing-wave ratio. Since it is just as important, however, to avoid 
large reflections in the local-oscillator waveguide as in the mixer wave- 
guide, this is not so. Although the resultant variation of the series 
impedance presented to the local-oscillator waveguide would be resistive, 
that presented to the mixer waveguide would be reactive and severe 
reflections would result. It is sometimes more convenient to use a 
c hann el three quarters of a wavelength long for such a coupling circuit. 
Then, an inductive susceptance at the midpoint, or a capacitive suscept- 

Fiq, 3*19. — Hiquivcdent circuit of clxaxixiel 
local-osoiUator coupler. 

ance at a position a quarter wave- 
length either side of the midpoint 
would produce a coupling that de- 
creased with increasing suscept- 
ance. An inductive susceptance 
used at the midpoint of the quar- 
ter-wavelength channel would give 
increased coupling with increasing 
insertion. The mismatch that 
would be introduced by such a 
coupling device would increase with 
increasing coupling and could be- 
come serious unless a limit on the 
range of adjustment were provided. 
It is difficult to set a limit on the 
adjustment since the susceptance 
of a structure introduced into the 

waveguide varies rapidly with frequency when the susceptance is large. 
Under most circumstances the amount of mismatch that can be tolerated 

is larger for conditions requiring sm a ll local-oscillator coupling because 
the crystals that have small conversion loss usually require small local- 
oscillator drive to achieve optimum over-all noise figure. 

Expressions giving the amount of coupling between the local oscillator 
and the crystal, and the reflection coefficient caused by the coupling 

Sec. 3-12] 



channel, as a function of the added capacitive susceptance can be derived 
from a consideration of the equivalent circuit of Mg. 3-19. All imped- 
ances and admittances are expressed in units of the characteristic imped- 
ance or admittance of the main waveguides and it is assumed that the 
local oscillator, dummy load, signal generator (receiver antenna), and 
crystal are all matched to the waveguides at the local-oscillator fre- 
quency. The series impedance introduced in the local-oscillator circuit 
by the coupling channel and mixer can be calculated by transforming the 
load admittance of the channel, 6'/26, through the eighth- wavelength line 
by the transmission-line formula for a lossless line, 

V - V W f-r\ 

° Yo+jYttein (kl) 

where To is the characteristic admittance of the line, Yt is the terminating 
admittance, k is the wave number equal to and I is the length of 

the line. For the eighth-wavelength 
lines kl is ir/A and the transmission- 
line formula is 

7= 7o 

Yt + iFo 
Vo + jt; 

( 8 ) 

3*20, — Equivalent of locol - OHoil - 
lator ciromt- 

Next, the variable susceptance B is 
added and the resultant admittance, 
again transfonned by this formula, gives the admittance Yc at the input 
end of the channel. The impedance Zo is the reciprocal of Ye and the 
entire circuit becomes eciuivalent to that of Fig. 3-20. The fraction of 
the available local-oscillator power coupled into the crystal is 

T = 


(2 -1- ReV + X*; 

and the absolute magnitiule of the reflection coefficient is 

r = 

1 - (1 + Ze) ^ r Rl -1 
i + (I + Ze) L(2 + Rc. 

+ XI V 

By algebraic manipulation, these relations become 

T = 


4/1 -b (2 + BY] 

+ (2 + BY + + A^B^ [(2 + B) - /I* (2 - B)Y 


( 10 ) 

( 11 ) 

irl - I - _ [(2 + 5) - /1M2 - B)Y y 

' ' \[A-^B^ + (2'+li)*T4I»j* + A^BH(2T'BT'- 'A^ (2 - B)?J 

( 12 ) 


where the quantity A is the admittance terminating the channel in 
units of the characteristic admittance of the channel. The value of 
which gives the required maximum coupling To may be found by setting 
B equal to zero in Eq. (11) and solving for A\ If this is done, 

A® = [(1 - 2To) - (1 - (13) 

For To compared with i, this expression may be simplified by the 
expansion of the second term in series and the neglecting of terms higher 
than the third. The result is 

= To. 

This is identical with the result obtained for the fraction of the total 
power delivered to the crystal, if the series impedance of the channel 

B B 

Fig. 3’21.— Fraction of LO power coupled V8. Fig. 3*22. — Standing- wavo ratio V8. atits- 
susceptance. coptuiK^c. 

in the local-oscillator waveguide is small compared with the character- 
istic impedance of the local-oscillator waveguide. 

A typical example of a 3-cm mixer would employ a 2K25 oscillator 
tube and a 1N23 crystal. The oscillator tube may be expected to give £Ltt 
least 15 mw of power and the local-oscillator drive required for the crystal 
is less than 1 mw. Hence, To could be 0.05. If this value is used in 
Eqs. (11) and (12), the coupling and reflection coefficient as functions 
of the adjustable susceptance can be found. In Fig. 3*21 the fraction 
of the power available from the oscillator coupled into a matc'.hed ciystal 
is plotted as a function of the susceptance. In Fig. 3 *22 the standing- 
wave ratio is plotted as a function of susceptance, found from Eq. (12) 
by the relation 

r = 

1 + r 
1 - r’ 



The standing-wave ratio has a maximum of 1.55 at infinite susceptance, 
corresponding to zero coupling. This amount of mismatch relative to 
the optimum load admittance for the tube has been found not to cause 
trouble with the great majority of tubes. 

3*13. An Exact Equivalent Ketwork for the Coupling Channel. — The 
analysis of the circuit on the basis of a simple series connection to repre- 
sent the junctions is not sufficiently accurate to allow exact specification 
of the length and width for a particular coupling factor. As in almost 
all microwave circuits, there are end effects, associated with the excitation 
of higher modes in the waveguide, or coaxial line, which cause some 
departure from the results expected on the basis of the simple circuit. 
However, by means of some exact equivalent circuits for a junction of 
this type, developed by J. Schwinger, it is possible to calculate the length 
and width for minimum mismatch (equivalent to a pure series resistance) 
for a given coupling factor. Schwinger 
derives an equivalent network for the 
junction where the terminals of the net- 
work are considered to lie in planes, in the 
respective waveguides, adjacent to the 
junction. Because many modes exist in 
the immediate vicinity of the junction, 
the admittances in these planes cannot 
be specified, but the equivalent circuit 
predicts the admittances which would be 
measured at planes an integral number 
of half wavelengths back from the junc- 
tion in the respective waveguides. The 
agreement of these equivalent circuits 
wth experiment is very good. By mak- 
ing use of them, the conventional tech- 
nique of cut and try can be eliminated. 

For waveguide and coaxial-line struc- 
tures of many other types, Schwinger^s technique has been used and the 
results are being compiled in Vol. 10 of this series. 

In Fig. 3 •23a is shown a cross-sectional view of the T-junction where 
b and 6' are the inside dimensions of the waveguides. In the same 
figure the equivalent network is shown where the terminal pairs are in the 
planes corresponding to the dashed lines of the structure. The com- 
ponents of the network are represented as capacitances or inductances 
depending upon whether the sign of the susceptances is positive or nega- 
tive. They do not necessarily show the corresponding frequency 
dependence. This is evident from the relation below giving the values 


( 6 ) 

Pia. 3*23. — EquivaJont circuit for an 
JS-plane T-junction. 


of these susceptances in terms of 6, V, and^fc the wave number, 'equal 
to %r/\. 

All the susceptances except B 2 have the direction of change with fre- 
quency normally associated with a low-frequency susceptance of the 
same sign but the dependence is inversely or directly with the waveguide 
wavelength and not the free space wavelength. 

A technique that can be used for the calculation of the length and 
width of a channel for a particular coupling is to estimate the width 
on the basis of the simple series-junction formula, To = (6')V4(&)®. 
Next, the admittance at terminal pair (3) with pairs (1) and (2) connected 
to matched loads, or unit admittances, can be calculated. From this 
admittance the standing-wave ratio and phase in the coupling channel 
can be found and from this a plane in the junction at which the load 
admittance would be real is found. The difference in position between 
this plane and the plane containing the terminals of the equivalent 
circuit is the end effect. The length of the channel is made to be 
physically the one-quarter or three-quarters of a waveguide wavelength 
between these corrected planes. If this length is used for the narrow 
waveguide, the admittance presented to the terminal pair (3) of the 
second network can be calculated and hence the amount of power coupled 
across found, as well as the standing-wave ratio and phase in the input 
waveguide. In examples the standing-wave ratio is found to corre- 
spond to that which would be found for a simple scries circuit coupling 
out the same fraction of power, and the choice of the length on the basis 
of the end-effect planes is considered to be valid. From the phase of 
the standing wave, the position of end-effect planes for the terminal pairs 
(1) and (2) can be found and, thus, the circuit can be considered as 
equivalent to the simple series circuit connected between these planes. 
All three of the planes are found to fall inside the junction from the 
planes defining the position of the terminals of the equivalent network. 

The algebra of this calculation is perfectly straightforward but quite 
tedious. There is no point in giving an example here, although some 
results to show the magnitude of the divergence from the simple idea of 
series connection may be of interest. For a mixer for 1.25 cm, using 



main waveguides 0.170 by 0.420 in. ID, the coupling and end corrections 
have been calculated for several channel widths. It was found that 
the end corrections amounted to about 0.025 in. at each end of the 
channel, thus shortening the length of the chaimel by about 0.050 in. 
from a quarter-wavelength in the waveguide for channel widths from 
0.060 in: to 0.100 in. In this range of widths, the power coupled into 
the mixer differed by less than 15 per cent from the value calculated 
from the simple series circuit with the formula (6')^/4(5)®. A calculation 
fot 3.2 cm, using a main waveguide having inside dimensions of 0.400 
by 0.900 in. and a channel width of 0.180 in. gave an end correction of 
0.060 in. The fraction of the local-oscillator power delivered to a 
matched crystal was found to be 0.042 compared with a value of 0.051 
calculated for the simple series circuit. Because the disagreement of the 
coupling factor calculated from the simple circuit with that calculated 
from the exact equivalent circuit is not large, for present purposes the 
choice of the width of the channel on the basis of the simple series 
junction is probably sufficiently precise. The main value of the network 
representation is the end-effect correction in the length of the coupling 
channel. This is simple to calculate compared with the calculation of 
the exact coupling factor. 

All of the foregoing discussion applies to a mixer that has no high-Q 
resonant circuit between the crystal and antenna, and the antenna, 
therefore, appears as a matched load to the local-oscillator wave. If a 
TR cavity is used between the mixer and antenna, as shown previously 
the coupling between the local oscillator and the crystal can be increased 
by a factor of 4 by proper choice of the position of the TR cavity relative 
to the coupling channel. The TR cavity should be so positioned that a 
short circuit appears in approximately the plane of the appropriate 
terminal pair in the equivalent network. The coupling can be made 
very small by placing the TR cavity in a position a quarter wavelength 
different from this, resulting in an open circuit at this plane, since the 
circuit of the junction does correspond approximately to the series 
circuit. . Since such a position must be avoided, a mixer intended to be 
operated in a wide freciucncy band should be designed with a line length 
between the TR cavity and the coupling circuit so short that the admit- 
tance presented at tliis plane by the TR cavity does not deviate appreci- 
ably from a short»-circuit admittance within the band. 

The exact position of the TR cavity relative to the junction can be 
calculated- with the aid of the equivalent network. The admittance at 
the terminals of the network, with the complete circuit assembled may be 
calculated. The TR cavity should then be so positioned that the suscep- 
tance of the waveguide terminated by the TR cavity is the negative of the 
susceptapee con^ponent of the calculated admittance The result of such 


a calculatioa shows that the TR cavity should be positioned somewhat 
closer to the junction than an integral number of half wavelengths and 
an equivalent plane for the simple series circuit representation can be 

given. , , 

For the example of the 1.25-cm waveguide cited previously, the 

correction is such that the position of a short circuit due to reflection 
from the TR cavity appears almost at the center plane of the junction. 
For this purpose, then, it appears that the series circuit is adequate and 
that the tedious calculation required to apply the exact equivalent circfdt 

gives a result too little different to be worth while, except for the calcula- 
tion of the length of the channel. 

When a TR cavity is used, the coupling factor is strongly dependent 
upon the crystal admittance since a wave reflected by the crystal is 
returned to it by the TR cavity in a phase dependent on the reflection 
coefficient of the crystal. As an illustration of this point, two plots are 
given in Figs. 3*24 and 3-26. Fig. 3*24 shows contours of constant power 
delivered to a matched crystal as a function of the impedance across the 
terminals of the network representing the junction in the mixer waveguide 
on the other side of the junction from the crystal. This impedance 
includes the susceptance of the capacitance jBi associated with the 



teiminals and is for the 1.25-cm waveguide 0.420 in. by 0.170 in. ID 
with a coupling channel 0.100 in. by 0.420 in. and 0.401 in. long. Also 
plotted on this diagram is a contour of the terminal impedance for a 
TE cavity, spaced such that the short circuit, when the TR cavity is 
detuned, appears 0.261 in. from the plane of the terminals of the equiva- 
lent network. The contour is valid for a typical 1B26 TR tube having 
about 1.6 db loss and equal coupling irises. The contour does not 

Fig. 3*25. — Contours of constant power doUvorod to crystal vs. crystal admittance, 
for TR admittances o(iual to (1,4 H-y2.4) 7o at LO frequency. The TR switch is the 
1B26; the intermediate frequency is 60 Mc/sec. 

represent the TR-cavity and signal-generator admittance alone, but 
includes the capacitance associated with the terminals of the juiu^tion. 
This plot is significant since the Q of the 1B26 tube, the standard TR 
cavity for this wavelength, is not high enough to allow the TR cavity 
to be considered as completely reflecting at the local-oscillator fr(^(iuen(y 
when the tube is resonant at the signal frequency with ordinaiy inter- 
mediate frequencies of 30 or 60 Mc/sec. 

Figure 3-26 shows, for this same coupling circuit, contours of constant 
power delivered to the crystal as a function of the crystal admittance as 



measured at the crystal terminals of the network. Here, the inter- 
mediate frequency has been assumed to be such that the TR cavity is 
detuned from local-oscillator frequency to an extent sufficient to transmit 
half the maximum power. A 60-Mc/sec intermediate frequency would 
about correspond to this situation with a 1B26 tube, since the loaded ' Q 
of these TR tubes is about 200. 

3*14. An Iris for Local-oscillator Coupling. — ^For operation with, a 
resonant TR cavity, because of the more efficient coupling resulting, a 

simpler type of circuit has been used 
extensively in the 3.2-cm band and 
adjacent regions. This coupling de- 
vice consists of a simple inductive 
window between two adjacent paral- 
lel waveguides with a common wall 
on their narrow sides. A circuit of 
this type is illustrated in Fig. 3*26. 
The aperture in the wall may be either circular or rectangular, although 
rectangular apertures running the full height of the common wall have 
usually been used. These apertures are made less than a half wave- 
length in width, and, to a fair approximation, the circuit may be con- 
sidered as a lumped inductive ftusceptance in the plane of the window. 
Circuits coupled to the narrow wall of a waveguide can be shown to 
behave approximately as shunt-connected circuits where the admittance 
at the wall is transformed by a quarter wavelength of waveguide into the 
center of the waveguide. This transformed admittance adds in shunt to 
the admittances of the loads at the ends of the waveguide. 

The simple aperture coupling is less efficient than the channel coupling 
just discussed in the sense that the reflection due to the aperture is larger 
than that due to the channel for a given coupling factor. That this is so 
can be shown from the simple equi- 
valent shunt circuit in the following 
way. Suppose that all four wave- 
guides in Fig. 3-26 are connected to 
matched loads representing the local 
oscillator and a dximmy load in the 
upper waveguide and the crystal 
and signal generator in the lower. 

The admittance in the lower waveguide at the center is 2 in units of the 
characteristic admittance of the waveguide. Transformed through the 
quarter wavelength of waveguide to the aperture, the admittance is 
i in the same units. To this is added the inductive susceptance of the 
aperture, — and then this is transformed through another quarter 
wavelength of waveguide to the center of the upper waveguide. Thus, 

.j, _ 2+i46 Dummy 

1 + 46 ^ 

Fiq. 3-27. — Equivalent shunt circuit for 
aperture-coupling circuit. 

Fig. 3*26. — H-plane ‘windoT^ for local- 
oscillator coupling. 




the .ftdeiittance of the mixer waveguide, appearing in shunt in the upper 
waveguide, is . 

1, 0.5 + jb _2 + j4b 

0.5 - jb 0.25 + b^ 1 + 4b*‘ 

Y„ = 

The equivalent shunt circuit is illustrated in Fig. 3-27 and from this the 
fraction of the available local-oscillator power delivered to the crystal 
can be shown to be 

t. 1 


4(1 + 60 

A plot of this function is given in Fig. 3-28a. 
on the other hand, is given by the formula 


The standing-wave ratio 

r = 

1 + 

1 - 



Fio. 3-28 a, 6,— The offo«t of susooptanoo of coupling iris, (o) Coupling factor vs. bus- 
^1er)tan<^o; (/>) voltage standing-wavo ratio vh. HUHceptanco. 

where iFal is the reflection coefficient for the load (y„ -|- 1) or 

This is to bo compared with the reflection (iocfficient for the channel 
circuit for whicsh the reflection coefficient is just 

IIM = T, 

for a coupling factor 2’ small compared with 0.25. Using the above 
expression for lr„| in the equation for the standing-wave ratio, a curve can 
be plotted with the result shown in Fig. 3'286 for the voltage standing- 
wave ratio as a function of the aperture susceptance. 

The symmetry of the circuit, neglecting the frecpiency dependence 
of the local-oscillator admittance, makes it apparent that the same 



standing-wave ratio would be produced in the’ mixer. From this it is 
evident that the simple aperture coupling circuit has considerably greater 
interaction between the signal and local-oscillator circuits than is neces- 
sary. For this reason it has been fotmd to operate satisfactorily only 
under the condition that a resonant TR cavity is used, so positioned that 
the admittance of the TR cavity at the local-oscillator frequency seen 
in the mixer waveguide in the plane containing the center of the coupling 
aperture is very small. Because the TR cavity reflects the wave incident 
upon it in such a phase as to reinforce the wave traveling toward the 
crystal, as in the other examples, the power delivered to the crystal is 
increased almost fourfold, for an aperture of large susceptance. The 
analysis on the basis of the simple shunt circuit is similar to the previous 
one except that the admittance of the mixer at the aperture is unity 

(o) (6) 

Fig. 3’29. — The effect of susceptance of LO coupling iris when a resonant TH cavity 
is used, (a) Coupling factor vs. susceptance; (b) standing-wave ratio in LO waveguide 
vs. coupling susceptance. 

instead of two. The coupling factor as a function of susceptance for this 
case is 

rn __ 4(1 + b^) 

9 + 56® + 46^ 

and this function is plotted in Fig. 3*29a. The standing-wave ratio vs. 
susceptance plot of Fig. 3*28& applies here for the signal standing-wave 
ratio in the mixer, with the crystal matched to the signal, but the stand- 
ing-wave ratio in the local-oscillator waveguide is changed by the presence 
of the resonant TR cavity. The reflection coefficient in the local- 
oscillator waveguide is 

- (91^)“ 

and for large susceptance the standing-wave ratio differs little from that 
in the previous example. Figure 3-296 gives a plot of the standing-wave 
ratio due to this reflection coefficient as a function of the susceptance. 

Sbc. 3*14] 



Because the space available for a radar mixer is usually limited, the 
applications of this LO coupling circuit have mostly been a variation of 
this scheme. Figure 3-30 shows, in a perspective view, a mixer using such 
a coupling circuit, with the positions of the coupling probe of the 2K25 
local oscillator, the crystal, and the 1B24 TR cavity indicated. The 
oscillator tube is mounted with a tube socket above the waveguide at the 
right with its antenna inserted the specified distance at an off-center 
position as recommended in the test specifications. The waveguide is 
terminated with a matched load at the near end. The waveguide is short- 
circuited at the other end and the iris that couples the local-oscillator 
power to the mixer is located in the side wall with its center about a 
quarter wavelength closer to the antenna of the tube than the short 
circuit. The antenna of the tube is located at a distance from the far end 
such that, at 3.33 cm, the admit- 
tance of the waveguide in this 
direction is the same as that of the 
short-circuited waveguide 1 cm 
long, as specified in the mount for 
the tube. This length was chosen 
by experiment and is electrically 
equivalent to a short-circuited 
line just less than 3\<,/4 in length, 
although its physical length differs 
from this considerably. In tins 
way the local-oscillator tube is 
operated into a load circuit differ- 
ing at the midband frequency from 
the recommended one, for a small 
coupling to the mixer, by a small 
conductance component in the admittance. The admittance loading the 
oscillator varies more rapidly with freciuency than it does in the test 
mount because the^ short-circuited waveguide is effectively a half wave- 
length longer than that recommended. Experience has shown that 
oscillators that operate satisfactorily in the test mount very rarely give 
trouble in this circuit. 

So far in this discussion the effect of the LO coupling circuit on the 
admittance presented to the signal has been calculated assuming that 
the local oscillator presents a matched admittance to the waveguide at the 
signal frequency. This is not true because the oscillator contains a 
resonant circuit tuned to the local-oscillator frequency. The reflection 
coefficient of the local oscillator is very likely almost unity at the signal 
frequency. There is a danger that this reflection may give rise to an 
admittance at the coupling window which can cause serious reflection 


Electrical length 
equivalent to a 
snort circuited 
waveguide x^/2 
plus 1 cm in 

off center 

Crystal 2K25 output ^Resistance 


t'la. 3-30. — Mixor circuit with iria-couplod 
local oucilLutor. 



of the signal. In the circuit of Fig. 3*30, this effect is less serious than in 
the circuit in which the local oscillator and dummy load are on opposite 
ends of the waveguide, since only at frequencies at which the output 
coaxial line of the oscillator tube resonates by itself does the presence of 
the oscillator antenna in the waveguide have a large effect. At other 
frequencies the local-oscillator waveguide is loaded with an open-circuit 
admittance from the side of the coupling iris away from the LO tube and 
an admittance approximately matched to the waveguide characteristic 
admittance on the other side of the iris. 

As shown previously it is necessary to adjust the coupling of the local 
oscillator if optimum results are to be achieved with production crystals, 
and oscillators. With this circuit the adjustment must be made by 

Fig. 3-31. — ^Adjustable rectangular coupling uda. 

variation of the iris susceptance. With a rectangular iris this can be done 
by making the whole side wall slidable, with spring contact between it and 
the top and bottom walls of the waveguide. Figure 3*31 shows such a 
slidable wall made from two curved strips of phosphor bronze about 
0.005 in. thick and spot-welded down the center line with their convex 
surfaces together. This spring slides in a channel between the top walls 
and the bottom walls of the two adjacent waveguides and contact is 
maintained by the wiping action on the sides of these channels. A strip 
is soldered over the outside of the channels to keep the strip properly 
aligned. With an adjustment of this kind, the effective position of the 
iris is altered as the width is changed, but for a small adjustment the 
change in position is not serious. 

A more commonly used adjustment that avoids the variation of 
position and the troubles usually encountered with sliding contacts is a 
combination of a circular or rectangular inductive iris with a capacitiver 
screw post. This is shown in Fig. 3*30 mounted above the center of 
the coupling iris. The screw structure is shown in more detail in Fig. 

Sue. 3*14] 



3-32. The capacitive screw is the same type that is used in matching 
transformers or in the channel coupling arrangement for coupling adjust- 
ment. It uses the quarter-wavelength-choke principle to minimize 
erratic behavior due to poor contact in the screw threads. In the 
3^3-cm mixers a 6-32 screw is a 
convenient size. An iris in. in 
width has been foxmd sufficiently 
narrow to allow the coupling to be 
made small enough for any combi- 
nation of a 723A/B or 2K25 tube 
and a 1N23 crystal with the screw 
completely retracted. In the dia- 
gram, a post projecting into the iris 
from below is dotted in and ordi- 
narily this is absent from the struc- 
ture. It is sometimes desirable, 
however, to have an adjustment in 
which the coupling decreases with 
increasing insertion of the screw, 
and then the post is added. The 
post is sufficiently long to give a 
capacitive susceptance more than 
enough to produce shunt resonance 
with the inductive susceptance of the iris. The entire structure, there- 
fore, appears as a capacitive susceptance that increases with increasing 
screw insertion. 

For mixers that must bo foolproof in operation it is important to 
provide an upper limit on the coupling that can be achieved with the 
adjustment. This can be done with the iris and screw structure by 
correct choice of the length of the screw. In applications where a wide 
band of frequencies must be covered, the frequency-sensitive nature 
of the capacitive susceptance of the screw does not allow the limit to be 
chosen precisely. A screw length that, at short wavelengths, gives the 
whole structure the desired minimum inductive susceptaiKJC gives, at 
longer wavelengths, a minimum inductive susceptance somewhat larger. 
In such a case the device cannot be made entirely foolproof. With 
the structure including a fixed post the limiting coupling is, of course, 
determined by the length of the post and the same arguments about the 
frequency selectivity apply except that the largest coupling occurs at 
the longest wavelengths. 

For smoothness in the adjustment and also to protect against changes 
caused by vibration, many locking schemes have been tried. The best 
from the viewpoint of simplicity and permanence was a triangular spring 

Fia. 3*32.- 

- Adjustable coupling iris using 
choko screw. 


made from spring wire fitting into a slot in the screw motmt and riding in 
a thread of the screw. This is illustrated in Fig. 3-32, with a top view of 
the screw mount and spring also shown. The diameter of the spring 
vrire is about the same as the distance between consecutive screw threads. 
It is important to make the slot in the screw mount at least as wide as two 
screw threads in order that the spring may ride freely in a thread, inde- 
pendently of the location of the threads vrith respect to the slot. 

Many variations of these schemes of local-oscillator coupling are 
possible and some of them will become apparent in mixers shown for 
illustration in later chapters. The general nature is the same, however, 
and it would not be worth while to attempt to describe all of these 
variations. The type that is best fitted to a given mixer is determined 
by the shape which the mixer may take and by some of the supplementary 
functions which it is sometimes called upon to perform. These supple- 
mentary functions are the subject of Chap. 4. 

3-16. Signal-input Circuit. — ^The only remaining problem in the 
design of a complete mixer is that of transferring the incoming signal 
power from the circuit connected to the antenna into the crystal mount. 
If the line to the antenna is similar to the line in which the mixer is built, 
the mixer may simply be connected to the antenna, line. The mixer 
tuning should be such that, vrith the local oscillator operating at the 
proper level and frequency and with a matched i-f load in place, the 
admittance of the inixer for small signals with all crystals is as near 
the characteristic admittance of the line to the antenna as possible. 
Measurement may show a small correction from the tuning arrived at 
with signals at the local-oscillator level to be desirable. For most mixers 
it has been found that the small-signal admittances did not differ suffi- 
ciently from those measured at local-oscillator level to warrant changing 
the mount. 

When the mixer signal comes from a TR cavity, the mixer circuit must 
be made to load the TR cavity properly. With TR tubes having integral 
cavities designed to operate between matched waveguides, the design 
procedure is not greatly influenced by the cavity, but with loop-coupled 
cavities or those designed to operate between coaxial lines, a coupling 
circuit must be a part of the mixer. With these cavities, the major part 
of the adjustment of the tuning of the mixer for the best scatter of admit- 
tances with all crystals and over the frequency band required can not 
be done independently of the design of tMs coupling circuit. For this 
reason the coaxial-line mixers have been designed for operation with 
defimte TR cavities, and the measurement of the matching conditions 
has been carried out almost exclusively on the input side of the TR cavity. 
If the effects, on the conversion loss and i-f admittance of the crystal, 
of the line length between the crystal and the TR cavity are neglected. 

Sue. 3*15] 



the matching conditions can be completely determined by measurements 
of the input admittance to the TR cavity. Such measurements show 
whether the TR cavity is properly loaded by the crystal circuit and from 
these measurements the total transmission and reflection loss of the 
circuit can be inferred. 

A schematic view of a TR cavity and an equivalent lumped-constant 
circuit are shown in Fig. 3-33. The equivalent circuit applies only with a 
special choice of the position of terminals on the input and output lines. 
To find the position of these terminals in the input and output lines a 
signal may be sent into one of these lines at a frequency far from the 
resonant frequency of the shunt resonant circuit. In the equivalent 
circuit, a short circuit would appear at both the input and the output 
pairs of terminals and, hence, the position at which a short circuit is found 
in the coaxial lines, with the cavity detuned, is the position of the ter- 
minals. If the cavity is then tuned to resonance, causing it to add zero 
susceptance to the circuit, the admittance that is measured at this point 



Ideal Ideal i 

transformer transformer 

Fig. 3*33. — ^Loop-coupled TR cavity and equivalent circuit. 

in the output line is proportional to the sum of the admittance presented 
by the load at the corresponding point in the output line and a conduct- 
ance that is a measure of the dissipative loss of the cavity. The output 
admittance is transformed by the two ideal transformers by a numerical 
factor and the conductance measuring the loss of the cavity is transformed 
by a numerical factor by the ideal transformer representing the input 
coupling. It is difficult to show that this circuit should apply exactly, but 
its use is justified by very extensive experience in which perfect agreement 
has been found between calculations from it of the transmission loss and 
frequency dependence and measurements on actual circuits. The 
transformation ratio of the ideal transformers is determined primarily by 
the fraction of the magnetic flux in the cavity which is linked by the loops, 
and the admittance stepup of the input-circuit loop can therefore be 
increased by the use of a smaller loop or by setting it at an angle in such a 
way that its plane is not perpendicular to the magnetic field of the cavity. 

Iris-coupled cavities can be described in exactly the same way, 
although the analogy between the iris and an ideal transformer is less 
obvious than for the loops. The position of the short circuit with the 
cavity detuned depends upon the length and diametei* of the loop» 



whereas with reasonably small irises it falls almost exactly in the plane 
of the iris. For loops of the sort used with the i^in. coaxial-line mixers, 
the position of the short circuit is a point approximately a half wavelength 
back along the line from the terminus of the loop, including the perimeter 
of the loop as a part of the line. 

The equivalent circuit of the TR cavity and mixer can be further 
simplified. At the terminals chosen in the manner explained, the 
equivalent circuit of Fig. 3*34 applies, where Qg is the antenna conduct- 
ance (equal to the characteristic admittance of the line), gs and jbe are 
the conductance and susceptance parts of the cavity admittance 
transformed to the terminals in the input line, and gm, and jbm are 
those of the load admittance transformed to the input terminals of the 
TR-cavity circuit. From this circuit, it is apparent that, if the TR cavity 
were tuned for maximum po^er delivered to the crystal, the resultant 

susceptance of the circuit would 
I r ! I T 1 be zero. For such tuning be is, 

AsignaKp < ^ ^ ^ therefore, just the negative of bm- 

1 means that if the mixer had 

I ,1 i -I -i 1 been made tunable, and Qm and 

Fig. 3-34.— Transformed equivalent circuit 5 be completely adjusted 

of TR cavity and mixer. , ^ 

m the mixer, there would bo an 
infinite number of equivalent tuning positions for the combination, 
corresponding to different values of &«. It is thus apparent that 
for complete tunability of a mixer-plus-TR-cavity combination it is 
only necessary to adjust in the mixer. Since the transformation 
ratio of the output loop is influenced by its position in the TR cavity, a 
completely tunable mixer can be made by using a loop of adjustable flux 
linkage in combination with the tuning of the TR cavity. To sot 
up a mixer and TR-cavity combination fixed in tuning, except for the 
TR-cavity tuning itself, it is only necessary to choose the size of the 
output loop of the TR cavity on the basis of admittance scatter diagrams. 
The largest bandwidth and smallest dissipation of signal power in the 
lines of the mixer are obtained when the crystals present a matched load to 
the noixer line, since then the admittance presented to the output ter- 
minals of the TR cavity is no more dependent on frequency than the 
admittance at the crystal. It is on this basis that the standard 10-cm 
loop-coupled mixer was designed. It was made to operate with four 
different TR cavities covering the band from 8 to 12 cm simply by 
choosing the flange on which it was mounted on each of the cavities for 
the best scatter of input admittances to the TR cavity with representa- 
tive crystals. The size of the input loop of the TR cavity is chosen on the 
basis of the function of the TR cavity of protection at high level, and it is 
this coupling that determines the values of g,. 

Sec. 3-16] 



The range of input admittances which can be tolerated with this 
circuit can be found as follows. Assuming the TR cavity to be tuned 
such that the susceptances cancel out, the fraction of the available 
signal power delivered to the crystal can easily be shown to be 

(gg + gfn + gy 


A measure of the input standing-wave ratio is (gm + g8)/gg sud if T 
in decibels of loss is plotted against this quantity, the curve given in 
Fig. 3*35 results. A typical value for g^ of 0.245, resulting in a 1-db total 
loss with a matched output load, has been assumed. Most TR cavities 
now in use show a loss under this condition between 1.0 and 1.5 db. 

Fig. 3 * 35 . — TruiiHinisHion plus rofloctioii loan for a. TR ouvit.y mixor, in dooibola, va. input 
atundiiig-wuvo ratio, in dooil>olH. 

The standing-wave ratio has been plotted in decibels, twenty times the 
common logarithm of the voltage standing-wave ratio, and the positive 
values correspond to a conductance at the input terminals greater than 
the characteristic admittance of the line, and the negative values to a 
conductance smaller than the characteristic admittance. From the 
plot it is evident that it is not sufficient to measure only the standing- 
wave ratio since the cuivc is very unsymmotrical. From the point of 
view of the loss of signal power, a very much larger standing-wave ratio 
can be tolerated with a phase corresponding to the positive side of the 
plot than vrith a negative phase. The positive phase corresponds to a 
standing-wave pattern with a minimum at the input terminals and such a 
minimum has the same position when the TR cavity is tuned for greatest 
transmission of signal as when the TR cavity is detuned. For negative 
values, the tuned condition shows a minimum position which is shifted by 


a quarter wavelength from the detuned position and the minin 
shifts rapidly with tuning. In most 3-cm applications, the loss ari 
from mismatch at the crystal has been kept below 1 db. In Fig. 3 
which applies to the 3-cm 1B24 TR cavity, the standing-wave-r 
limits that correspond to such a loss are — 3 db and +11 db. ] 
narrow frequency band the spread need not be this great, but for 
wideband mixers covering a band 12 per cent wide, these limits were 
met using the crystals representative of the borderlines of the admitt£ 

The ability of the tuning of the TR cavity to compensate for 
susceptance part of the load admittance has been used to reduce 
spread in transmission loss with various crystals over the requ 
frequency band. In the course of measurement of admittance scatt€ 
large numbers of crystals in the 3-cm band, it was observed that 
scatter was not purely random about a center point but that it cov< 
an area longer in the susceptance direction than in the conducts 
direction. It is also foimd that the major direction of change of ad] 
tance with frequency is in the susceptance direction. Because the mi 
were intended to be used with a tunable TR cavity and because 
standard time-up procedure would be to tune for maximum recei 
signal, it was thought possible to use the TR cavity in combina 
with the mixer to obtain a reduced resultant scatter for the combinat 
Such a utilization of the TR cavity as partial tuning for the mixer 
been called * ^ TR-aided tuning” and has been used in many fixed-tuned 3 
mixers. To be most effective in reducing the admittance scatter at a fi 
wavelength, the effective electrical position of the TR cavity should b< 
integral number of half wavelengths from the crystal. This causes 
large susceptance scatter at the center line of the crystal mount to api 
as a susceptance scatter in the load admittance presented to the TR cav 
That this should hold over the widest possible band requires the miniir 
number of half wavelengths. Consequently, most wideband mixers h 
been made only one -h alf wavelength long from the position of the si 
circuit with a detuned TR cavity to the center line of the crystal moi 
In this way it has been found possible to keep the loss caused by cry 
mismatch less than 1 db over the ±6 per cent band from 8500 Mc/se 
9600 Mc/sec. 

Iris-coupled coaxial-line mixers have been used in the 10-cm ban< 
conjimction with a TR cavity, and some advantages can be had thro 
the use of the TR-aided tuning principle. The shape of the admitta 
scatter found for 10-cm crystals does not show a decided elongation in 
direction, although there is a common direction of change of admitta 
with frequency. The actual direction of the change depends upon 
nature of the crystal mount as well as on the position in the mourn 

Sec. 3-16] 1JV26 CRYSTAL MOUNTS 171 

which the admittance is measured. It can be specified only for the unit 
as a whole, and the best length of line between the coupling iris and the 
crystal does not necessarily bear any integral relationship to a half wave- 
length. The coupling his loads the TR cavity with an admittance that 
increases mth increased height (along the lines of electric field in the cavity) 
and Avith increased projection of the coaxial line into the cavity. 

3-16. Mounts for 1N26 Crystals and a Waveguide Mixer for the 
10-cm Band.— At the end of this chapter is given a group of drawings of 
several representative simple mixers. The coaxial-line mixers are all 
designed for use with 1N21A, 1N21B, and 1N21C crystals, and the mixers 
having a 1 by i-m. waveguide for 1N23, 1N23A, and 1N23B crystals. 

Fkj. 3*3(). — 1N2() crysl-ul mounts, (a) Tumtablo mounts; (6) crossbar mount. 

Also included are a 1.25-cm noixer designed for operation with 1N26 
coaxial-linc crystals and a mixor having a similar structure designed for 
lN211i crystals in the lO-cm band. The design of the 1N26 crystal 
mount for 1.25-c.m opei-ation is based on different principles from that 
of the two types described in previous sections. The 1N26 crystal was 
designed to match a mount having particular properties at this wave- 
length. The crystal mount was, therefore, particularly easy to design. 
The 1N26 is testrrd in a mount in which it terminates a coaxial line having 
an inner conductor with a diameter of in. and an outer conductor 
with a diameter of -fV The mount is adjusted so that a matched 

load on this coaxial lino absorbs aU the available power of the signal 
generator. It is, thus, necessary only to make a matched transformer to 
transform from a waveguide 0.170 by 0.420 in. ID to a coaxial line of this 


size with, suitable provisions to bring out the i-f voltage and rectified 
current. An average crystal unit will then terminate the waveguide in a 
matched load. 

Mounts of two different types or, more exactly, waveguide-to-coaxial 
line transitions have been used for this purpose. These are shown in 
cross-section in Fig. 3-36 a and b. The type fabricated in ordinary 
waveguide, with an adjustable plunger and screw, was adopted as standard 
for testing purposes, with each unit pretuned. The tuning adjustments 
were fixed by wax, such that there was no reflection in the waveguide 
section, with a dummy matched load in the crystal socket. The other 
unit, shown in Fig. 3-366, is made from a solid block using a crossbar- 
supported probe waveguide-to-coaxial-line transition. In this way the 
crossbar, with a choke a quarter wavelength from the side wall, is used to 
bring out the low-frequency components. The crossbar unit has been 
used most extensively in system mixers because it fits conveniently into 
complex mixers and because it is less frequency-sensitive than the other 

A critical dimension on these 1N26 crystal mounts is the length of the 
slotted center conductor from the shoulder in the outside conductor to 
the end of the fingers. If it is too long it may strike a shoulder on the 
center conductor of the crystal unit before the outer conductor of the 
crystal meets the shoulder in the mount. If it is too short, a considerable 
length of the small-diameter center conductor of the ciystal unit is left 
exposed and this has a transforming effect on the ciystal admittance. 

The 10-cm mixer designed by the same principle as this crossbar 
mount does not have the simplicity of being just a matched waveguide- 
to-coaxial-line transformer. It was developed to fill the need for a 
waveguide crystal mixer to be used with the wide bandpass fixed-tuned 
TR cavity which has an output iris designed to couple to a matched 
3- by l-^-in. wavegmde. As in the 1.26-cm crossbar mount, the conduct- 
ance part of the admittance at the plane of the crossbar is controlled 
primarily by the distance from the top of the waveguide to the crossbar. 
The susceptance part is determined primarily by the distance from the 
crossbar to the short circuit in the waveguide beyond the crossbar, 
although the crystal itself projects into the waveguide. A complete 
imxer is made from this mount by the provision of the LO coiiplinf^ 
circuit on the opposite end of the crossbar from the end from which 
f'he i-f signal is derived. Several of these units having different crossbar 
positions but basically the same circuit, have been designed to cover the 
region from 8 to 11 cm, each covering a band about ±4 per cent in width. 

347. Self-protection of the Mixer Crystal.— Crystals operated as 
mixers m radar systems have been plagued with burnout caused by 
insufl&cient protection from high-power signals by the TR switch. For 


this reason several special features have been adopted in an effort to 
reduce the frequency of burnout in operating and nonoperating systems. 

At the time when the flat power, lasting for the duration of the 
transmitter pulse, was thought to be responsible for burnout, considerable 
effort was made to include in the mixer design a feature called “self- 
protection.^' This feature was based on two special properties of the 
TR cavity and crystal mixer. First, the TR tube, while firing, maintains 
an essentially constant voltage across the arc, independent of the input 
and output couplings. The arc can therefore be considered as a constant- 
voltage generator having no internal impedance and the power delivered 
by it to a load circuit is directly proportional to the load conductance. 
The second property of the combination is that the crystal, since it is 
a nonlinear device, shows a different admittance at high level than at low. 
Because the TR leakage power is at a considerably higher level than the 
local-oscillator power in the mixer, the crystal may be expected to show an 
admittance considerably different from match and, therefore, the flat 
leakage power of the TR cavity into the crystal may be considerably 
different from that delivered to a matched load. It could be either 
greater or smaller depending upon the direction of change of the admit- 
tance as seen by the TR cavity. In order to ensure that the leakage was 
reduced by this admittance change, the admittance as a function of 
power level was measured for many ciystals. The line length was then 
chosen so that the conductance seen by the TR cavity decreased with 
increasing power and a mixer designed in this way was said to have 

During the early stages of the design of 3-cm mixers it was apparent 
that there was something to be gained in low-level operation through the 
use of TR-aided tuning described in Sec. 3T5. This required a half- 
wavelength spacing between the TR cavity and the crystal. Measure- 
ments of the change of admittance with power level showed that the 
conductance at the center line of the ciystal increased with increased 
power. The two criteria for choice of the line length from the TR cavity 
to the crystal were thus incompatible, since the half-wavelength spacdiig 
resulted in the inverse to self-protection, because more power would 
delivered to the crystal than to a matched load. An investigation of the 
magnitude of the effect was tlierefore undertaken and it was found that 
the crystal conductance for most units increased by about 30 per cent, 
when the incident power level was increased from 1 mw to 50 mw or more. 
Beyond this level there was veiy little change. With this amount of 
change and if at least 50 mw of leakage power is assumed, the power 
delivered to the crystal would be about 80 per cent greater for the half- 
wavelength spacing than for a spacing equal to an odd number of quarter 


At about this time it was learned that the spike energy was most 
frequently responsible for burnout, and it was therefore apparent that the 
dependence of the spike energy on the load admittance is more important, 
A reliable determination of this dependence or of the eifective admittance 
of the crystal as a function of spike energy has not been made. It is 
felt, however, that the spike energy absorbed by the crystal is less 
dependent on the admittance than is the flat power. A serious burnout 
problem has not been encountered in practice with the improved (uystals 
now available so long as the TR tube is in good condition and the keep- 
alive electrode is functioning properly. The low-level operation and 
matching of the ciystals have been used in almost all mixers to determine 
the line length between the TR cavity and the crystal, at the sacrifice of 

8-18, Harmonic Chokes and Shutters, — ^Another source of crystal 
burnout, especially in very-high-power radar systems (500 kw and up) is 
leakage of harmonic frequencies and spurious intermittent high-freciuoncy 
radiation through the TR cavity. Since the cavities are usually heavily 
capacitively loaded at the breakdown region, the lowest mode giving 
unattenuated transmission with the arc firing is at a frequency two or 
three times the fimdamental frequency. Frequencies this high and 
higher are, however, generated in fairly large quantities, at least sufficient 
to cause crystal burnout by high-powered transmitters. For this reason, 
some of the 10-cm coaxial-line mixers designed for operation with high- 
power systems include a filter circuit that strongly reflects the third 
harmonic. This filter consists of a pair of concentric-line cups on or in 
the center conductor. The cups are a quarter wavelength long at. the 
third harmonic (3 cm) and so spaced that the reflections at tho funda- 
mental frequency cancel one another. These cups can be seen in 
the iris-coupled coaxial-line mixer included in the group of drawings at 
the end of this chapter. The operation of the filter can be easily worked 
out with the aid of an impedance chart. Because the reflections of tho 
two chokes cancel at the fundamental frequency, the effect they have on 
the mker is to produce a phase shift making the electrical length of the 
line (Merent from the physical length. There is also some frcciuoncy 
sensitivity of admittance added because their reflections cancel exactly 
only at the frequency for which the electrical length of the line between 
them is exactly right. 

It has never been established conclusively that the incoi-poration of 
these chokes improves the protection of the crystals. The frequency 
range in which they are highly effective in attenuating unwanted power 
from the transmitter is very restricted. In the course of design of a 
particular high-powered 10-cm radar set, it was established that crystals 
were being burned out by spurious high-frequency signals notwithstand- 

Sxc. 3-18] 



ing the reflection of the chokes. Considerable effort was expended 
in an attempt to eliminate these signals by alteration of the modulator- 
pulse shape, but the difl&culty was not solved until a new ts^pe of gas- 
discharge cavity was added to the conventional TR switch. This 
additional cavity, known as a pre-TR switch, is simply a section of 
waveguide with low-Q input and exit irises with ^ass windows. The 
cavity is filled with gas at a low pressure. When a transmitted agnal 
enters this cavity, the electrical breakdown that takes place is extensive 
in volume and covers a large part of the input iris. Under this condition, 
it is effectively cut off for all frequencies in addition to the fimdamental 
frequency, although the fundamental-frequency leakage is still sufficient 
to operate the conventional TR switch following it. A circuit of this 
type is considerably more effective than harmonic chokes in b ringing 
about complete crystal protection and it is certainly the task of the 
TR-cavity system and not the mixer to provide such protection from 
high-level signals. The more recent TR cavities having wide bandpass 
characteristics, using several resonant irises as well as resonant input 
and output windows, include protection of this kind. Harmonic chokes 
are therefore superfluous for operation with such TR switches. The 
details of these two TR-switch systems and their functions will be found 
discussed in Vol. 14 of this series. 

Another device often added to the mixer in radar systems is a switch 
for protection against signals coming into the anteima during inoperative 
periods. The TR cavity, when properly operating, protects the mixer 
crystal from burnout not only by the signal of the local transmitter, but 
also by any other signal coming into the antenna. Any signal suffi- 
ciently strong to damage the crystal will cause the arc in the TR tube 
to fire and, therefore, the signal power is limited to a safe level in the 
mixer. Satisfactory operation of the TR switch, however, depends on 
the universally used keep-alive electrode, which maintains a small steady 
discharge in the gas volume of the tube, maintaining a small supply of 
ions to initiate an arc when a large voltage is built up across the gap of 
the cavity. If this keep-alive arc is not operating, as it is not when the 
supply voltage is shut off, the breakdown of the TR tube at high level 
requires considerably greater voltage and time to occur, and the result 
is that very large leakage energy is allowed. Thus signals may be 
transmitted through a TR cavity, in which the keep-alive electrode is 
not activated, in sufficient strength to damage the mixer crystal. It 
is also possible that the first few pulses of the local transmitter, which 
may occur before the keep-alive is fully operative, may damage the 
crystal. For protection against these two sources of power, a mechanical 
switch has sometimes been included in the mixer. The switch decouples 
the mixer crystal from the TR cavity when the system is turned off. 


and thi'ough the action of a magnetic solenoid or a motor the switch is 
opened with a small time lag after the system is turned on. 

Devices that are useful as switches for this purpose are few. Many 
structures can be coupled to a coaxial-line mixer or to a waveguide mixer 
to reduce the signal arriving at the mixer crystal by 30 or 40 dp. 
Usually, however, it is found that the principal effect is one of detuning 
and that the attenuation of signal power at some adjacent frequency is not 
many decibels greater than at the original frequency with the stmcture 
removed. This is true, for instance, of a simple short-circuiting rod 
between the inner and outer conductors of a coaxial-line mixer. Such 
a rod has a large self-inductance and it acts like an inductive susceptance 
across the line. Its effect can be resonated out by a susceptance at the 
TR cavity to a degree depending upon the electrical line length between 
the short-circuiting rod and the TR cavity. 

The most foolproof method of obtaining the required protection 
during shutdown periods is to disconnect the crystal completely from 
the circuit. This has actually been done in some 10-cm coaxial-line 
mixers by use of a structure like that shown in Fig. 3*37. The smaU- 
diameter rod is pulled back by a spring when the power is turned off and 
advanced into the fingers at the upper end by a solenoid when the power 

is on. The gap between the fingers and the 
end of the small rod is a waveguide beyond 
cutoff for the signal frequencies and, there- 
fore, a large attenuation is introduced if the 
rod is retracted from the fingers by an 
amount of the order of the diameter of the 
coaxial line. The particular mixer in which 
this mechanism was used possesses a rather 
large standing-wave ratio, paitly because of 
the presence of lengths of line of differing 
characteristic admittances. As a conse- 
quence, the admittance at the iris is fre- 
quency-sensitive and the mixer must be 
retuned if the frequency is changed by 1 per 
cent or more. The tuning is provided 
by making the coaxial line variable in length by a telescoping joint. A 
disconnect mechanism of this kind has not been applied to the wideband 
mixer where the coaxial line must be of uniform impedance to avoid 
large standing-wave ratios. 

Figure 3*38 shows another mechanism that has been applied to 
10-cm coaxial-line mixers. A resonant stub a half wavelength long is 
used to produce a short circuit across the mixer line. A short circuit 
on the stub, actuated by a solenoid, makes it effectively a quarter-wave- 

r^G. 3-37. — Crystal discon- 
nect mechanism, in 10-cm iris- 
coupled coazial-line mixer. 

Sec. 3-18] 



length, stub when the system is operating. It thus has little effect on 
the circuit during operation, but during shutdown periods it is effective 
in decoupling the crystal in a narrow frequency region for which the stub 
produces a very large shunt admittance across the line. The systems in 
which this device was used all operated inside a ±1 per cent band, and 
the main protection they needed was from radiation in the same band. 
The narrow band of large decoupling was therefore considered sufficient. 
It does not give protection against power at other frequencies or against 
damage by the local transmitter which sometimes occurs during the 
first few transmitter pulses. 

The most effective devices not involving an actual disconnection from 
the crystal are sliding metallic shutters. In 10-cm systems uang TR 

Fia. Ji- 38 . — Hiilf-wavoloiigth-line crystal-disconnect switch. 

switches liaving external cavities, a metallic shutter made from curved 
thin phosphor bronze with two pieces spot-welded with their convex 
surfaces together can be used. The shutter enters the cavity through 
a slot in the side wall and slides in grooves in the top and bottom walls, 
completely covering the output loop or iris. A drawing of this device 
is shown in Fig. 3-39. A shutter of this kind gives very good protection 
against radiation at all frequencies and has as its major disadvantage 
the requirement of an operating device capable of moving it through a 
large distance. 

A shutter of the same kind is the most effective one for use in wave- 
guide mixers and TR switches having integral cavities. The shutter 
enters a slot in the side wall (narrow dimension) of the waveguide between 
the ciystal and the TR cavity and slides in channels in the top and bottom 
walls. It again requires a large motion since it must be all the way across 


the waveguide when closed and completely removed when open. A 
ratchet-relay motor has been used to operate such a shutter, although 
it should also be possible to use a rotary motor with proper springs and 
limit switches. 

A simple post has been used as a shutter with fair success in the 3-cm 
band. The post, sliding in a choke mount such as used for tuning screws, 
enters the center of the wide side of the waveguide and crosses to the 
bottom wall. At a given frequency, the post can be made to attenuate 
most effectively when it projects just less than the full width, for it is 
then resonant and completely short-circuits the waveguide. For com- 
plete protection, however, it is 
better to make the post contact 
the bottom wall of the waveguide; 
thereby it presents a large induc- 
tive susceptance across the wave- 
guide. The effect of the post 
increases with the post diameter, 
and to minimize the danger of 
resonance with the TR cavity a 
spacing of one-quarter wavelength between the post and the effective 
position of the TR cavity is best. With a waveguide 1 by i in. OD in 
the 3.13- to 3.53-cm band, a -jf^-in.-diameter post gives attenuation greater 
than 30 db at all frequencies in the band. 

3-19. I-f Output Admittance, — It is not within the scope of this volume 
to give a discussion of the circuit coupling the mixer crystal to the i-f 
amplifier. Such coupling circuits, however, must be designed with 
knowledge of the admittance associated with the output terminals of 
the mixer. The most widely used circuits are wideband doubled-tuned 
admittance transformers, or their equivalent, designed to give the 
best possible noise figure compatible with the bandwidth requirements. 
The susceptance part of the mixer is a part of the first tuned circuit where 
it is resonated in shimt. Obviously, the circuit will be incorrectly tuned 
if the susceptance of the mixer is not the expected value and the noise 
figure and bandpass characteristic suffer. The conductance part of the 
mixer admittance determines the degree of coupling in the double-tuned 
circuit and values smaller than the design value result in the double- 
peaked frequency response characteristic of double-tuned circuits with 
more than critical coupling. 

It has been customary in the design of i-f amplifier input circuits to 
use a “ dummy '' mixer, that is, a mixer with a resistor replacing the 
crystal and having the i-f resistance of an average crystal in the same 
mixer under operating conditions, in place of an actual operative mixer. 
Such a procedure is not strictly correct since the susceptance component 

Fig. 3*39. — Protecting shutter in a 10-cm TR 

Sec. 3.19] i-F OUTPUT ADMITTANCE 179 

of the mixer is not that of the linear parts of the circuit if a resonant 
circuit is used ahead of the crystal in the r-f system. As shown in 
Chap. 2, the reflection of the image frequency can change not only the 
conductance part of the i-f admittance from the value obtained if the 
image wave is not reflected, but also the susceptance part. This effect 
mth good crystals and with a 30-Mc/sec intermediate frequency can be 
equivalent to adding or subtracting 3 or 4 /ijuf of capacitance at the output 
terminals of the mixer. Coupled with the fact that the conductance of 
the ciystal in the mixer may be from one-half to twice the value for the 
same ciystal in a nonresonant circuit, it is obvious that the i-f input 
circuit must be designed on the basis of measurements on the particular 
mixer to be used, with representative crystals and under operating 
conditions at the frequency to be used. 

It'ui. l-f aidinittHiico vs. LO frequency with the TR tuning fixed. 

The situation is further complicated by the fact that the phase 
length” between the TR cavity and the crystal seems to vary from crystal 
to ciystal, es])ecially for ciystals made by different manufacturers. 
This means that, even at a fixed frequency, the i-f admittance may 
vaiy more from crystal to ciystal in a resonant mixer circuit than in the 
nonresonant test mixers. For this reason, it becomes necessary to design 
the input circuit in such a way that changes in conductance by a factor 
of about 2, and in susceptance of about 2 ^/xf or more at 30 Mc/sec can be 
tolerated. When the mixer is to be used over a wide band, changes as 
large as these are (jertain to occur, even with a single crystal, because of 
the change in effective line length between the TR cavity and the crystal 
and the consequent change in phase of the image-frequency reflection, 
even though this (^ITec.t is minimized by the choice of a line len^h as short 
as possible. Measurement of the i-f admittance of the mixer should 


therefore be done at several frequencies scattered through the operating 
band before the final form of the i-f input circuit is decided. 

It was shown in the previous chapter that, if the signal-frequency 
admittance connected to the input terminals of the mixer is kept matched 
to the crystal and the image-frequency admittance is varied through tht’i 
full range of pure susceptance, the i-f admittance should traverse a circle 

on an admittance chart, with a diameter related to tlm c^Btal loss 
crySSL described above are most serious wth tho best. 

S fi ^ receiver with optimum valuta of 

eifects^Stb characteristics by completely ignorinff these 

eifects mtb cryst^s havmg conversion losses of 10 db or more As tho 
c^tals improve it may become more important to dL^ tho r^ixtr 
on the basis of the i-f output characteristics than on theT-f matching 

Sec. 3-19] 



characteristics if, indeed, it is not so already with crystals having conver- 
sion losses of 6 db and less. 

In order to nunimize the effects of the variation of i-f admittance from 
crystal to crystal and with frequency, it may be found that the line length 
from the crystal to the TR cavity which gives an i-f admittance falling on 
a particular part of the admittance circle may be preferred. For instance, 
the line length might be chosen in such a way that an average crystal at 

— Jo.312'W 

Fig. 3*42. • CJroHH-Hootioual view of loop-coupled mixer. 

midband frequency gives an i-f admittance with the maximum conduct- 
ance. Variation of frequency or of line length with different crystals, 
would then result in a small variation in conductance, since the conduct- 
ance is stationaiy with i-espect to line length. However, the largest 
possible variation in susccptance results. The same would be true for a 
line length giving minimum conductance, as a consideration of the circle 
on an admittancci diagram will show. On the other hand, if a variation 
in conduc.tarice is more tolerable than a variation in susceptance, the 
lino length can be chosen between theses two values, where the susceptance 


is stationary with small variation in line length, but has a value differing 
from zero by the marimum amount. There is also the desire for mini- 
mum possible crystal conversion loss to be considered, which may set a 
different requirement on the phase of the image-frequency reflection. 

In one instance in the author's experience the variation in i-f output 
admittance of a mixer with change of crystals and with frequency was 
considered so serious that a makeshift remedy had to be applied to the 
mixer to change its effective line length. This mixer was a 10-cm iris- 

or m21B crystal withotit. a 

mput Une is sj|p^?Sd C a stub^U^ TbSSiK LoToupliS®in^iho njo. “The 

coupled coaxial-line roixer used tvith selected low-loss crystals. It was 
found that the line length was such that the maximum possible variati<in 
in conductance occurred in the 8 per cent frequency band for whic^h it was 
intended. The makeshift remedy was the insertion of a polystyrene 
deeve into the coaxial line of the mixer, in order to change the elToc.tive 
length to one giving maximum conductance at midband frequency with 
an avera^ c^tal. With the iris-coupled mixer, the image is reflecstcd 
Tb TR ca,vity but by the short circuit in the coaxial line on the 

instance, added an 

extra half wavelength to the image-frequency line, bince the crystal 

Sec. 3 - 19 ] OUTPUT ADMITTANCE 183 

was about one wavelength, from the TR cavity, the total image-frequency 
lirift length was large and the variation of admittance with frequency was 
sufficient to make the susceptance change from minimum to maximum 
in the 8 per cent band, after the sleeve was added. This was less 
serious than the previous large variation in conductance. The proper 
insertion of the coupling iris into the TR cavity had to be redetermined 

Kig. 3.44.— TriH-oouplMl mixer for 1N21B cryHtiil« in S.O-to-fi.fUoii Imi.d with TU cavitj’ 

shown in Fiff. -MS (24 -179). 

after the addition of the sleeve because of the effin-.t of the sle(w<^ on tlu^ 
admittance prestmtetl by the crystal at the iris. 

Figure 3-40 shows a (lualitativo picture of the result of an expenment 
that was done in connection with the measurement of the variation of 
i-f admittance with freciuoncy. Here many effects arc obvious at one 
time. The TR cavity, detennining the most sensitive signal frequency, 
was fixed at a frequency at about the middle of the chart. Ihe i-f 
admittance was then measured as the local-os<“,illator frequency was 
varied. The main effect observed is a variation of conductance in an 
approximately sinusoidal fashion, except in the region of the two fr(^- 


quencies that differ from the resonant frequency of the TR cavity by just 
the intermediate frequency. In the example shoAMi, these frequencies 
occur near minimum conductance, and the conductance rises about half 
way to the mean value at each of these frequencies. Associated with 

Fig. 3*45. -Cavity for 1B27 TR tube for 8.0-to-8.8-cm band and iris-coupled mixer. The 
cavity is 1.400 in. ID and the mixer center line is 0.783 in. from the cavity center. 

6-32 Machine 

Crystal mount 
Adjustment screw - 
2K25 antenna-^ 

SCTO IX/sq.' 

Detail of coupling- 
adjustment screw 

I ■ r r r i f i.a 

Fig. 3*46.— a crosa-sectional view of the mixer, shown in Fitr fOA e 

each IS an exc^ion of the susceptance and its value passes through zero 
m the opposite sense at each of the two frequencies. These two frc- 

frequencies at wMch the local oscillator 

th^ W T !l frequency of the TR cavity, 

and the line length and frequency of the TR cavity correspond to mini- 

Sec. 3 ‘ 20 ] 



mum conductance variation and maximum susceptanoe variation with 
frequency. Outside these two regions the susceptanoe is approximately 
zero because of the compensating effect of the reflection by the TR cavity 
of both sidebands. The susceptanoe component appears when one of 
the two sidebands is not completely reflected to the crystal by the TR 
cavity. The excursion of the conductance is about twice what it would 

Km. viow of inixor for 3.2, with channel for LO coupling. 

ThiH mixer iH UMod with 1N23A and IN23B cryntals, no TK cavity, and 2K26 LO tube in 
the 7()-volt mode. 

1)(^ if the ''PR cavity wore kept at a frequency differing from that of the 
local oscillator by the intermediate freciuenc.y and the two were tuned 
together. This figure is given only as a sample of the ])ossiblo variation 
of the i-f admittance. The effects for various line kmgths can be esti- 
mated with the aid of the linear network representation of the mixer 
and an admittancjc chart. 

3-20. The Completed Mixer —There follows a set of drawings, 
Figs. 3*41 to 3*52 inclusive, giving important dimensions of each of 


several mixers representing applications of the foregoing circuits. On 
each drawing is indicated the type of crystals and the wavelength band 
for which it is intended. Those units intended for use in conjunction 
with a TR cavity and those which operate directly from a wideband 
antenna are identified. For the iris-coupled 8.5-cm mixer, the position 

of the iris in the TR cavity is an important detail, since it determines 
the tuning condition. A separate drawing of the part of the TR cavity 
for a 1B27 tube in which the mixer is to be mounted is included among 
the drawings. 

A drawing has also been included of a tunable resonant mixer known 
as a “pot” nuxer. This is the only available example of a resonant 

Sbo. 3-20] 




mixer. It was used in very early radar systems but was soon di Bc n,r ded 
in favor of the sim pler fixed-tuned mixers. The resonant feature is 

I^a. 3-60. — Tunable resonant niizer for 10-om band. 

unnecessary in a radar system since it already includes a cavity filter in 
the form of the TR cavity. The tuning procedure with a tunable TR 
cavity and a tunable mixer is very complicated, because these two 

Fig. mixer for ±4 per cent band centered at 10.7 cm; for use with 

1K21B crystals, 2K28 LO tube. A resonant TR tube is not required. 

devices cannot be tuned independently. A tunable resonant mivAr may 
be useful in other applications, however, and for this reason the drawine 
has been included. * 



It is often desirable to Lave, in a radar system, a mixer that serve^ 
several purposes in addition to the principal one of converting 
received’ reflected signal of the transmitter into the intermediate fr^ 
quency. Some of these functions are peculiar to radar systems and thei^ 
operational applications and are of little interest to the designer of mixer^ 
for other purposes. Since, however, a very large part of the task oj 
mixer design has been concerned with the problems associated witl^ 
these multiple-function mixers, and since it is probable that similar needsj; 
will exist in many future mixers, a description of these problems and thei^ 
solutions will be given in this chapter. As is true for the simple mixer^ 
there is no unique solution to a given design problem. The material 
given can only serve to show what has been done and to point out some 
of the relative merits of various solutions. 


4 * 1 . The Beacon Problem. — ^An example of the kind of device 
described by the term “multiple function mixer, is the mixer -vyuth the 
beacon feature for airborne radar systems. In conjunction with t-he use 
of radar as a navigational aid, a system of coded-pulse bea(*-ons has been 
set up. A switch in the airborne radar changes the system from a radar 
system to a system which sends out pulses of the proper cluiriw*.tcM-istics to 
trigger a response from a beacon transmitter. The beacon i-(>sponse 
comes back to the airborne radar after a time deteimincd, in th(^ same 
way as for a radar echo, by the distance to the beacon, and at an azimuth 
that shows the direction of the beacon with respect to the heading of the 
airplane. The beacon feature requires of the receiver the same general 
things as does the radar system, except that the beacon frcxpKmcy is 
usually different from that of the radar transmitter. For instance, 
most airborne radars for the 3-cm band operate anywhere in a fre<iiiency 
band from 9320 to 9430 Mc/sec, the precise frequency depending upon 
the particular transmitter, tube used. The beacon receiver responds to 
this whole band of frequencies but its transmitter replies at 9310 Me /sec — 
outside the band — ^to reduce confusion between echoes and beacon signals. 
Thus it is required that the switch that turns on the beacon fe^ature 
change the tuning of the receiver from the local transmittei* frequency to 


Sac. 4*2] 


9310 Mc/sec. A similar arrangement is used in airborne radar for the 
9-cm band. 

To accomplish the change in receiver frequency, it is necessary to 
alter the local-oscillator frequency. In the 9-cm systems that have 
2K28 local-oscillator tubes with external cavities this is accomplished 
through the use of a switch-actuated solenoid that changes the position of 
a tuning plug in the cavity by the correct amount. When the system is 
correctly tuned, the limiting positions of this plug are so adjusted that 
the local oscillator is at the right frequency to receive the radar signal 
at one limit and the beacon signal at the other. To miniinize the amount 
of tuning required of the plug, the local oscillator can be operated on the 
low-frequency side of the transmitter frequency and on the high-fre- 
quency side of the beacon frequency, if the beacon is just outside the band 
on the low-frequency side. With this choice of sidebands, however, there is 
danger of interference between the beacon and the radars at the low- 
frequency end of the band because, if the local oscillator is tuned for 
beacon reception, the image frequency of the receiver is in the radar band. 
Because of the danger of such confusion it was at first considered neces- 
sary to tune the local oscillator to the low-frequency side of the beacon. 
The difficulty of making a tuning plug that would give such a large range 
was, however, very great. 

With tubes of the 723A/B, 2K25, and 726 types, in which the cavity 
is an integral part of the tube, a tuning plug cannot be used. In radar 
sets in which these tubes are used — ^notably the 3.2-cm airborne systems — 
two separate local-oscillator tubes and coupling circuits are therefore 
provided for each mixer. The tubes are tuned, respectively, to the 
proper frequencies to receive echoes or beacon signals, and the radar- 
to-beacon swit(ffi turns one off and the other on. One of these oscil- 
lators is called the radar IjO and the other the beacon LO. When the 
723A tube was coupled to the mixer by the insertion of its antenna an 
adjustable amount into the mixer waveguide, an odd number of quarter 
wavelengths away from the effective position of the TR cavity, the 
provision for the beacon feature could be made easily. All that was 
necessary was to drill another hole in the same side of the waveguide or 
in the opposite side and use a second adjustable tube mount. Since 
the oscillators did not operate well in this kind of coupling circuit, and 
because provision for radar and beacon automatic frequency control 
(AFC) demanded more complex arrangements, such mixers are com- 
pletely obsolete. Instead, the coupling circuits described in Chap. 3 
have become more extensively applied. 

4*2. Single-channel Automatic Frequency Control. — One major- 
source of loss of performance of a radar system is the mistuning of the 
receiver resulting in a less-than-maximum sensitivity to echo signals. 



[Sbc. 4*2 

As shown in Chap. 1, the requirement of frequency stability of the local 
oscillator in the superheterodyne receiver is very stringent. It has 
consequently been found almost impossible to obtain as good results from 
a radar system in which the local oscillator is tuned manually as from 
one in which it is tuned automatically. As a consequence, all recent 
radar systems include automatic frequency control of the local oscillator. 
This not only removes the frequency-stability requirement from the 
local oscillator but ensures that the oscillator will maintain the i-f differ- 
ence from the transmitter frequency, even if the transmitter drifts. A 
detailed discussion of the various electronic control circuits is given in 
Chap. 7, and it is the task of the present section to present the details of 
the special microwave components that are used in conjunction with 
these circuits. 

The amplest AFC circuit is one which branches from the i-f amplifier 
after two or three stages of amplification, where such a branch has a 
ne^gible effect on the receiver noise figure. Since the TR cavity does 
not give complete elimination of the transmitted signal, an i-f beat is 
produced between the local oscillator and the leakage signal from the 
TR cavity. This beat-frequency can be used to actuate the frequency- 
control circuits. A circuit of this type was used in some of the first radar 
sets having AFC but it has never been found satisfactory for field- 
operated sets. There are several possible reasons for this, no one of 
which has been isolated as the prime source of trouble and eliminated. 
They all stem from the facts that it is impossible to control the power 
level of the leakage signal from the TR cavity, and that this leakage 
sigixal does not necessarily have the same frequency spectrum as the 
main transmitter signal. The leakage signal has a power level, at the 
mixer crystal, at least 10 and sometimes 100 times the power level of 
the local oscillator. As a result, the mixer is operated at a level far 
above that for which it was designed. There is also the spike energy, of 
very large amplitude but short duration, which definitely gives the TR 
leakage signal a frequency spectrum different from that of the ti-ue 
transmitter pulse. In addition, spurious transmitter frequencies, which 
may include a very small fraction of the energy in the main pulse, may 
be tr ansmi tted throu^ the fired TR switch to the mixer with the same 
amplitude as the main pulse and the AFC circuit may lock to such a Hignal 
instead of to the correct one. 

^ Another argument against this simple kind of AFC is its suscepti- 
bility to interference signals. A signal, from an external source, just 
large enough to overload the mixer crystal would produce an i-f Bignn.1 
of about the same amplitude as produced by the transmitter. It is 
therefore conceivable that such a signal could compete for control of the 
local oscillator. Schemes involving the use of time-selective gates, 

Sec. 4*3] 



synchronized with the transmitter pulse, have been suggested to eliminate 
this difficulty by making the frequency-control circuit sensitive only 
during the period of transmission. Because of other difficulties involved 
in their use, however, gated systems have not been widely employed. 
The net conclusion drawn from experience with the simple AFC scheme 
is that a particular radar system with a given set of components — ^trans- 
mitter tube, local-oscillator tube, TR tube and crystal — can be adjusted 
so that it will operate satisfactorily, but that the adjustment is not 
permanent and the system requires frequent readjustment to remain 
operative. A change of any one of the components involved may 
require readjustments of the circuit to eliminate spurious output voltages 
from the control circuit. The device, therefore, does not stand up well 
under field conditions. 

4-3. Separate-mixer AFC.— As an alternative to the use of the AFC 
system just described a completely separate mixer may be provided for 
the AFC circuit. The input signal is derived from the Tr\A.m transmitter 
signal by way of a path having high attenuation but containing no 
nonlinear elements. The input signal obtained in this way has amplitude 
and frequency characteristics that are identical with those of the trans- 
mitted pulse. The local oscillator must be the same one that is used 
for the radar mixer, since it is the frequency of this oscillator that must be 
controlled. The AFC circuit following the mixer is thus completely 
separate from the receiver circuit and can therefore have different 
bandpass characteristics if necessary. All the objections to the single- 
channel system are eliminated by this scheme, provided that signals 
from the TR switch in the radar mixer do not leak by way of the local- 
oscillator path, into the AFC mixer. Under this condition, the amplitude 
of the transmitter signal in the mixer can be set at the most desirable 
level by choice of the attenuation used. The danger of losing control 
to a jamming signal is eliminated because any signal in the main line of 
the system suffers the same attenuation as does the transmitter signal. 
A jamming signal, to cause any trouble, would have to be of about the 
same strength as that of the local-transmitter signal, which is obviously 

The major prol)lcm of the separate-channel-AFC system is to operate 
two similar mixers from a single local oscillator, with as large an'attenu- 
ation as possible between the signal circuits of the two mixers by way of 
the local oscillator. In addition, the signal-coupling circuit for the AFC 
mixer must be designed to give the required signal level over whatever 
frequency band is to be used. With regard to the problem of local- 
oscillator coupling, it is immediately apparent that the branching to the 
two circuits must occur on the local-oscillator side of the mixer-to-LO coup- 
ling circuits, since then a signal leaking from one mixer to the other must 



[SBC. 4-8 

suffer the coupling attenuation twice. The percentage of leakage signal 
reaching the local-osdllator circuit is the same as the percentage of 
the available LO power coupled to the crystal. From the local-oscillator 
circuit to the second mixer, the leakage signal suffers the same attenu- 
ation as does the LO power. Thus it is advantageous to have a local 
oscillator with a large available power, coupled to the crystal through 
a large amount of attenuation. 

In the 10-cm region where coaxial-line mixers are used, coupled to the 
local oscillator by means of cables, the double-mixer scheme is provided 
through the use of two simple mixers connected by separate cables to 
separate pickup loops in the local-osciUator cavity. Each of the loops is 
tightly coupled to the cavity so that sufScient power is incident in the 

Fig. 4*1. Block diagram of r-f cirouit for separate-channol radar and AFC ooaxinl lino 
mizers. (o) Double-loop LO coupling; (b) single-loop LO coupling. 

LO injection circuit of each mixer to allow reasonably weak couplini^. 
The attenuation between the two signal circuits, known as the cross'' 
attenuation, is increased because the signal must travel between the 
loops in the oscillator cavity. Since the cavity is resonant at the local- 
oscillator frequency, which differs from the signal frequency by th(' 
intermediate frequency, there is some reflection of the signal and a 
consequent increase in cross attenuation. If oscillator tubes having 
only a single output line (such as tubes of the 726 type), are used, th(^ 
two mixers must be connected by a branched line or T-junction. Thc^ 
effect of the detuned local oscillator can be obtained through the choice 
of the line length between the local oscillator and the T-junction. If 
this length is so chosen that the line into the local oscillator acts as a 
short-circuiting stub when the local oscillator is detuned, the maximum 
attenuation is obtained. With tubes such as those of the 726 type, 


the proper length of this line varies greatly with frequency because of the 
relatively long line included in the tube. Consequently, the amount of 
attenuation gained over a frequency band of several per cent is small and 
perhaps not worth the effort of determining the best line length. Single- 
loop T-junctions have been used with cavity oscillators such as the 2K28. 
For these oscillators the effective stub-line length can be made only 
one-half wavelength and the attenuation gained is therefore large. A 
block diagram illustrating these two connections is given in Fig. 4* la and 
6. Figure 4-2 shows the added cross attenuation due to reflection at the 
T-junction as a function of frequency. It has been assumed here that 
the admittance of the stub line 
ending in the loop has the frequency 
dependence of a half-wavelength 
short-circuited line, and that the 
local-oscillator cavity is completely 
nonresonant at the signal frequency. 

The reflection coefficient for a wave 
traveling toward the cavity in this 
line is therefore unity. The line is 
made to be resonant at the midband 
wavelength, and the curve shows 
the reflection loss as a function of 
the ratio of the actual signal fre- 
quency to this midband frequency. 

In practice, somewhat less attenu- 
ation than this will be achieved, especially near resonance. For a longer 
line, sucli as would result with a tube of the 726 type, the frequency 
scale may ])c changed by the appropriate factor. 

It is important, when trying to supply two mixers with local-oscillator 
power from a single oscillator, that the standing-wave ratio in the local- 
oscillator cables be small. This can be accomplished through the use of 
attenuating cables or by means of the resistor-disk ternoinations in the 
local-os(illator circuits of the mixers, as described in Chap. 3. The 
splitting of the power between the two circuits at the T-junction is 
determined l)y the admittances which appear in parallel. If a large 
standing-wave ratio existed in the lines between the mixers and junction, 
a large conduc.tanc.e could result for one line and a small one for the other, 
with the result tliat one mixer would receive almost all of the available 
local-oscillator power, and the other almost none. With a situation 
giving equal splitting of the power, about 20 mw of power may be sent 
to each mixer. Sinc(^ each crystal requires about 0.5 mw of local- 
oscillator drive, the attenuation between the mixer circuit and the local- 
oscillator circuit is al)out 16 db. Thus the cross attenuation, neglecting 

Fia. 4*2. — Added cross-attenuation due 
to reflection at T-junction vs. relative fre- 
ciuoncy, with half-wavelength line between 
the T-junction and the local-oscillator 



[Sec. 4*4 

the contribution of the power-splitting circuit, is about 32 db. If the 
amount of TR leakage power is 50 mw, the signal that it produces in 
the AFC mixer is, therefore, reduced to about 0.03 mw. Since the AFC 
signal is set at about 2 mw, it exceeds the spurious signal from the TR 
switch by at least 18 db. A larger safety factor than this is to be desired, 
and the additional attenuation by the LO cavity or by the T-junction 
is helpful. 

44. The Coupling of the Transmitter Sample. — ^The sample of trans- 
mitted power that constitutes the signal in the AFC mixer is usually 
coupled through a cutoff” attenuator to the mixer. This consists of a 
circular pipe of too small a diameter to allow unattenuated propagation 
of the wave in question. The coupling of this attenuator to the main 
transmitter waveguide or coaxial line is accomplished by means of a hole 
in the wall of that line; the coupling to the mixer is done by the conven- 
tional loop or iris. The action of the cutoff attenuator may be analyzed 
in the following way. The wave traveling along any waveguide is 
described by the relation 

where co is 2?r times the frequency, E is the amplitude at the point x and 
at the time t and is the maximum amplitude. The quantity k is the 
wave number and is equal to 2w/\gy where is the wavelength in the 
waveguide. This is 

where \e is the cutoff wavelength of the waveguide and Xo is the free-space 
wavelength of the wave in question. Thus, the wave is described by 

times the term in the time. For wavelengths longer than the cutoff 
wavelength, the quantity in the radical is negative and the wave does not 
propagate in the ordinary sense. Equation (1) can then be written in 
the form 

E = Eoe (xO ]* ^ 

showing that an exponential decrease in amplitude occurs for a wave- 
length longer than the cutoff value. The ratio El/E^ is the power 
attenuation between points that are x centimeters apai*t in the w^aveguide, 
if Xo is expressed in centimeters. Written in decibels, this attenuation is 


For a guide of circular cross section, the cutoff wavelength of the lowest 
mode is 1.71 times the diameter. Thus 

If the diameter is small compared with the wavelength, the attenuation 
is independent of the wavelength. This is a desirable property for an 
AFC mixer that is to be used over a wide band. For diameters this small, 
the attenuation is just 31.9 db per diameter. 

The amount of attenuation needed is the ratio of the transmitted 
power to the signal level desired in the mixer. For a 600-kw system and 
2 mw in the mixer this is 2.5 X 10«, or 84 db. It is not possible to use an 
attenuator pipe giving 84 db in its length, however, because the coupling 
factors between the main waveguide and the attenuator and between the 
attenuator and the loop of the mixer must be taken into account. For 
this reason the attenuator should be designed for an attenuation about 
30 db less than the total, to allow a large decoupling factor, so that the 
reflection of the main signal in the transmitter line of the system will be 
small. It is diflSicult to calculate the end effects and the final design of 
the attenuator is best found experimentally. One tentative unit can 
be built and tested and then corrected, by means of Eq. (2), to give the 
right power level at the mixer crystal. 

A serious shortcoming of the cutoff attenuator in this application is 
that it has no attenuation at wavelengths shorter than its cutoff wave- 
length. In a particular example a cutoff attenuator was used that did 
not transmit frequencies as high as the sixth harmonic but transmitted 
the seventh and higher. It was found that trouble with the AFC circuit 
was attributable to the presence of signals in this high-frequency range 
in the mixer. The system operated at 10 cm but a large signal could be 
detected in a crystal mounted in a 1.25-cm waveguide (0.170 by 0.420 in. 
ID) of sufficient length to attenuate the 10-cm signal to a negligible level 
when that waveguide was held in the position of the AFC mixer at the 
output iris of the cutoff attenuator. It might be argued that an attenu- 
ator of smaller diameter would be the solution, but just how much smaller 
it would have to be would be a difficult question. It was thought better 
to add to the cutoff attenuator a device that would have increasing attenu- 
ation with increasing frequency. A satisfactory device of this kind was 
found in the form of a sheet of carbon-coated Bakelite resistance card of 
500 ohms per square. The card was cut into a rectangle of a width equal 
to the diameter of the attenuator and a length about a quarter-inch less 
than the distance from the waveguide end of the attenuator to the loop 
of the mixer. When this sheet was inserted into the attenuator so that 
its plane was in the plane of the electric field vector in the attenuator, 
the high-frequency transmission was reduced well below the point of 



[Sbc. 4*4 

being troublesome. The attenuation of the power at the fundamental 
frequency was affected very little and the specific resistance of the strip 
was found to be of little importance to its efficiency in attenuating the 
high-frequency components. All attenuators subsequently designed 
contained dissipative attenuators as a precaution against trouble with 
high frequencies. For the 3-cm band a short cylinder of polyiron, 
inserted into the attenuator, is found to be more effective than the 
resistive sheet. At 1.25 cm, a matched polyiron attenuator in the mixer 
waveguide is used in addition to the cutoff attenuator. This polyiron 
attenuator is designed to give an attenuation of 20 db at the fundamental 
frequency. It is used also to reduce the leakage of transmitter signal into 
the AFC mixer at the joint between the cutoff attenuator and the mixer 

Side wall of 

Fig. 4*3. — Coupling attenuator for AFC, used in 10-cm, 500- to lOOO-kw waveguide 


waveguide. Because the polyiron pad is matched into the waveguide 
from both directions, it also provides a matched generator for the AFC 
signal at the mixer crystal. The direct use of the cutoff attenuator, on 
the other hand, provides essentially a constant-voltage generator, with 
the result that the power level at the mixer crystal is strongly dependent 
on the crystal admittance. The matched resistive attenuator, however, 
cannot be used with a mixer having an LO coupling circuit that requires 
reflection of the local-oscillator wave that travels toward the signal line. 
Mixers intended for use with a narrow-band TR switch, therefore, cannot 
be used with such an attenuator. 

Figure 4-3 shows an attenuator used to derive the AFC signal in a 
10-cm, 500-kw waveguide system. The attenuator can be coupled on 
either the wide or the narrow side of the waveguide, but on the wide 
side it must be in the center. A loop-coupled mixer (see Fig. 3*40) is 
mounted on the other end of the attenuator and the plane of the loop is 



the same as the plane of the resistance strip and the electric field vector 
in the attenuator. 

4*6. Two-channel Mixers for All-waveguide Systems. — In the 
1.26-cm and the 3.13- to 3.53-cm bands, where the local oscillator must be 
coupled to the mixer through waveguide, the two-channel mixer is made in 
a single unit. By means of the coupling circuit of the channel or iris type 
described in Sec. 3-5, one mixer is coupled on each side of the local- 
oscillator waveguide. Figures 4-4 and 4*5 show the most commonly 
used mixers employing these principles in the two bands mentioned. 
All indicated dimensions are equivalent electrical lengths and must be 
corrected for end effects, as discussed m the preceding chapter. The 
entire 1.25-cm mixer, including the coupling chokes, is machined from a 
solid brass block. Figure 4-5 shows the 20-db polyiron attenuator just 

Fig. 4-4. — Two-ohannol mixer for use in the 3.3-cm wavelength band. 

described, in place in the AFC mixer. The coupling to the main wave- 
guide is through a small hole in the wall at the end of the waveguide 
running from the main guide to the mixer, and the size of the hole is 
chosen to give the ro(iuired total attenuation between the transmitter 
and the AFC mixer crystal. 

Because it would l)c very difficult to make the duplexer and mixer to 
such close tolerances that both tlic radar mixer and the AFC mixer could 
be rigidly conncc^ted to the duplexer, these two pieces have been so 
designed that one limit of the tolerances brings both channels into contact 
witli their corre^sponding members on the duplexer and the other limit 
leaves a gap on the AF(1 side. The only danger this entails is that of 
leakage of signal into tluii AFC mixer from the outside. As has been 
mentioned, the dissipative attenuator in the 1.25-cm mixer reduces that 
danger. In the mixer, this difficulty is eliminated by the inclusion 
of the cutoff attenuator as a part of the mixer rather than as a part of the 



[Sbc. 4-6 

In both these mixers a resistance strip is used as a matched load in 
the local-osciUator waveguide. This strip has an effect analogous to 
that of the resistor disk used in the coaxial-line mixers. It has a con- 
ductance equal to the characteristic admittance of the waveguide plus a 
capacitive susceptance due to the dielectric constant of the Bakelite 
base. This susceptance is resonated out by short-circuiting the wave- 
guide less than a quarter wavelength behind the strip. The specific 

resistance used at 3.3 cm is 500 ohms per square and the distance from the 
back of the strip to the end wall is 0.265 in. In the 1.25-cm waveguide a 
400-ohm-per-square material and a distance of 0.048 in. gives the best 
match. These terminations are very compact and simple to construct, 
and give a degree of match and a bandwidth adequate for the purposes 
used here. The voltage standing-wave ratio obtained in this way is less 
than 1.10 at midband and remains under 1.4 over a band of plus or minus 
5 per cent. 

The redection produced in the local-oscillator waveguide by the two 
coupling devices is more serious than that produced by one. In the 

Sec. 4-6] 



3.3-cm example the coupling iris on one side has been operated with a 
fixed post so that it is beyond resonance with the adjustment screw 
removed, as has been discussed in Sec. 3*5. With the other iris operated 
as an inductive susceptance, the reflections from the two irises tend to 
compensate each other. In the 1.26-cm example no serious trouble was 
caused by the reflections by the coupling channels, but the reflection 
could be reduced, if necessary, by placing the two channels a quarter 
wavelength apart on the local-oscillator waveguide. This would require, 
however, that the mixer be asymmetrical. The coupling channels used 
at 1.25 cm are different from those discussed in Sec. 3*6 in that they are 
connected to the mixer waveguide behind the crystals. An equivalent 
network for this junction has been worked out by Schwinger's method 
and may be found in Vol. 10 of this series. Coupling of this type gives 
less freedom than the symmetrical couplers between the crystal and the 
TR cavity because the spacing between the crystal and the TR cavity 
must be so chosen that the reflection of the local-oscillator wave by the 
TR cavity does not produce a voltage node at the position of the crossbar 
transition to the crystal. 

All the other details of the mixers, such as the crystal mounts, the 
methods of bringing out the beat frequency, and the method of adjusting 
the local-oscillator coupling have been discussed in Chap. 3. More 
detailed dimensional drawings of these mixers will be found in the group 
of drawings at the end of the present chapter. The cross attenuation 
achieved with these mixers is determined, as in the 10-cm example, by the 
available local-oscillator power and, in decibels, is about twice the attenua- 
tion between the local oscillator and a single ciystal. Measurement on 
the 3.3-cm mixer with a 2K25 local-oscillator tube shows that a cross 
attenuation of at least 30 db can be obtained at all wavelengths in the 
3.13- to 3.53-cm band. 

4-6. A Mixer Employing Directional Couplers. — A mixer with greater 
cross attenuation, if needed, could be made using the directional-coupler 
principle. A sketch of a mixer of this kind is shown in Fig. 4*6. The TR 
leakage power that reaches the local-oscillator waveguide travels toward 
the dummy load, and only that which is reflected by the load passes 
the directional coupler that leads to the AFC mixer. The TR leakage 
power that is coupled into the AFC mixer, therefore, travels toward the 
AFC attenuator and, since a matched dissipative attenuator is used, 
none of this power arrives at the AFC crystal. There is a reflection of 
TR leakage power by the radar mixer crystal and some of this is coupled 
into the AFC mixer waveguide, but this also travels toward the attenu- 
ator and not toward the crystal. The only coupling between the TR 
leakage signal and the AFC mixer crystal is by reflection of the wave 
reflected by the radar crystal from the local-oscillator attenuator. 



Since the local-oscillator attenuator must have a small attenuation (only 
sufSoient to give the required adjustment range) the reflection may be 
large. Thus, the cross attenuation is the attenuation of the two^ direc- 
tional couplers plus an amount dependent on the reflection coefficient of 
the mixer crystal at the level of the TR leakage power and on the refl^- 
tion coefllcient of the local oscillator and attenuator. No mixers of this 
type have been used because the simpler ones seem to have sufficient 
cross attenuation with most oscillator tubes. This mixer would be diffi- 
cult to fit into the space available in the usual duplexing system. A 

Fig. 4*6. — Two-cliaimel mixer "with directional coupler, for lai'n^c cross attoiiuation. 

much better two-channel mixer, which can be used with a local oscillator 
of limited output power, will be described in Chap. 6. 

In all of the mixer designs so far presented, provision has boon made 
for a very definite kind of load admittance at the local-oscillator tube. 
Before proceeding with the discussion of multiple-fun(*.tion mixers, the 
behavior of local oscillators, as a function of the load admittance jire- 
sented to them, will be qualitatively described. From this discussion it 
should become evident that the provision of a definite load admittances 
for the local oscillator is a very important part of the design of a micro- 
wave mixer. Previous to the general recognition of this fae^t, many 
mixers were designed without such provisions (the coupling obtained 
by varying the antenna insertion of the 723A/B tube is an exampkO, 
and their operation in field radar systems was anything but trouhlc-frce. 
For the separate beacon local oscillator in one mixer, for example, a 
special selection of oscLQator tubes was required, since only a small 
percentage of otherwise perfect tubes would operate properly in the cir- 
cuit. The property of the tube which governed its proper operation 
in the circuit was not included in the tube specifications. It was there- 

Sec. 4 - 7 ] 



fore possible to design a circuit in which all tubes of a given type would 
operate at the time of the circuit design, but in which later samples of the 
same type of tube might be unsatisfactory. 

4-7. The Rieke Diagram. — In order to decide upon an output load 
for any kind of self-excited oscillator, it is helpful to plot a ‘‘Riekc 
diagram of the tube. This is done by measuring the oscillator power 
and frequency as a function of the load admittance presented at some 
point in the output circuit of the oscillator. A plot of these data, in the 
form of contours of constant power and contours of constant frequency, 
on a Smith admittance diagram is called the Rieke diagram for the tube. 

Suppose that the oscillator may be represented as the shunt-tuned 
tank circuit of Fig. 4-7. For a simple reflex klystron, this tank circuit is 
the cavity resonator of the oscillator. The voltage built up across the 
resonator is not independent of the load admittance. From this repre- 
sentation, however, it is obvious 
that the power delivered to the 
load must depend upon the con- 
ductance of the load and must go 
to zero if that conductance goes to 
zero, because of the presence of 
the shunt conductance result- 
ing from resistive losses of the 
cavity. If the load conductance 
increases unduly, the oscillator 
may become overloaded to such an 
extent that the power circulating in the tank circuit is insufficient to 
maintain the oscillation through the feedback circuit and the oscillations 
cease. Thus, there must be a load conductance that gives a maximum 
of power delivered. 

The susceptance component of the load admittance, on the other 
hand, adds to the susceptance of the tank circuit. If the susceptance 
of the load varies slowly with frequency, a change in its value causes the 
oscillator frequency to change until the tank circuit contributes a sus- 
ceptance that cancels the load susceptance. This is because the feedback 
efficiency is greatest at the frequency of zero total susceptance, and the 
voltage built up across the tank circuit is therefore largest at this fre- 
quency. It is now apparent that plots of contours of constant delivered 
power and contours of constant frequency against the load admittan<‘.e, 
as measured in the tank circuit, would resemble Fig. 4-8. The contours 
of constant power are circles of constant conductance and the contoui's of 
constant freciuency are the circles of constant susceptance. The amount 
of frequency change per unit susceptance depends upon the Q of tlu^ 
resonant cavity of the oscillator. The “pulling figure” for the tub(^ 

Oscillator tank circuit 

Fig. 4 * 7 . — Circuit ropreHOutiiig OBC.illator tank 
circuit and loud udinittaucc. 



[Sec. 4-7 

that is, the maximum frequency change when a load admittance causing 
a voltage standing-wave ratio of 1.5 is varied through all phases — ^is 
closely related to the Q of the resonator. These relationships are not the 
subjects of the present discussion; for a detailed discussion of the Rieke 
diagram, the reader is referred to Vol. 7 of this series. The important 
region for the present purposes is the circular region of the diagram, 
called the ‘‘sink,” in which the oscillator does not operate at all. Load 
admittances that fall in this region must be avoided if the oscillator is to 
be expected to operate. 




Fig. 4-8. — Rieke diagram for ideal oscillator. Curves of constant power are labeled with 
percentages of maximum power available. 

The discussion so far has been concerned with the load admittance as 
measured at the tube itself. In practice there is some kind of output 
coupling circuit and, therefore, the admittances that can actually be 
measured are those at some point in the output line. Since the electrical 
distance between this point and a reference point within the tube varies 
with frequency, the actual Rieke diagram is a distorted version of that 
shown in Fig. 4*8. The fact that the coupling circuit cannot be com- 
pletely nondissipative limits the range of admittances presented to the 
tube when the whole complex plane is covered at the point of measure- 
ment. As a result, the contours of constant power do not follow the 
constant-conductance circles and do not close in the regions of large 
susceptance. Moreover, the region of the sink does not remain circular. 

Sec. 4-7] 



The contours of constant frequency are no longer the circles of constant 
susceptance, but qualitatively they retain the property of being ortho- 
gonal to the contours of constant power. An actual Rieke diagram for 
a 2K25 oscillator is shown in Fig. 4-9. The admittance plotted is that 
measured in the waveguide of a standard test mount, at the plane of 
the antenna of the 2K25. 

The Rieke diagram for the 2K26 oscillator changes rapidly with the 
‘^matched load'' frequency of the tube. This change can be accounted 
for by the relatively long length of the output coupling line between the 
tube cavity and the point in the waveguide at which the admittances are 

Fro. 4-9. — llioko diaisrain for a 2K25 oscillator. 

measured. The electrical length of this line varies with wavelength 
and, as a result, the Rieke diagram rotates on the admittance chart as the 
wavelength is altered. If a matched load on the waveguide docs not 
result in unity standing-wave ratio in the coaxial output line there is 
also a radial shift of the diagram with wavelength. Two things become 
apparent from this consideration. First, a given load admittance must 
not be crossed by the sink for any wavelength in the band to be used. 
Second, if the rotation encountered over the band becomes as much as 
one-half wavelength, the only safe region for the load admittance is 
very near the center of the diagram, provided there is not excessive 
translation of the diagram with wavelength. The specification test of 
the 2K25 ensures that the sink does not overlap the portion of the dia- 
gram which represents the matched-load condition of the mount when the 
tube is operated in a mount identical with the test mount, because the 



[Sbc, 4-7 

tube must operate contmuously in this mount from one end of its tuning 
range to the other. Thus, it is evident that the only load admittance 
that is safe to use in mixer design is that presented by the test mount. 

When the output coupling circuit is not a part of the oscillator tube, 
as is true for the 10-cm 2K28, the situation is different. For a given 
frequency the output coupling loop can be adjusted to give the required 
output power, up to the maximuin power obtainable from the tube. 
If the loading is increased beyond the value for maximum power, the 
conductance may be in the region of the sink. If, however, the output 
line is several wavelengths long and there is a large standing-wave 
ratio in the line, the load admittance presented by a given output-loop 
adjustment changes rapidly with wavelength and a good adjustment at 
one wavelength may easily result in overload at an adjacent wavelength. 
This is a good argument for the resistor-disk matched load provided in 
the LO coupling circuit of the 10-cm coaxial-line mixers. 

A more careful consideration of the Rieke diagram of the transmitting 
oscillator is necessary, since the pulling figure is of considerable signifi- 
cance. The output circuit is designed on the basis of a compromise 
between pulling figure and delivered power; hence, somewhat less than the 
maximum available power is obtained. For local-oscillator applications 
the puUing figure is not of the same importance, although it must be 
considered under some conditions. 

It should be pointed out that the Eieke diagram of a reflex-klystron 
oscillator is not independent of the reflector mode in which the tube is 
operated. Usually the sink covers a larger region on the diagram as the 
reflector voltage is increased from one mode to the next. It is not 
sufficient, therefore, to provide a load circuit identical with the test 
mount unless the tube is to be operated in the same mode as that specified 
in the tests. Although it may often seem that somewhat greater output 
power is available in a mode of higher reflector voltage than in the one 
used in the tests, designing on this basis is not safe. At some frequencies 
the sink may enclose the matched-load point of the diagram for a higher- 
voltage mode and there will be no output power at these frequencies. 

The presence of the overload condition at some frequency cannot 
always be discovered by merely tuning the tube through the frequency 
range and observing that power is obtained at all positions of the tuning 
mechanism. The tube may jump suddenly over the frequencies at wliich 
it cannot oscillate, if the frequency sensitivity of the load admittance is 
high. The tube may be more thoroughly tested for operation in a 
mixer by superimposing on the steady reflector voltage a sawtooth sweep 
voltage of sufficient amplitude to sweep the tube through the desired 
mode of oscillation. If the same voltage is applied to the horizontal 
deflection plates of a cathode-ray oscilloscope and if the vertical deflection 

Sec. 4*7] 



is made to show the rectified voltage of the mixer crystal, a plot of the 
oscillator output power vs. frequency results. A plot of such a presenta- 
tion is shown as the solid curve in Fig. 4-10. As the tube is timed, this 
mode pattern moves slowly along the voltage axis because the reflector 
voltage required to maintain oscillation changes, but it maintains 
substantially the same shape. It may, of course, grow larger or smaller, 
in the vertical direction, as the coupling factor for the LO coupling 
circuit changes with frequency. If, however, the overload condition 
occurs at some frequency, the curve becomes suddenly smaller as this 
frequency is approached and usually shows sharp drops at the sides, as 
shown by the dashed lines of Fig. 4*10. The evidence of oscillation may 
disappear altogether over a short range of the tuning mechanism and 
reappear as the tuning is continued, but with the pattern centered at a 
different- voltage. Finally, the pattern will regain its original shape as 

Fig. 4*10. — Output power va. LO Kia. 4*11. — Overload condition, allow- 

refloctor voltago for normal and for over- iiig oscillation at frequencies on both 
load conditions. sides of a discontinuity, in a single mode. 

the frequency becomes sufficiently removed from the critical frequency on 
the other side. In some cases the overload at a particular frequency 
appears over so narrow a frequency range as to allow oscillation on both 
sides of this range in a single reflector-voltage mode. Then the ampli- 
tude falls abruptly to zero over a small range of reflector voltage, as 
shown in Fig. 4*11. As the tube is tuned away from this region, the 
half of the mode that corresponds to frequencies on this side of the over- 
loaded frequencies swells and finally becomes the full mode of the nor- 
mally loaded oscillator. The other half disappears completely for a 
small tuning away from the symmetrical case. The beginning of this 
effect is indicated by the dashed cuivc of Fig. 4*11. 

That the situation of a broken cuivc such as shown in Fig. 4*11 does 
correspond to a frequency jump can be confirmed through the use of a 
reaction wavemeter, c-ouplcd to the mixer in siicli a way that a dip in the 
crystal current occurs at resonance for the wavcmieter. Since each 
point of the curves of rectified crystal voltage vs. reflector voltage 
corresponds to a different fre<iuoncy, in acc-ordanc-e with the ekiictronic 
tuning principle, a dip in tluj curve, which moves along as tluj wavemeter 
is tuned, results. In a situation such as that illustrated in Fig. 4*1 1, tlu^ 
wavemeter dip moves smoothly through one-half of the ciuve and tlu^n 



[Sec. 4-7 

disappears for a considerable range of frequency as the wavemeter is 
tuned. Finally, it reappears at the inside edge of the second part of the 
mode and moves smoothly on to the end of the mode. The region of 
frequency skipped is usually much greater than that covered by the 
ordinary ^ectronic tuning for a change of reflector voltage equal to 
that of the blank region. This is understandable because the two sides 
of the sink of the Eieke diagram represent extreme values of frequency 
pulling in opposite directions. 

A less noticeable but very serious kind of frequency discontinuity 
sometimes occurs if the load on the oscillator is highly frequency-sensitive. 
Such a load results with a 2K25 if the tube is tightly coupled to a wave- 
guide in which a very large standing-wave ratio exists. In a situation 
of this kind, the test described in the preceding paragraph may show a 
normal oscillator mode at all tuning conditions, except for a small cusp 
which moves through the mode as the tube is tuned. This is shown in 
Fig. 4T2. The cusp is often so small that it can go unnoticed unless the 
observer is looking specifically for it. The cusp would almost certainly 
be regarded as of little consequence since it appears to be no more serious 
than a small drop in available 
power, similar to that produced by 
the reaction wavemeter. If, how- 
ever, the wavemeter test is made, 
a continuous variation of frequency 
is found up to the cusp, and at this 
point the wavemeter indication dis- 
appears. Before the wavemeter 
indication reappears on the other 
side of the dip, the wavemeter may 
have to be tuned through 1 or 2 per cent, showing that there is a 1 or 
2 per cent gap in the spectrum of available frequencies from the tube 
operating into this load. If the tube is mechanically tuned, the dis- 
continuity moves in the mode, but the wavemeter test shows that substan- 
tially the same frequency band is always skipped with a particular tube. 

This effect can also be explained as a result of the sink of the Rieke 
diagram, the difference being that the load circuit is sufiSiciently frequency- 
sensitive to allow the tube to find a frequency at which it can oscillate at 
any tuning condition. As the frequency of the tube approaches the 
frequency at which the load is in the overload region it simply jumps 
across to a frequency on the other side of the sink. This change in 
frequency alters both the position of the sink on the Rieke diagram and 
the admittance presented by the load. 

Attempts were made to use the 723 A/B tube in a double-mixer 
circuit in which the oscillator was coupled directly into a resonant 

Fig. 4*12. — OsoiUator-mode pattern, show- 
ing discontinuity. 

Sec. 4-8] 



cavity. The load presented to the antenna of the tube by the resonant 
cavity was very frequency-sensitive and was far from the center of the 
Rieke diagram of the tube. For any tube a frequency discontinuity of 
this type could be found but the frequency region skipped varied con- 
siderably from tube to tube, corresponding to a variation, among tubes, 
of the electrical length of the coaxial output line. Thus, a measurement 
of the Rieke diagram of these tubes would show a considerable variation 
in the position of the sink. To make a mixer that would operate with 
any tube, in even a narrow band of frequencies, it was found necessary to 
make the discontinuity caused by the resonator circuit fall at a frequency 
several per cent outside the band, for an average tube. As a result the 
load condition on the average tube was such that only a small amount of 
energy was stored in the resonator. The coupling required between 
the resonator and the mixer to give sufficient power at the cryst^ resulted 
in a large reaction of the local-oscillator circuit on the signal circuit in 
the mixer. The aim of achieving increased cross attenuation between 
the AFC and radar mixers was not realized, and in fact, the mixers 
designed on this principle were quite unsatisfactory. All subsequent 
designs were based on the provision of matched-load conditions for the 
local oscillator, in the fashion already described. 

4*8. Frequency Discontinuities Caused by High-Q Load Circuits. — 
A discontinuity of another type in the operation of an oscillator results 
if the load circuit is highly frequency-sensitive. In many cases it is 
desirable to couple a resonant cavity to the local oscillator of a mixer 
for frequency reference. If this is attempted it is usually found to be 
very difficult to make the coupling in such a way that the oscillator may 
be tuned smoothly through the cavity resonance. For almost any 
reasonable coupling a discontinuity results, if not for all tubes at least 
for some samples. 

At first thought it might be supposed that it would be necessary only 
to restrict the admittance contour of the load circuit to a region of the 
Rieke diagram not including the sink. If this is done, frequency dis- 
continuities can still bo found if the rate of transit of the load contour 
with respect to frequency is sufficiently rapid. To understand how this 
comes about, let us consider an idealized example. Associated with the 
tank circuit of the oscillator there is a susceptance which changes at a 
certain rate with frequency in the vicinity of resonance and which is 
zero at the frequency of oscillation. Tuning the tube either electronically 
or by alteration of the cavity resonator (the microwave tank circuit) 
may be considered as adding a positive or negative susceptance to the 
circuit so that the zero occurs at a different frequency. To a very good 
approximation, the susceptance of the tank circuit increases linearly with 
frequency as shown in Fig. 4-13. To tune the oscillator from the fre- 



[Sec. 4*8 

quency corresponding to A to that corresponding to the addition 
of a susceptance varying from — to +S is required. This statement is 
valid, however, only if the load offers no susceptance in addition to that 
of the tank circuit. If the load does add a susceptance that varies only 
slowly with frequency, the effect is similar to that of the hypothetical 
timing susceptance, and the oscillator frequency is said to be pulled 
by the load. 

Suppose the load includes a resonant cavity, in addition to a matched 
load at frequencies at which the cavity is nonresonant. In Fig. 4T4 such 
a load circuit, conforming to the load specifications for the 2K25, is 
shown. The cavity appears as a short circuit at frequencies removed 
from the resonant frequency and the circuit is identical A\ the test 

Fia. 4*13. — Susceptance of oscillator tank Fig, 4*14. — Resonant load circuit for 
circuit vs. frequency; 2K25 oscillator. 

mount is those regions. In the vicinity of resonance, the cavity admit- 
tance traverses a circle on a Smith chart in accordance with the formula 

where 5o is the reciprocal of Qo, the unloaded Q of the cavity, 8 i is the 
reciprocal Q of the input circuit, 82 is the reciprocal Q of the output 
circuit, V is the oscillator frequency and vq is the resonant frequency of the 
cavity. This formula can be derived from the equivalent shunt-circuit 
resonator at low frequency where the admittance is given by 

Y = + 

where cg is 27rv, ^0 is the shunt conductance of the tuned circuit, and 
gf 2 is the conductance of the output circuit. Using the lumped-constant- 
circuit formula for Q, 



and the resonance condition, coj = 1/LC, the equivalent circuit admit- 
tance is 

or, to a very good approximation, for \(v — vo)/vq\ << 1, 

r- {». + «, + 

The admittance terminating the input line is this quantity transformed by 
an amount dependent on the input coupling, which is measured by 

where 8i is the reciprocal Q of the input circuit with the input line matched 
back. Dividing by gi thus gives the admittance in units of the char- 
acteristic admittance of the input line, as in Eq. (3). 

The load presented to the antenna of the tube in the circuit of Fig. 
4-14 consists of the sum of the matched-load admittance Fo and that of 
the cavity, transformed to its reciprocal by the quarter-wavelength line. 
Thus the total load admittance is 

Yj. = r„ (l -h 

where Av is substituted for {p — vn)/vQ, or 

6*0 + 25o52 + 5i3o + + 51 + 4Aj/^ ]2Av5i^y 

(5o + «2)» -h 4A>' J “• ^ 

On an admittance chart this result can be obtained by the steps illus- 
trated in Fig. 4*15. In Fig. 4*15o is shown the admittance of the cavity 
alone, traversed in the direction of the arrow with increasing frequency 
and with resonance corresponding to the intersection with the conduct- 
ance axis. In Fig. 4’15/> is sho^vn the circle representing the admittance 
of the cavity at the end of a quarter wavelength of line, and in Fig. 4-15c 
is shown the locus of this admittance combined with the matched-load 
admittance terminating the line in the other direction. The point to be 
made now is that the contour of load admittance may lie entirely within 
the acceptable region of the Rieke diagram for the oscillator, but may 
give rise to frequency discontinuities in the operation of the tube by 
virtue of an excessive rate of change of susceptance with frequency. 
The tendency for this to occur is greatest, for the circuit under discussion, 
if the effective length of the line between the oscillator tube and its 
antenna in the waveguide is an integral number of half wavelengths. 

5i "S 
(3o + 52 ) + j2Av/ 




The added susceptance of the load circuit has a negative rate of ch£ 
with respect to frequency in the vicinity of resonance for the load ca\ 
Thus, it tends to counteract the positive rate of change of susceptanc 
the oscillator cavity. Since the frequency stability of the oscillate 
derived from the positive rate of change of susceptance of its tank circ 
the addition of this load circuit reduces the stability by an amo 

(a) (6) <c) 

Fig. 4*16 a, 6, c , — ^Loous of load admittance vs. frequency, for cavity in place of the s] 
circuit in the standard tube mount. 

depending on the ratio of the negative rate of change of susceptance of 
load circuit to the positive rate of change of susceptance of the ts 
circuit. The situation may be illustrated graphically as in Fig. 4* 
The susceptance of the tank circuit is the straight line, as in Fig. 4- 
that of the load circuit is the curve passing from positive values 
frequencies less than the resonant frequency of the cavity to negat: 

Susceptance of 

Fig. 4*16. — Diagram of susceptance vs. fre- Fig. 4*17.—— Cavity transmission 
quenoy, iUustrating the origin of frequency dis- reflector voltage, illustrating a frequer 
continuities caused by a high-^ load circuit. discontinuity caused by the cavity- 

values at higher frequencies; the total susceptance is the sum. In tl 
example the rate of change of total susceptance is negative in the vicini 
of the external cavity resonance; hence the oscillator must be unstat 
at that frequency. Its actufid operation, using the concept of the tunu 
mechanism discussed in connection with Fig. 4*13, is the following, 
the tube is tuned from low frequency through resonance of the extern 
cavity, its frequency of oscillation must jump discontinuously from tl 

Sac. 4-8] 



frequency at A to that at B. . Returning, the frequencies between C 
and D are skipped. If the tube is swept in frequency by a sine-wave 
voltage applied to the reflector, and the cavity transmission is recorded on 
an oscillograph as a function of this voltage, a pattern like that of Fig. 
4-17 is found. 

To avoid the discontinuity, the absolute value of the rate of change of 
susceptance of the load circuit must be kept less, at all frequencies, than 
that of the oscillator circuit itself- It is necessary to have a measure of 
the rate of change of susceptance of the oscillator circuit at a point in the 
line where the maximum rate of change of the susceptance due to the load 
circuit is known. It is possible to obtain this quantity from a measure- 
ment of the pulling figure of the oscillator, since a susceptance added 
to the load admittance of the oscillator must produce a frequency change 
sufficient to make an exactly counterbalancing change of susceptance 
in the oscillator circuit. Thus, the quantity desired is just the reciprocal 
of the measurable frequency pulling per unit susceptance change in 
the load admittance in the waveguide. If C is defined as the frequency 
change in cycles per second per unit change in load susceptance, the 
condition for continuity of oscillation is 

dAv . 

From Eq. (4), this becomes 

os (5o + ^ Vo 

‘ [(5o + 52)2 + 4.^vM " C 

or, since the left-hand side is a maximum when Aj' is equal to zero, 

28 i 

(5o + Sa)^ C 


The evaluation of this formula for some typical conditions will serve 
to point out its implications. First, it is necessary to have a typical 
value of C/vo. This quantity has been ascertained for some 2K25 tubes 
by finding the values of 5i, 5o, and §2 that give continuous operation, and 
applying Eq. (5) . It has been found that the value is not constant for 
different parts of the same mode of the oscillator but is higher off center on 
one side (low-frequency side) than at the center (maximum power) or on 
the other side. In order to obtain continuous operation to the half- 
power point on the low-frequency side of the reflector-voltage mode, 
the left-hand side of Eq. (5) must be made less than about 10® for most 
tubes, so C/vo may be taken as 10"®. Thus C represents a frequency 
change of about 11 Mc/sec per unit susceptance at a frequency of 9000 
Mc/sec. Suppose that it is desired to find the input coupling that can 



[Sec. 4-8 

be used with a cavity having an unloaded Q of 20,000 and a Q of 10,000 
when the cavity is loaded by the output circuit alone. Application of 
Eq. (5), with (5o + 5*) equal to 10“*, gives 5i less than 6 X 10“®, or the 
Q of the input circuit must be greater than 2 X 10®. Since the conduct- 
ance at resonance, as seen at the antenna of the oscillator tube, is 

the admittance contour described by the load circuit as a function of 
frequency, corresponding to Fig. 4-15c, must go through Fo far from 
resonance and through a point somewhere between Yo and 1.06 Fo at 

resonance. This is certainly a very small excursion and would, at first 
thought, have been regarded as an easily tolerable load line for the tube. 
Thus it is evident that this source of frequency discontinuites in the 
operation of the oscillator must be taken into account when a resonant 
cavity is to be included as a part of the load circuit of the oscillator. 

A possible way in which the tendency of the cavity to produce fre- 
quency discontinuities can be reduced is to use a different effective line 
length between the cavity and the oscillator. In this way the part of 
the load line which is traversed most rapidly is made to correspond, at the 
oscillator, primarily to a changing conductance, or, for a line differing in 
length by a quarter wavelength from that in the example above, a positive 
rate of change of susceptance. In the latter case the load circuit tends 
to stabilize the oscillator frequency through increasing the total rate of 
change of susceptance. Then a much larger coupling between the 



oscillator and the cavity can be used. Although discontinuities may still 
be produced when large coupling is used, they will be of a different kind. 
The tube may oscillate, at the resonant frequency of the cavity, mth 
greater frequency stability than with a nonresonant load, but two 
discontinuities, one on each side of resonance, occur for high Q’s and tight 
coupling. This effect is shown on the susceptance-vs.-frequency plot 
of Fig. 4*18, where discontinuities occur between A and B, C and D and, 
tuning from right to left, between E and F and O and H. The frequency 
stabilization obtained when the oscillator is operating in the region 
between the two discontinuities is such that tuning that would ordinarily 
cause a frequency change from H to D causes only the change from G to C. 
Circuits of this type have been used for frequency-stabilization purposes, 
but the dependence on the line length between cavity and oscillator 
makes them difficult to put into proper adjustment. When using tubes 
such as the 2K25, in which the coupling line is a part of the tube and 
varies in effective electrical length both with frequency and from tube to 
tube, it is safest to design a cavity load circuit that is satisfactory even 
when the line length is such that the greatest tendency for causing 
discontinuities occurs, if these discontinuities are to be avoided at all 
frequencies and with all tubes. Thus Eq. (5) must be satisfied. 

4-9. The Design of Load Circuits Containing Transmission Cavities. — 
A transmission cavity may be used as a part of the load circuit of the 
local oscillator of a mixer to serve as a frequency reference, either for 
frequency measurement or for automatic frequency control. If the 
presence of the cavity did not affect the operation of the oscillator no 
matter how high its Q, it would be desired to design the circuit to load 
the cavity in such a way as to give the maximum rate of change of 
voltage with respect to frequency at the output terminals of the detector 
following the cavity. This means that, with a cavity of given unloaded 
Q, (Qo = l/5o), and with a square-law detector, the loading should be 
such that (TQl) is a maximum, where T is the fraction of the available 
input power to the cavity transmitted to its load and Ql is the loaded Q. 
The quantity T can, by arguments similar to those used for Eq. (3-15), 
be shown to be 

m _ ^$162 

(5i + §2 + 5o)^ 

so that 

( 6 ) 

TQl = 


(3i + 32 + 5o)® 

( 7 ) 

If the partial derivatives of TQl, first with respect to 3i and then with 
respect to 3^, are taken, and each set equal to zero, the values of 3i and 32 
giving maximum TQl are found to be 



[Sec, 4*9 

81 = 252 — 80 \ 

82 = 25 i — 5 o 1 








Thus equal loading by the input and the output circuits is desired, and 
the loaded Q is one third of the unloaded Q of the cavity. The fraction 
of available power transmitted to the load is 0.44; that is, the cavity 
has an insertion loss of 3.5 db at resonance. 

The situation is different in practice, however, since, in addition, 
the inequality of Eq. (5) must be satisfied. The limiting case occurs 
when Eq. (6) becomes an equality, or when 

5i — b(do + ^ 2 )^ = 0, (10) 


If the condition of Eq. (10) is applied to Eq. (7), there results 

“ [6(52 + So) + mh + So) 

The maximum value of TQl can be found by differentiation, and the 
values of 81 and 82 at this maximum are 

If 6 is taken as the true value of the oscillator, the limiting values of 
5i and 82 are given by Eqs. (12). With these values the oscillator is 
just on the verge of a discontinuous operation at the cavity resonance 
for the most restrictive cavity-to-oscillator line length. In practice 
a certain safety factor is desirable and this can best be achieved through 
the use of a value for 6 smaller than the true value by a reasonable 
factor. Equation (12) should be used only when b 8 o is less than 0.25. 
Application of Eqs. (12), when 65o is greater than 0.25, is not desirable, 
because then the inequality of Eq. (6) holds for the optimum value of 
TQl for the cavity alone. Use of Eq. (12) would result in loading that 
gives the maximum TQl compatible with keeping the oscillator on the 
verge of discontinuous operation. In Fig. 4-19 are plotted the values of 
81/ 8q and 82/80 vs. b8o for values of h8o less than 0.26 as given by Eqs. (12). 
From these curves it is evident that an increase in the output loading of 
the cavity is much more effective in reducing the pulling of the local 
oscillator than is decoupling through a decrease in the input loading. 

Sec. 4-9] 



By the use of the condition expressed in Eq. (6), the amount of coup- 
ling which just allows continuous operation with equal input and output 
irises can be calculated. Th i s condition maintains the maximum loaded 
Q for a given transmission loss. The result is 

These values also are plotted in Fig. 4-19. To compare the usefulness 
of the cavity loaded in these two ways, the expressions for TQl may be 


Ficj. 4-19 — Values of di/So and 52/5o giving maxiinuni {TQl), subject to the condition 
required to avoid frequency disco ntinuitioSy that ^ The dotted curve gives 

5i/fio and 62/60, as a function of 680, for equal input and output windows. 

used. When the effect on the oscillator may be neglected, Eqs. (7) and 
(9) give 

(rQ0m« = ^i- (14) 

In Fig. 4*20 curves are plotted showing the ratio of the product TQl 
obtainable through the use of Eqs. (12) and for the condition of equal 
input and output loads to the maximum for the cavity, given by Eq. (14). 
The calculation for the equal-loading case is simplified for small 5o6, 
since Eq. (13) can be reduced to 

^ ^ 

5o 5o 




[Sec. 4*10 

by expansion of the radical by the binomial theorem, neglecting terms 
in to powers higher than the second. The product TQl for small 
hoh is reduced to 


4 {hby 

do (1 + 28oby 

by this means. 

From these curves the advantage of using larger output loading and 
smaller input loading than those that give minimum transmission loss for 

a given loaded Q is quite evident. 
In practice, a further considera- 
tion enters: that of the detuning 
of the reference cavity by the in- 
put and output circuits by varia- 
tions in the admittance of the 
oscillator circuit or the detector 
circuit. The formulas and curves 
show that, if the rate of change of 
susceptance must be lower than 
that obtained by loading for maxi- 
mum TQl, the product TQl for 
a given cavity suffers least if the 
reduction is made by increasing the output coupling and decreasing the 
input coupling in accordance with Eqs. (12). Therefore, variations in 
the oscillator admittance pull the cavity frequency less than for maximum 
TQl and variations in the output admittance pull it more. In practice a 
crystal is used as the detector. To reduce the pulling of the cavity by 
the change in admittance with 
changes of the crystal, a dissipative 
buffering attenuator is used be- 
tween the cavity and the crystal. 

4-10. Load Circuits with Reac- 
tion Cavities. — One more example 
of the application of Eq. (5) may 
be of interest. It is sometimes 
desired to couple a reaction wave- 
meter cavity to the oscillator. A 
possible circuit would be that of Fig. 4-21, which is identical with Fig. 
4*14 except that the load circuit and output hole of the cavity are not 
present. The condition for continuous operation with this circuit becomes 

Fig. 4*21. — Cinsuit for ooiiplitig a rouctioii 
cavity to the local oscillator. 


Fig. 4*20. — Ratio of the product TQl, 
obtainable without LO-frequency, discon- 
tinuities, to the maximum values of TQl 
obtainable from the cavity as a function of 

8i K, 

The marginal condition is given by 




Seo. 4*11] 



which a few representative numbers will show to be a very restrictive 
condition. For the example cited where h, for the 2K25^ was taken as 
500, a cavity with an unloaded Q of 6000 can have a value of 5i/$o at most 
equal to 0.1. Thus the voltage standing-wave ratio at resonance cannot 
be less than 10, with the minimum in the plane of the input iris, corres- 
ponding to the ''undercoupled” condition. An absorption of only about 
10 per cent of the available oscillator power gives the circuit, as a reaction 
wavemeter, only about a 10 per cent dip at resonance in the power 
delivered to the main load on the oscillator. With a high-Q cavity, 
such as the Tj&oi-mode wavemeter commonly used in the 3-cm band, 
bSo would be about 0.02 so that 
Si/So could not exceed 0.02 and only 
a 2 per cent dip could be obtained. 

441. The Prevention of Fre- 
quency Discontiunities by Padding. 

A common method of preventing 
discontinuities in frequency caused "patched load 

by having a bavity as a part ot tha ^ 

load circuit is to provide matched for decoupling to prevent frequency 
dissipative attenuation between the 

cavity and the oscillator, as illustrated in Fig. 4-22. The amount of 
attenuation required may be calculated as follows. The reflection coeffici- 
ent from the cavity is given, without attenuation, by 

Fo + 7. 

where Vn is the cavity admittance from Eq. (3). If an attenuator 
inserted between the oscillator antenna and the cavity reduces the power 
by a factor r, the reflection coefficient measured at the oscillator antenna 
is also reduced by the factor r, since the wave must transit the attenuator 
twice. Thus the admittance at the oscillator antenna is 

V _ I - rr 
" 1 + rr 

for a total path length of an integral number of half wavelengths between 
the cavity and the antenna. 

The 1 ‘eciprocal of this admittance is the quantity desired, since it is 
when the cavity and the oscillator are placed an odd number of quarter 
wavelengths apart that the rate of change of susceptance with frequency 
is negative and so produces frequency discontinuities. Thus 

1 +rr 
1 - rr‘ 



[Sec. 4-11 

For continuous operation of the oscillator, the condition that must be 
met is that the derivative of the imaginary part oi Yt with respect to 
frequency at the resonance frequency of the cavity vo is less in magnitude 
than the reciprocal of the rate of change of frequency with respect to 
susceptance, defined previously as C, for the oscillator, or 

dBL . Vo 
dAv C' 


where Av, vo, and C are all as defined in the previous analysis and Bl is 
the imaginary part of Yl- The result is 

8ra ^ Vo 

M (1 “ r)a + (1 + r )]2 ^ C ' 

where 8t is 5o + ^2 and a is 8i/8t- This may be written 


(1 - 0!)V* + 2 



r + (a + 1)* > 0. 


For the marginal condition, that is, with the oscillator just on the verge 
of skipping frequencies, the left-hand side may be taken as equal to zero, 
and thus a minimum value of r compatible with continuous operation is 
found. This value, designated as ri, is 




(a ^ 1)2 



1 - 

r (a-l)*(a + l)n 

/ - . 4 aC' 

r VJ 


If the last term in the bracket is small compared with unity, the radical 
may be expanded by the binomial theorem and an approximation may be 
obtained by neglecting terms in the expansion of order higher than the 
first. Thus the attenuation factor for this condition may be written 

(g + 1)^ 

\ OtVo ) 


Application of these formulas to two special cases are of particular 
interest. First, for the use of a transmission cavity loaded for maximum 
TQi, in accordance with Eq. (9), 8t is 28o and a is i. Thus Eq. (18) 

Sec. 4-11] 

and Eq. (19) becomes 



A curve of these functions is plotted in Fig. 4*23. This curve becomes a 
straight line for small values of i>5o. Thus, in this region, the real limit 
on the product tTQl is imposed q 
by the limit in the rate of change 
of susceptance that the oscillator c 
can stand. With a given value '*| ® 
of b for the tube, little is gained J 12 
by the use of a cavity of higher ^ jg 
unloaded Q, since additional 
attenuation is required which al- ir 24 

most exactly compensates the in- 1.0 0.2 0.1 0.02 0.01 0.002 0.001 

crease in TQl- This is also true **^^0 

when no attenuation is used and 4-23.— Attenuation, in decibels, 

. . • j j required between the cavity and the oscillator 

discontinuities are avoided to avoid discontinuities, plotted as a function 

through the use of Eqs. (12), of**.- 

although the limit is approached less rapidly as Q, is iucreased. In the 
limit, Eq. (21) becomes 

r, » f 65o 

and the product txTQl becomes, from Eq. (14), 

tiTQl « ( 22 ) 

Without the attenuator, and with loading according to Eqs. (12), the 
product TQl becomes, in the limit, 

TQl « 46. (23) 

Thus, the rate of change of output power from the cavity achieved 
in this way is 12 times as great as that which can be obtained using the 
attenuator. In practice the difference is not this great. For 5o6 = 10”®, 
the smallest value usually encountered, the rate of change of output 
power is greater by a factor of 10 when no attenuator is used. For a 
more usual value of 606, in the region of 0.02, the advantage is only a 
factor of 7. Against this advantage, however, must be weighed the 
greater tendencjy of the cavity to be pulled by the input- and output-load 
susceptances when no attenuator is used. There is no decoupling from 
the oscillator admittance cxcjcpt that afforded by the reduced input 
iris, and the coupling to the load admittance increases as the square root 
of (1 /65()), as bh is decn^ased, Thus the pulling of the cavity by the load 



[Sec. 4-11 

susceptance would be about 18 times as great, for bdo equal to 10“®, as it 
would be if an attenuator were used. 

Equations (18) and (19) may be applied also to the reaction cavity, 
that is, the cavity with no output loading. For this case, 8t = do and 
a = 8i/8o. With a coupling coefficient a of unity, which is optimum 
for many applications of a reaction cavity, Eq. (19) is exact and reduces to 

ri = 550. (24) 

If a is not unity, but is small compared with l/55o, the attenuation 
required is given approximately by 

As in the previous examples the limit on the rate of change with frequency 
of the reflected power from the cavity is imposed by the pulling figure of 
the oscillator tube. Although an increase in the unloaded Q or a change 
in the coupling factor increases the possible percentage rate of change of 
the reflected power with frequency, the required increase in attenuation 
just compensates for this; consequently the absolute rate of change is 
unaffected. As with transmission cavities, the higher-Q cavities have 
the advantage of being less susceptible to pulling by the external circuits. 
The presence of the large attenuation makes it possible to control the 
external admittance more carefully than if the oscillator were coupled 
directly to the cavity. 

The maximum rate of change of reflected power, for the two methods 
of decoupling, may be compared. The reflection coefficient T for the 
cavity is 



The rate of change of reflected power with frequency is proportional to 
the attenuation factor ri and to the derivative of the scpiare of the 
absolute magnitude of r with respect to Av, 

dlr|* _ 325, 

dAv [(5i + So)" + 4 Ax2]2‘ 

The maximum of this expression with respect to frequency occurs for 
Av = V3(Si + 5o)/6, as is found by setting the second derivative of 
lr|® equal to zero. Thus the maximum rate of change of reflected power 
with frequency is proportional to 

Sbc. 4-12] 



R = Ti 

d*lr|* _ sVsfilSo 

dAp^ (5i + 8o)8''i- 


When an attenuator is used for decoupling, and 5i = 5o, thia becomes 

R^ = 


With no attenuator and with 3i = So{S,jb), Eq. (26) becomes 

Thus the reaction cavity, like the transmission cavity, has a greater 
effectiveness (this time by a factor of 8 in the limit) for the circuit in 
which the decoupling is achieved through the choice of the cavity loading, 
without the addition of attenuation. In all cases the rate of change of 
power with respect to frequency is also proportional to the output 
power of the oscillator. The absolute rate of change of power can there- 
fore be increased by increasing the output power of a given oscillator if 
this can be done without decreasing 5. 

All these calculations are directed toward obtaining the maximum 
absolute rate of change of power. It is sometimes desirable to obtain 
the maximum percentage rate of change and the conditions are then 
different. Calculations can easily be carried out for these or other 
requirements by the use of the general condition that the rate of change 
of susceptance of the load circuit must not exceed the reciprocal of the 
rate of change of frequency with load susceptance for the tube. 

4-12. Provision for Beacon Local Oscillator. — In the introduction of 
this (ihapter the problem of provision for beacon reception was mentioned 
and its solution for 10-cm oscillators and mixers was indicated. The 
only other frequency band in which a radar beacon has been used is the 
band from 9320 to 9430 Mc/sec. As mentioned previously, the early 
solution to the problem of beacon provision was to add a second local 
oscillator, tuned to produce the intermediate frequency when beating 
with the beacon signal, and coupled to the mixer by means of the insertion 
of its output antenna into the mixer waveguide. This kind of coupling 
was, for reasons already mentioned, replaced by one of the coupling 
mechanisms described in Chap. 3, which provides a matched load for the 

The design included the addition of a second local-oscillator wave- 
guide and coupling iris, with an adjustment screw, on the side of the radar 
mixer opposite the radar local oscillator. Such a mixer is shown in 



[Bbo. 4-12 

Fig. 4*24. The separate AFC mixer is included in this sketch. The 
mixer consists of four parallel waveguides with coupling irises between 

them. To minimize the interac- 
tion of the two coupling-window 
adjustments on the radar mixer, it 
is helpful to have the screw in one 
window always inserted beyond 
the window resonance and the 
screw in the other window inserted 
less than the amoxmt giving reson- 
ance. The two irises tend to com- 
pensate each other in their effects 
on the received signal. Thus a 
fixed post long ejnough to put the 
iris just beyond resonance may be 
inserted into the plane of the coup- 
ling iris between the beacon local 
oscillator and the radar mixer. 

A mixer with an extra local oscillator can be made using any of the 
coupling schemes or combinations discussed in Chap. 3. The recent 
introduction of the 2K45 tube, a thermally tuned triode, has made 
possible a return to the use of a single local oscillator which may be 
changed from radar reception to beacon reception by means of a switch. 
Remote control over the oscillator freauencv. with tunabilitv over a 
wide band, is possible with a tube 
of this type. 

It has so far been assumed that 
the only change necessary to con- 
vert the radar receiver to a beacon 
receiver is a change in the local- 
oscillator frequency. Most radar 
systems, however, have some r-f 
preselection in the form of the TR 
cavity tuned to the radar frequency. 

There is some loss at the beacon 
frequency, the magnitude of which 
depends upon the difference be- 
tween the beacon frequency and the radar transmitter frequency. This 
loss is large for a transmitter located at the end of the scatter band 
farthest from the beacon frequency. In Fig. 4*26 is plotted a curve 
of the additional loss at the beacon frequency resulting from the 
fact that the TR cavity is tuned to the transmitter frequency. The 
value taken for the loaded Q of the TR cavity was 350 — approximately 

frequency in Mc/sec 

Fio. 4-25. — Boacon-Hif;iuLl loss duo to 
miatuned TH cavity vs. radar transniittor 

1B24TR cavity 
AFC attenuator 

Coupling iris 
and screw 

C mixer 

Resistor - 
strip load 

Fig. 4*24. — Fiinctional drawing of a double 
mixer with beacon local oscillator. 

Sec. 4 * 12 ] 



that of the 1B24. The abscissa of the curve is the transmitter frequency. 
This signal loss is sometimes not a serious impairment to the beacon 
feature of the radar set because the radar signal fails to trigger the 
beacon at a shorter range than that at which the beacon signal would be 
lost in the radar-receiver noise. The beacon receiver, because of its wide 
pass band (the whole 110-Mc/sec scatter band), has a minimum detect- 
able signal greater than that of the receiver in the airplane. In addition, 
the beacon receiver has much lower antenna gain, since it must receive 
from and radiate to all directions. Thus, if the beacon signal is received 
at all, it may be a signal very many times greater than noise. 

In some systems there is, however, a large loss on receiving beacon 
signals because the antenna spends such a small fraction of the time 
pointing in the direction of the beacon. It has, therefore, become 
common to add to the 3-cm airborne-radar mixers a special device to 
reduce the loss in the TR cavity at the beacon frequency when the set is 
switched to receive beacon signals. Because the beacon frequency is 
outside the radar transmitter band, on the low-frequency side, the TR 
cavity must be tuned in the same direction for all transmitter frequencies. 
Since the beacon frequency is lower than the radar frequency, the input 
susceptance of the TR cavity is inductive at the beacon frequency and 
has a magnitude proportional to the difference in frequency between 
the radar and the beacon. To tune the cavity to the beacon frequency a 
capacitive susceptance must be added. 

To accomplish the retuning of the TR cavity to the beacon frequency, 
the inverse of ‘*TR-aided tuning” is used. That is, the capacitive sus- 
ceptance is not added in the TR cavity, but in the mixer waveguide, at a 
distance behind the TR tube effectively equal to one-half wavelength. 
Thus the waveguide between the TR cavity and the tuning susceptance 
contains a very largo standing wave. The distance between the TR 
cavity and the crystal must be increased from the conventional half 
wavelength to one wavelength in order to accommodate the tuning 
device. For a mixer to be used only in the frequency band for airborne 
radar (9320 to 9430 Mc/scc), this is not of much consequence, since its 
only effect is to narrow the frequency band over which TR-aided tuning 
is effective. Figure 4-20 shows a vertical-plane cross section of the 
radar-mixer part of the converter, including the beacon tuner. The 
tuner is identical in principle with a tuning screw of the choke type and 
has a rod -jV m. in diamctc^r. The rod is pulled out from the waveguide 
by a coil spring in a mechanism above the choke when the radar-beacon 
switch is in the radar receiving position. When the switch is thrown to 
the beacon position, an armature in a magnetic solenoid causes the rod 
to be pushed into the waveguide by an amount determined by an adjust- 
able stop. The adjustable stop becomes the tuning control of the TR 



[Sbc. 4-12 

cavity for beacon reception. It is adjusted for maximum received Ri gnni 
at the beacon frequency when, with the rod pulled out, the TE, tube 
is tuned for maximum signal strength at the radar frequency. In this 
way the timer is adjusted to give the correct amount of p ullin g for the 
particular radar transmitting frequency being used. Since the armature 
of the solenoid must move the rod through about | in., it is found that a 
starting current well in excess of the required holding current is needed. 
To prevent the solenoid from overheating while holding the tuner in. 

Fig. 4*26. Oross-seotioziBl view of airborne-radar mixer showing boaoon-TIi tuner. 

it has been found convenient to cause the rod to throw a switch as it 
comes against the stop. This switch causes sufficient resistance to be 
placed in series with the solenoid to lower the current to a value such that 
the tuner is held in place but the solenoid is not overheated. In this 
way the electromechamcal part of the tuner can be made very compact. 

There is a limit to the amount of pulling of the TKrcavity frequency 
that can be obtained by a tuner of this kind. As the standing-wave 
ratio in the section of waveguide between the TR cavity and the tuner is 
increased, the circulating currents in the waveguide walls and in the tuner 
increase. The ohmic losses due to these large currents eventually limit 


the susceptance that can be added to the TR cavity as well as introduce 
a signal loss at the beacon frequency. In Fig. 4-27 is shown a comparison 
of the beacon-frequency losses with and without the tuner. The plot of 
loss without tuner vs. radar fre- 
quency is taken from Fig. 4-25. It 
win be seen from this plot that the 
loss for any transmitting fre- 
quency within the airborne band 
can be held to less than 3 db by 
the use of the timer. The loss 
becomes rapidly greater than this 
for a pulling somewhat larger than 
that required to cover this band. 

As might be expected, the action 
of the tuner is very sensitive to the 
spacing between the TR cavity and 
the tuner, as well as to the depth of insertion of the rod. A tolerance of 
less than ±0.005 in. on the total effective distance from TR cavity to 
tuner may add 1 db to the 3-db loss remaining for the largest pulling 
required for the airborne band. To make possible the setting of the limit 

stop so that the tuner gives less 
than 1 db additional loss to the 
3-db minimum the adjustment 
mechanism must be capable of 
setting the insertion to within 
0.001 in. It is thus seen that very 
high precision is required in the 
positioning of the tuner on the 
waveguide, in the bearing surfaces, 
and in the limit-stop mechanism. 
In Fig. 4'28 is shown a drawing of 
a complete two-channel converter 
including beacon local oscillator 
and tuner for the beacon TR 
cavity. Both mixers are increased 
in length by the half wavelength 
required for the luklition of the TR-tube tuner so that the AFC attenuator 
Tised in the convertor shown in Fig. 4-4 may be used. 

4-13. R-f Provision for Beacon AFC. — ^Automatic frequency control 
is even more necessary in beacon reception than in radar reception to 
assure satisfactory performance. When a radar set is used to receive 
beacon signals it is because the operator does not know his location with 
respect to the beacon. Thus, the receiver must search in range and 

Fig. 4-2S. Fiiiuition;;! drjiwing of inixor with 
boii<t()»-TR tunor. 

Radar frequency in Mc/sec 

Fig. 4-27. — Beacon-frequency signal loss 
vs. radar frequency, with, and without the 
TR tuner. 



[Sbo. 413 

azimuth for the beacon signal. If, at the same time, it is necessary 
to search in frequency, the chance of the frequency and direction of the 
receiver being right simultaneously is very small. As a result the operator 
would be very lucky to find the beacon at all. 

Since the system is already searching in the spatial sense, it cannot 
be depended upon to search in frequency for the beacon signal, find it, 
and lock onto it, in frequency, in a reasonable time. The beacon program 
has therefore been based on standard beacon-transmitter frequencies, 
maintained with precision, so that the receiver may be tuned to an 

Fig. 4*29.— Cutaway view of the 1Q23 

absolute frequency and receive a 
beacon signal if one is available. 
For this purpose, a reference cavity 
is used in the airborne-radar re- 
ceiver to indicate when the beacon 
local oscillator is tuned to the cor- 
rect frequency to receive the stand- 
ard beacon frequency. The cavity 
is pretuned to resonate at a fre- 
quency differing from the beacon 
frequency by the intermediate fre- 
quency. For the 9310-Mc/sec bea- 
con, cavities resonant at 9280 
Mc/sec have been commerically 
produced, for 30-Mc/sec intermedi- 
ate-frequency receivers, and cavi- 
ties resonant at 9250 Mc/sec for 
60-Mc/sec intermediate-frequency 
receivers. These cavities, called 
the 1Q23 and 1Q22 respectively, are 
similar in mode to the TR cavity 

but have only one post and, consequently, smaller capacitive loading. 
They are evacuated and sealed, with glass input and output irises, and 
include a copper and invar temperature-compensating strut to ensure 
a low temperature coefficient of frequency. In Fig. 4*29 a cutaway 
view of one of these cavities is shown. The cavity is mounted in an 

aluminum block containing input and output waveguides and is put into a 
circuit by connecting waveguides with standard choke joints to this block. 
The specifications of this cavity are such that, when the cavity is mounted 
between a matched generator and detector, the peak in its transmission 
curve occurs at a frequency within about ±1 Mc/sec of the desired 

absolute frequency (9280 or 9260) at any temperature or pressure 
encountered in airborne-system operation. The cavity has an unloaded 
Q of about 5000 and the loaded Q, when matched loads are connected 

to the input and output waveguides, is about 2500. 

Sec. 4-13] 



A cavity of this sort can be used either as an indicator to aid manual 
tuning of the beacon LO or as a source of error signal for an AFC circuit. 
For either use the r-f circuit requirements are the same if the cavity is 
operated as a transmission cavity. It is also possible to block the exit 
waveguide and use the cavity as a reaction device, although this possi- 
bility will not be discussed here. The pitfalls are, of course, similar to 
those for the transmission wavemeter and are chiefly concerned with the 
application of the results of Secs. 4-8 to 4-11. 

Figure 4*30 shows an extension of the converter shown in Fig. 4-28 
to include the reference cavity and an output crystal detector in the 

TR tuner 

AFC attenuator 

AFC mixer 

cavity, 1 Q 23 

6 db attenuator 



2K25 output 



ChoKe joint 

Fig. 4-30. — FuiiGtloual drawing of ooiupleto niixor with boacon LO, beacon-TH tuner, 
and roforonco cavity for boacon AFC. 

beacon-LO circuit. The cavity is connected as a stub line on the side 
of the beacon-LO waveguide with the center line of the stub waveguide 
one-quarter waveguide wavelength back from the short-circuited end of 
the LO waveguide. Since the cavity is completely reflecting at fre- 
quencies well removed from its re, sonant frequency, the length of the line 
from the cavity to the wall of the IjO waveguide is made one-half wave- 
guide wavelength. The admittance presented at the IjO antenna is thus 
approximately the same as in the circuit without the cavity, except for 
frequency sensitivity. Since the beacon local oscillator need function 
only in the region of the beacon frequency and since this frequency 
differs by only about 1 per cent from the oscillator specification-test 
frequency, the added frequency sensitivity is not serious. 



[Sec. 4 

It is found that, with a matched load on the beacon cavity, ma 
local-oscillator tubes have frequency discontinuities in the region of t 
cavity resonance. This has been interpreted as indicating that i 
condition of Eq. (6) is not satisfied. Experiments have shown that, 
discontinuities are to be avoided, the left-hand side of Eq. (5) must 
less than 10*. Since the cavity design was fixed, it was not possible 
adjust the coupling irises and apply Eqs. (12); instead, continue 
operation was obtained through increasing the output loading Sa, 
means of a mismatched load circuit. The crystal detector was mount 
in the crystal mount of a standard nuxer and was buflfered with a 6- 
dissipative attenuator to reduce both pulling in frequency and variatic 
in S 2 due to changes in admittance from crystal to crystal. The inp 
admittance of this attenuator was very close to Fo for any cryst 
the input voltage standing-wave ratio was less than 1.25. An inducti 
iris was introduced, by inserting a vane from one side of the wavegui< 
a sufficient amount. to produce a voltage standing-wave ratio of 4 on t 
input side of the iris. The distance from the iris to the output windi 
of the cavity was then chosen so that the apparent load on the cavity \s 
4Fo instead of Fo. The proper distance was found by measurement, 
frequencies on either side of resonance, of the position of the apparc 
short circuit when a wave was sent toward the output iris of the cavii 
A voltage minimum in the standing-wave pattern produced by t 
inductive iris was made to fall at this position. Thus ^ 2 , the inve] 
output was increased fourfold. With this load circuit, all oscillai 
tubes that were tried oscillated continuously when tuned through t 
resonance frequency of the cavity provided that this frequency fell abo 
the one-quarter-power points in the reflector-tuning mode. 

For this cavity and coupling circuit, the left-hand side of Eq. 1 
can be calculated. Since the unloaded Q is known to be 5000 and sir 
the Q loaded by matched waveguides is 2500, 


5o = 2 X 10-" 

= 52 = 10 “^ 

for a matched-waveguide output load. The output load used, hdwev 
resulted in 

52 = 4 X 10-S 

and the total S was 7 X 10”^ or the loaded Q was reduced to 141 
Using these values m Eq. (5), it can be inferred that pq/C should be tak 
to be about 5.5 X 10* to achieve continuous operation. The quant; 
65o, the abscissa of Fig. 4-19, is thus 0.055. Figure 4-19 shows that t 
input and output loadings, for maximum TQz should be 0.58 So a 

Sbo. 444] 



2.26o, respectively. Thus, fortuitously, the load conditions achieved are 
very close to the optimum for this consideration, since 5i was 0.505o 
and ^2 was 2.05o. 

In Fig. 4-31 a second circuit using the beacon reference cavity is 
shown. This is a converter for a beacon receiver, and the cavity is 
used only as an aid to manual tuning. The cavity is so positioned that, 
at frequencies removed from the resonance frequency, it presents a short 
circuit at such a distance behind the resistor strip that the resistor strip 
appears as a matched load for the waveguide. The admittance as 
measured in the plane of the resistor strip is thus Yo plus the reciprocal 

nAfA/«4v^r /M itni it 

Fia. 4-31. — Single mixer with reference wavemeter for local oscillator. 

of the cavity admittance, just as is the admittance at the antenna of 
the oscillator tube in the circuit of Fig. 4*14. The conditions for con- 
tinuous operation of the oscillator tube are identical with those in the 
previous discussion, and thus the same cavity load circuit is used. 

4-14. Representative Mixers with Multiple Functions. — Included at 
the end of this chapter is a group of drawings showing, in somewhat more 
detail than in the sketches of the text, some mixers representative of the 
methods described in the text. 

First in the group. Fig. 4-32, is a broadband two-channel mixer for 
use with a broadband duplexer using the 1B24 TR tube. This mixer 
uses 1N23A or 1N23B crystals and has a lass due to crystal mismatch 
of less than 1.5 db for any crystal of this type when operated in the band 
from 9600-Mc/sec to 8500-Mc/sec. Many variations of this basic mixer 
have been designed for use in particuar radar systems. The differences 



[Sbo. 4-14 

are in mechanical devices; for example, a plate may be attached to the 
mixer so that the crystals and the local oscillator can be included in 
the shield box mth the i-f amplifi^ while the TR tube and AFC attenu- 
tor are outside the box. The plate thus becomes a part of one wall of 

or 2K26 local oBcillator, and 1 N23A 

DOW from 8600 to 9600 Mo/sec., at a transmitter 

power level of 50 kw. (For perspective view see Fig. 4.4.) 

the shield box and the duplexer waveguide runs parallel to this wall 
outside the box. 

Kgure 4-33 is a drawing of the two-channel mixer for the 1.25-cm 
band. This mixer uses 1N26 crystals, a 2K33 or 2K50 local-oscillator 
tube and a 1B26 TR tube. This mixer is representative of an LO coupling 

orrTrS t and operates at 

24,000 Mc/sec m a band ± 2 per cent in width, 

Sac. 4- 14] 




2 > 

Fig. 4-33.— Cross^tioiial view of double mixer for use with 1B26 TR cavity, 2K33 locri oscillator, and 1N26 crystal, in the 1.26 ± 1 per cent 

wavelength band. 

' 0 . 662 |y 


[Sbc. 4-14 

The last of the drawings, Fig. 4-34, shows the beacon provision for 
the band from 9320 to 9430 Mc/sec. The beacon-tuner and beacon-LO 

-j [-0375" 

“Position of beacon 
TR tuner 

Crystal mount 




Fig. 4-34.— 

circuits, wii 
mixer also, 
1B24 TR c 



In Secs. 1-4 and 2-3, the effective over-all noise figure of a super- 
heterodyne microwave receiver was shown to depend on three quantities; 
the conversion loss and noise temperature of the crystal mixer and the 
effective over-all noise figure of the i-f amplifier. At frequencies below 
3000 Mc/sec, independent measurements of these three quantities give 
results which, when applied in Eq. (1-26), are in good agreement with 
the results of direct measurements of the effective over-all noise figure of 
complete receivers. At higher frequencies, however, especially when low 
intermediate frequencies are used, the results of over-all measurements 
are larger than those predicted by the independent measurements of 
loss, noise, and i-f noise figure. 

In the apparatus described in Sec. 2*13, for measuring noise tempera- 
ture, a resonant cavity is included between the r-f oscillator and the mixer 
circuit. The purpose of this cavity, which is tuned to transmit the oscil- 
lator signal, is to remove spurious frequencies from the oscillator signal. 
If such spurious signals were to arrive at the mixer with the local-oscillator 
•.ngnal, they would be converted by the mixer to a frequency equal to the 
difference between the frequency of the local-oscillator signal and that 
of the spurious signals. Thus, any such signals lying above or below 
the local-oscillator frequency by an amount equal to the intermediate 
frequency of the test apparatus would be converted to the intermediate 
frequency and, therefore, would increase the apparent noise temperature 
of the crystal. It is found experimentally that the result of the. noise- 
temperature measurement, in the bands above 3000 Mc/sec, is always 
significantly smaller when a filter cavity is used. The conclusion is, there- 
fore, that some spurious signals in the two bands to which the receiver is 
sensitive do accomi)any the local-oscillator signal. This must be true of 
the system receiver also; in the absence of a filter cavity in the local- 
oscillator circuit, a noise figure must result that is larger than the mini- 
mum possible for the given crystal and i-f amplifier combination. 

6-1. Generation and Effect of Local-oscillator Noise. — The spurious 
signals accompanying the local-oscillator signal are termed “local- 
oscillator noise.” The electron beam passing through the oscillator 
cavity contains noise-current components at all frequencies, because it is 
made up of discrete electronic charges. If a klystron oscillator tube is 
operated at a reflector voltage that docHS not cause it to oscillate, a. noise 




[Sec. 5-1 

spectrum can be detected in its output circuit. The noise voltage in the 
output circuit is largest at the resonant frequency of the oscillator 
cavity, because the coupling to the electron beam is most efficient at this 
frequency. A curve of the noise voltage in the output circuit as a 
function of frequency closely resembles a resonance curve for the oscil- 
lator cavity. Reflex-klystron oscillator tubes, operated in this way, 
have been used as noise generators for use in the measurement of over-aJl 
noise figures of microwave receivers. 

It is reasonable to expect that when the tube is oscillating the noise 
voltages in the output circuit developed from spurious frequencies will 
be the same at frequencies on either side of the oscillation frequency. 

In addition, low-frequency noise 
components in the electron beam 
may, through amplitude and fre- 
quency modulation of the oscillator 
signal, produce noise sidebands lying 
at frequencies above and below that 
of the oscillator signal. These side- 
bands too, will be coupled to the 
output circuit with decreasing effici- 
ency at frequencies removed in- 
creasingly far from the resonant 
frequency of the oscillator cavity. 
Thus, the oscillator may be expected to have a noise spectrum in its out- 
put circuit similar to that shown in Fig. 6T. 

Whether or not the local-oscillator noise causes deterioration in the 
receiver noise figure depends upon the noise power in the local-oscillator 
spectrum at the signal and im age frequencies of the receiver. For a 
low-frequency receiver and, for example, a 30-Mc/sec intermediate 
frequency, the loaded Q of the oscillator cavity is usually sufficiently 
high to reduce the signal- and image-frequency noise components from 
the local' oscillator to a negligible level. For a given intermediate fre- 
quency, as the receiver frequency is increased the filtering by the local- 
oscillator cavity becomes less effective. To maintain the same filtering 
effect with a constant oscillator-cavity Q, it is necessary to increase the 
intermediate frequency proportionately to the increase in the local- 
oscillator frequency. In practice, oscillator tubes at high frequencies 
have cavities of lower loaded Q, because the skin depth decreases with 
increasing frequency and because the volume-to-surface ratio of the 
cavity decreases. Thus, local-oscillator noise would be expected to 
become increasingly apparent as the signal frequency is increased, even 
if the ratio between the local-oscillator and intermediate frequencies 
were held constant. 

Oscillator signal 

Image frequency 

Fia. 6*1. — ^Local-osciillator noise as a func- 
tion of frequency. 

Sec. 6*2] 



The presence of a significant amount of local-oscillator noise may be a 
factor determining the choice of the intermediate frequency. Especially 
for receivers at 9000 Mc/sec and above, the selection of an intermediate 
frequency has involved a choice between the reduced local-oscillator noise 
at high intermediate frequencies, on the one hand, and the lower amplifier 
noise at low intermediate frequencies on the other hand. Although the 
intermediate frequency most widely used at the Radiation Laboratory 
was 30 Mc/sec, an intermediate frequency of 60 Mc/sec was used in 
many 3-cm and most 1.26-cm receivers, in order to obtain a somewhat 
improved over-all noise figure in the presence of local-oscillator noise. 
The relative merits of several possible intermediate frequencies for a 
particular receiver must be decided from a knowledge of the magnitude 
of the noise contribution from the local oscillator at these frequencies, 
and from the i-f-amplifier noise figure that can be achieved at each 
intermediate frequency. 

6*2. Magnitude of Local-oscillator Noise for Typical Tubes. — To 
facilitate the choice of intermediate frequencies and of other operating 
parameters in converters, a program of measurement of local-oscillator 
noise was undertaken by Kuper and Waltz. ^ Measurements were made 
in the 3.2-cm band on 723 A/B tubes, and in the 1.25-cm band on 2K33 
tubes and on a few samples of other types. The quantity that was 
measured was the apparent noise temperature of a crystal driven, 
through an adjustable dissipative attenuator, from the local-oscillator 
tube under measurement. Measurements were made at intermediate 
freqxiencies of 30, 60, and 90 Mc/sec, at several points in the electronic 
tuning range of the tube. For each point in the electronic tuning range, 
the coupling between the crystal and the oscillator was set so that 0.5 
ma of rectified crystal current was produced. The 3.2-cm crystal had a 
conversion loss of 7 db and a noise temperature, in the absence of oscil- 
lator noise, of 1.2, and so was typical of the crystals used in a 3.2-cm 
receiver. For the 1.25-cm measurements the crystal, a type 1N2C, 
had a conversion loss of 8.5 db and an intrinsic noise temperature of 2. 
The results for a typical 723 A/B oscillator are given in Table 5*1. The 
data given in the table represent the increase in apparent noise temper- 
ature of the crystal over its value in the absence of incident r-f noise 
power (1.2). Values are given for the different reflector-voltage modes, 
for each of the three conditions of electronic tuning at each value of 
intermediate frequency. The column labeled “Center” corresponds to 
the reflector voltage giving maximum power for each mode and the 
columns labeled, “Half-power” — “High” and “Low” — denote respec- 
tively the values at reflector voltages giving half maximum output power 

1 J. B. H. Kuper and M. C. Waltz, “Measurements on Noise from Reflex Oscilla- 
tors,” RL Report No. 872, Dec. 21, 1945. 



on the high- and low-frequency sides of the center frequency. To 
maintain the 0.5-ma crystal current, it was, of course, necessary to 
decrease the attenuation between the oscillator and the crystal at these 
half-power points. 

Table 51. — Incbbasb in Crystal Noise Temperature for Typical 723A/B 

Oscillator Tube 






intermediate frequency, 
reflector tuning 

60- Me /sec 

intermediate frequency, 
reflector tuning 


intermediate frequency, 
reflector tuning 































































The over-all noise figure of a receiver, using this typical 723A/B and a 
crystal with a conversion loss of 7 db in a nonresonant mixer circuit is 
found from the expression 

+ 1 ) ( 1 ) 

where is the crystal noise temperature tc plus the appropriate value 
from Table 5*1. These values apply exactly only if the conversion loss 
is 7 db, but are approximately correct for any crystal operated at 0.5-ma 
crystal current. This is because the rectified current is roughly propor- 
tional to the reciprocal of the conversion loss. A crystal having a smaller 
loss would convert the incident noise power to the intermediate frequency 
more effectively, but the reduction in incident power, in both the local- 
oscillator signal and the noise sidebands, involved in reducing the 
rectified current to 0.5 ma would approximately compensate for this 
improved conversion efficiency. In systems use, the LO power level is 
set to give about 0.5 ma of crystal current. The values of Table 5*1, 
therefore, are significant for most crystals used in systems. 

Table 5*2 shows similar data from the experiments at 1.25 cm. 
These data were taken with a 2K33 tube, operated in the 200-volt 
reflector-voltage mode, and again the crystal current was held at 0.5 ma. 
The data are similar to those for the 723A/B tube, in that more noise 
is found when the tube is tuned electronically to the half power point 
in the high-frequency direction than when it is tuned in the low-frequency 
direction. It has also been found from these experiments that the noise 



Table 5*2. — Inobbasb in Noise Tbmpbbatube op Ceystal at 1.26 cm Dub to 
Noise prom 2K33 Oscillator Tube 

30- Mc/sec 

intermediate frequency, 
reflector tuning 


intermediate frequency, 
reflector tuning 


intermediate frequency, 
reflector tuning 



















spectrum is not as simple as that shown in Fig. 5*1. By means of a 
cavity resonator coupled to the waveguide between the attenuator and the 
crystal, it was possible to reflect the noise components in one sideband 
without affecting the transmission of the local-oscillator signal or of 
the other sideband. In this way the noise in the two sidebands could be 
compared by reflecting first one and then the other. It was found that 
the noise power was not the same in the two sidebands and that the 
relative magnitudes of the two noise powers depended upon the operating 
point in the reflector tuning range. The details of this effect and the 
theoretical explanation will be found in VoL 7 of this series. 

6'3. Effect of Local-oscillator Noise on Over-all Noise Figure. — The 
amount of deterioration in over-all noise figure that results from the 
existence of local-oscillator noise depends upon the other quantities that 
appear in Eq. (1). To show its ’ approximate value, however, a few 
examples will be considered. It is convenient to express the noise figure 
in decibels, because the relative merit of two receivers is determined by 
the ratio of two noise figures. Thus, in decibels, 

/r* = 7, + 10 logxo {Fti + t'c - 1). (2) 

At 3.2 cm a good crystal might have a conversion loss of 6 db and a noise 
temperature very close to unity. At 30 Mc/sec it is possible to obtain 
an i-f noise figure of about 2 db, or as a numerical factor, 1.6. With such 
a combination, Kq. (2) gives 8 db for the over-all noise figure in the 
absence of local-osc-illator noise. The ratio, expressed as a difference in 
decibels, of the noise figure that includes local-oscillator noise to the 
noise figure in the absence of such noise is 

Ftr = 10 log, 0^1 + 

where t' is the quantity tabulated in Tables 5*1 and 5-2. The quantity 
Fif expresses the deterioration in over-all noise figure due to the presence 
of local-oscillator noise. - '^rhe interesting range of i-f amplifier noise 



[Sec. 5-3 

figures is from 2 db to 6 db, or from a factor of 1.6 to a factor of 3. In Fig. 
5*2, the quantity Fjy hi decibels is plotted as a function of t' (F5 + — 1) 

for a range from 0 to 10. Table 6*3 gives values, in decibels, of the 
increase in over-aU noise figure due to the presence of the amounts of 
local-osciUator noise taken from Tables 6*1 and 6*2. The values given 
for 3.2 cm correspond to the 170-volt mode of the typical 723A/B tube. 

These are given for four assumed 
values of (F5 + — 1) and for inter- 

mediate frequencies of 30, 60, and 90 
Mc/sec. The value of 1.6 for this 
expression could correspond to an i-f 
noise figure of 1.6 (2 db), and a crys- 
tal noise temperature of unity. The 
higher values allow for larger crystal 
noise temperatures, higher i-f noise 
figures, or both. Thus, the value 3 
could result from an i-f noise figure of 
2 (3 db), and a crystal noise temperature of 2. Similar numbers are also 
given for the 1.2^cm receiver using the typical 2K33 tube used for the 
data of Table 6*2. 

Fig. 6*2. — Deterioration of effective 
over-all noise figure vs. 

- 1 ). 

Table 5-3. — ^Inceeasb in Ovbb-all Noise Figure or Receiver (in Decibels) for 
Various Values of (Ftf + ic — 1) Corresponding to Local-oscillator 
Noise op Tables 6-1 and 5-2 

Fjf te 1 

30 Mc/sec 

60 Mc/sec 

90 Me /see 










3.2 cm 






















723A/B in 























1.25 cm 













































From this table it is evident that the effect of local-oscillator noise on 
the effective over-all noise figure of a receiver is large, even at 3.2 cm 
and with a 60-Mc/sec intermediate frequency. The difference between 
the numbers in the columns for 60 Mc/sec and those in the columns for 
30 Mc/sec, in the same crosswise row, represent the decrease in noise 

Sec. 64] 



figure that could be achieved through the use of the higher intermediate 
frequency, if the same i-f amplifier noise figure were obtaiaed at these two 
frequencies. In practice the i-f amplifier noise figure achieved at 60 
Mc/sec is larger than that at 30 Mc/sec; consequently the full advantage 
indicated by the table cannot be realized. For 3.2-cm receivers the 
relative advantages of 30-Mc/sec and 60-Mc/sec i-f amplifiers have been 
the subject of considerable controversy, and little thought has been 
given to the use of frequencies higher than 60 Mc/sec for the purpose of 
reducing the effect of local-oscillator noise. In the 1.25-cm band, it 
has usually been considered advantageous to use an intermediate fre- 
quency of at least 60 Mc/sec and the trend was toward even higher 
frequencies. Another solution to the LO-noise problem, to be discussed 
in Chap. 6, allowed the use of 30 Mc/sec as an intermediate frequency, 
however, even for receivers at 1.25 cm. Intermediate frequencies higher 
than 60 Mc/sec were therefore not used extensively. 

In practice, when the local oscillator is tuned off center in the elec- 
tronic tuning range, the local-oscillator noise is not so large as is indicated 
in the tables, because the local-oscillator coupling is left fixed at the 
value giving about 0.5 ma at the center of the tuning range. The cou- 
pling at the half-power points in the electronic tuning range is thus only 
one-half as great as that to which the data apply, and the crystal current 
is only about 0.25 ma. Accompanying this reduction in local-oscillator 
power is a small increase in conversion loss but this is less than 0.5 db in 
most cases. Because the smaller coupling reduces the incident noise 
power correspondingly, the increase in noise temperature of the ciystal, 
caused by incident local-oscillator noise at the half-power points, is only 
half that given in Tables 5T and 5*2. For most conditions this gives 
almost the same effect at the low-frequency half-power point as at the 
center of the tuning range. The increase in over-all noise figure at the 
center frequency, therefore, holds approximately over the low-frequency 
part of the electronic tuning range. In the high-frequency portion of the 
electronic tuning range there is an increase in local-oscillator noise, but 
its effect is somewhat less than that indicated in Table 5*3. Thus the 
value at the center of the electronic tuning range is the most significant. 
In order to minimize the deterioration due to local-oscillator noise it is 
helpful to operate the tube principally in the low-frequency half of the 
reflector mode. 

6-4. Reduction of Local-oscillator Noise by the TR Cavity. — The 
measured values of local-oscillator noise and its effect on the over-all 
noise figure of the receiver apply to a converter circuit only when there 
are no resonant parts in the LO coupling circuit. For most converters 
used in radar, therefore, this condition does not hold, becaxise the reso- 
nant TR cavity influences the coupling between the local oscillator and 



[Sbc. 54 

the crystal. For circuits in which iris coupling is used, it is required that 
the local-oscillator wave reflected by the TR cavity reinforce the wave 
travding directly from the iris to the crystal. The coupling of power 
from the local oscillator to the crystal is therefore almost four times as 
great as it would be if the resonant TR cavity were not present. The 
coupling of local-oscillator noise at the image frequency is also increased 
by this factor, because of reflection by the TR cavity. At the signal 
frequency, however, the TR cavity is resonant and its reflection coeffi- 
cient is small. Local-oscillator noise in the signal sideband does not 
become reinforced by reflection from the TR cavity; thus only one- 
quarter as much power at the signal frequency is coupled from the local 
oscillator to the crystal. If the available noise powers in the signal- and 
image-frequency sidebands were equal, the ratio of total noise power to 
LO signal power coupled to the crystal would be only five-eighths as large 
as in a nonresonant mixer circuit. Allowing for some reflection of signal- 
frequency noise by the TR cavity, a value for the increase in crystal 
noise temperature 0.7 times the values given in Tables 5T and 6-2 may 
be used to estimate the effect on over-all noise figure in a converter 
circuit of this kind. Similar results are obtained for the other coupling 
schemes that depend upon reflection of the local-oscillator wave by the 
TR cavity. Coupling of local-oscillator power to the crystal through a 
directional coupler, however, does not result in this reduction in local- 
oscillator noise. 

In Table 54 are given values of the increase in over-all noise figure 
similar to those of Table 5*3 but computed on the assumption of a reduc- 

Table 54. — ^Inckbase in Overfall Noise Figueb op Receiver, in Decibels, for 
Various Values op (Fjf + ie — 1), with Reduction in Local-obcillator 
Noise by TR Cavity and with Coupling Independent op Point 
IN Electronic-tuning Range 

30 Mc/sec 

60 Mc/sec 

90 Mc/sec 










3.2 cm 






















723A/B ia 























1.25 cm 





















2K33 in 
























Sec. 5'5] 



tion to 0.7 of the measured values, for the radar converter with a reso- 
nant TR cavity. The noise power at the half-power points has been 
reduced by an additional factor of two from the measured values of 
Tables 5T and 5-2, on the assumption that the coupling from the local 
oscillator to the crystal is set for 0.5 ma of crystal current at the center of 
the electronic tuning range and held fixed when the electronic tuning is 

For the 3.2-cm tube, the advantage of an intermediate frequency of 
60 Mc/sec over one of 30 Mc/sec is small and can be easily lost because of 
increased i-f amplifier noise figure. At 1.25 cm an advantage of more 
t.hnn 1 db is obtained, and this is more than would be lost because of 
increased i-f amplifier noise figure. Even with the filtering effect of the 
TR cavity, however, the presence of the local-oscillator noise adds to the 
over-aJl recover noise figure 2 to 3 db in the 3-cm band, and 4 to 5 db in 
the 1.25-cm band, with good i-f amplifiers and quiet crystals. It is 
therefore well worth the effort to try to find some method of further 
reducing the effect of local-oscillator noise on the over-all noise figure. 

5«5. Reduction of Local-oscillator Noise by Resonant Filters. — The 
most direct method of removing the effect of local-oscillator noise would 
be to use a filter cavity m the local-oscillator circuit, similar to that used 
in the apparatus for measuring the noise temperature of crystals. Two 
difficult problems are met if this is done. First, the tuning of the 
receiver becomes much more complicated because the filter cavity and 
the local oscillator must be kept together, as the receiver is tuned by 
alteration of the local-oscillator frequency. If an AFC circuit is to be 
used it must include provision to track the cavity and the local oscillator 
automatically. The second problem involves the LO coupling circuit. 
As shown in Sec. 4*8, a cavity can be coupled to a local oscillator without 
producing frequency discontinuities, only if stringent conditions on the 
coupling are met. Either a large dissipative attenuation must be used 
between the oscillator and the cavity or the input coupling hole must be 
small. Both of these methods of avoiding frequency discontinuities 
result in considerable reduction in the output power of the cavity com- 
pared with that available from the oscillator. The prevention of inter- 
action between the signal circuit and the local-oscillator circuit is a 
major problem in mixer design because the available local-oscillator 
power is limited. An additional reduction of available power has 
serious consequences on the design of the coupling circuit. It is obvious 
that the filter cavity cannot simply be placed between the local oscillator 
and any of the coupling circuits described in Chap. 3. 

The tracking between the local-oscillator frequency and the cavity 
resonant frequency could be accomplished by use of an AFC circuit 
causing the local oscillator to be controlled at the cavity frequency. 



[Sisc. 5-5 

similar to the beacon AFC circuits described n Chap. 7. With a ther- 
mally tuned oscillator such as the 2K45 or 2K50, this AFC circuit could 
cause the oscillator to track the cavity frequency over a wide band. 
A low-frequency component on the mixer-crystal current could be 
used to supply the error signal in the same way as in the beacon-cavity 
AFC schemes.’ The primary frequency control of the local oscillator 
wou’d then be the cavity-tuning control. With electromechanical 
devices, this control could be made to maintain the correct receiver 
frequency through a separate AFC channel operating from the i-f circuits. 
For a receiver designed to operate at a fixed absolute frequency, as is 
desired for beacon reception, the filter cavity would also be the frequency 
standard and no further automatic frequency control would be needed. 

In Chap. 4 it was shown that the maximum value of the product of the 
loaded Q and the transmission eflSciency compatible with the condition 
ensuring continuous operation of the oscillator, for a cavity with a given 
unloaded Q and for a given pulling figure for the oscillator, is obtained 
by the method of decoupling by adjustment of the cavity-load conditions, 
without dissipative attenuation. In the present case it is desired to 
obtain a loaded Q suflBicient to reduce to a negligible level the noise 
power in the sidebands. The goal would be to make possible the use of a 
30-Mc/sec intermediate frequency vrithout a substantial contribution 
to the over-all noise figure from the local-oscillator noise. At 3-2 cm, 
a 10-db increase in the ratio of available local-oscillator power to available 
noise power in the sidebands would reduce the effect of the lo(‘.al-os(nllator 
noise to less than 1 db under most circumstances. A selectivity great 
enough to give a 10-db increase in the ratio is obtained at 9000 Mcs/sec 
with a cavity having a loaded Q of 450 or more. To be able to deliver 
1 mw of local-oscillator power to the mixer, from a tube having an 
available power of 15 mw, the fractional transmission must be at least 
0.067. If the cavity is operated with equal input and output loading 
and is decoupled from the oscillator by a dissipative attenuator, the 
maximum output power from the cavity, compatible with the condition 
for continuous oscillation is 

from Eqs. (4*6) and (4-21). For a 2K25 or 723A/B oscillator, the value 
of h may be taken as 2.75 X 10^ corresponding to the measurements 
quoted in Sec. 4T4. The maximum unloaded Q that can be used under 
these conditions is about 4800. The loaded Q resulting would be about 
1600; thus the noise power in the 30-Mc/sec sidebands would be reduced 
by 21 db. This is sufficient attenuation of the noise sidebands but 

Sec. 5‘6] 



provides only sufi&cient local-oscillator power to drive the crystal. 
Fortunately, the resonant nature of the cavity can be used to provide 
the decoupling of the signal circuit from the local-oscillator circuit. A 
circuit for a two-channel mixer such as that shown in Fig. 5*3 might be 
used. The attenuator should have a minimum attenuation of about 
9 db, and it therefore provides a load of small reflection coefficient for 
the oscillator. Since the cavity is nonresonant at the signal frequency, 
the reflection of signal-frequency waves by the interaction of the cavity 
in the mixer is small and the cross attenuation from the radar mixer to 
the AFC mixer is large. For a larger safety factor in the available local- 
oscillator power in the radar mixer, a cavity of lower unloaded Q could be 
used and it would then be safe to use a smaller decoupling attenuation in 
the local-oscillator circuit. Since less dissipative attenuation is needed 
if the output loading of the cavity is increased and the input-circuit 
loading is decreased, somewhat 
larger available local-oscillator 
power could be obtained if the 
cavity were coupled in this way. 

An increase in the output loading 
and a decrease in the input load- 
ing, in the manner indicated by 
Eq. (4T2) would reduce the re- 
quired amount of dissipative 
attenuation sufiiciently to more 
than compensate for the decreased 
transmission efficiency of the 
cavity circuit. This, however, 
could be done only at some sacri- 
fice in loaded Q, and thus in sup- 
pression of the local-oscillator noise. A combination of a higher unloaded 
Q and unequal input and output loading would give the desired result 

Fiu. 5*3.- 

"Douhlo tnixer witli (uivity filter 
for LO noiao. 

without a decrease in noise suppression. 

6-6. Reduction of Local-oscillator Noise by the Use of a Cavity as 
Part of the Oscillator Taxik Circuit. — Another method by which a cavity 
could be used to decrease the power in the noise sidebands of the local- 
oscillator signal is to use the cavity as a part of the tank circuit of 
the oscillator. It was shown in Sec. 4-11 that a cavity load circuit on 
an oscillator can give frequency stabilization of the oscillator, if the line 
length between the cavity and the grids of the oscillator resonator is 
effectively an integral number of half wavelengths. For very close 
coupling between the oscillator and the cavity, the tuning of the oscillator 
is disci mtinuous in freciuency but oscillation at the resonant frequency of 
thc^ external cavity is stabh^ ''Phis cumclition amounts to a substitution 



[Sdc. 6-6 

of the external cavity for the tank circuit of the oscillator and a con- 
sequent oscillator-resonator Q determined primarily by the external 
cavity. Tuning of the oscillator can be accomplished directly by tuninp 
the external cavity. Since the best control of the oscillator frequency 
by the external cavity results if the external cavity has the hipest 
possible unloaded Q, the filtering of local-oscillator noise sidebands is 

This method is rather difficult to apply because the locking of the 
oscillator frequency to that of the cavity is critically dependent on the 
length of the line between the cavity and the oscillator. Because this 
line has some disapative loss, there is a limit to the magnitude of sus- 
ceptance that can be developed by the external cavity at the grids of the 
oscillator resonator. This maximum susceptance sets a limit on the 
frequency range over which the oscillator can be pulled by the external 
cavity without retuning of the oscillator resonator. If the oscillator 
resonator is retuned, there is a limit on the range of frequency for which 
a fixed length of line between the oscillator and the external cavity will 
give the desired frequency control by the external cavity. This limit is 
determined by the rate of change of the effective electrical line length 
with frequency, and must thus depend upon the number of ha.]f wave- 
lengths of line used. For the largest tuning range, the smallest possible 
number of half wavelengths of line must be used, and refiections increasing 
the dissipative loss or the frequency-sensitivity of the line must be 
avoided. With 2K25 oscillator tubes, which have a coaxial output line 
several half wavelengths long, a fixed length of line between the oscUlator 
and the external cavity can be used for only a small frequency range* — 
perhaps 2 per cent. The oscillator can be tuned, by means of the 
external cavity alone, through a range of about 1 per cent if the 
cavity has an unloaded Q of 25,000. 

Because of lire variation, among tubes, in the electrical length of the 
output line, a given external circuit, containing a fixed line length between 
the tube antenna and the cavity, does not give frequency control by the 
external cavity over the same range for all tubes. This vaiiation 
causes one of the principal difficulties in setting up the circuit, since 
it necessitates a variable antenna-to-cavity line length. For each tube 
this line must be adjusted to allow control by the external cavity over the 
desired raiige.^ Another difficulty encountered in setting up a circuit of 
this kind lies in the fact that, although the oscillator, when it has been 
locked to the cavity, can be tuned over a considerable range by tuning 
of the external cavity alone, the range of oscillator tuning for which 
locking can be produced is very small. A monitoring circuit is required 
to make sure that locking has occurred. 

Oscillators locked to cavities in this way have been use<l in the 10-cm 

Sec. 6-6] 



band for the stabilization of frequency. With a 2K2S tube, a single 
half-wavelength line between the oscillator cavity and the external cavity 
can be used. The operation is considerably more satisfactory than that 
obtained at 3.2 cm with 2K25 tubes, because of this short line length. 
This method is not useful in decreasiag the over-all noise figure of a 
10-cm receiver because, with a 30-Mc/sec intermediate frequency, local- 
oscillator noise contributes a negligible amount to the over-all noise 
figure. When used with a very high-Q cavity, such as a resonant echo 
box, however, it is useful as a frequency-stabilization circuit. 

In the 1.25-cm band, only enough experimentation has been done with 
this kind of circuit to show that locking can be obtained and that fre- 
quency control by the external cavity can give tuning over 100 or 200 
M c/sec. With the 2K33 tube, with its special double-resonator circuit, 

Line length adjusted to suit 


Fig. 6*4.— Circuit for the uso of a 2K26 oscillator locked to an external cavity for LO noise 


difficulties are again encountered because the same external line length 
does not give control over the same frequency range for various tubes. 
For the purposes of LO-noiso suppression and of frequency stabilization, 
this circuit offers much in the way of simplicity. It may in the future 
be developed to the point of being practicable from an operational view- 
point, especially if the high-Q cavity and coupling circuit are included as 
parts of the tube. Ho far, however, it has not been developed to the 
point of being usable in a receiver intended for field use in the wavelength 
regions below 10 cm. A tube incorporating a high-Q resonator in this 
way loses the vciy useful property of electronic tuning, through the 
frequency-stabilization effect, and the tuning mechanism must produce 
a dimensional change in the high-Q cavity. 

In Figs. 5*4 and 5-5 are shown two possible 3.2-cm mixer circuits 
incorporating this type of circuit for the suppression of local-oscillator 
noise and for frequency stabilization. The circuit of Fig. 5*4 provides 
for the extraction of local-oscillator power for the mixer through a 
variable coupling iris in what would normally be a shoiii-circuiting end 



[Sac. 5-6 

wall of the waveguide behind the oscillator antenna. This iris must be 
about one-quarter wavelength behind the antenna, to allow the antenna- 
to-waveguide coupling to operate eflSiciently. A large standing-wave 
ratio may exist in the line between the cavity and the oscillator, however, 
especially imder the condition that the external cavity causes a consider- 
able pulling of the normal oscillator frequency. At a given iris setting, 
the efficiency of the coupling of local-oscillator signal into the mixer is 
greatest when a voltage loop of the standing-wave pattern ocuuirs at the 
antenna, and would be zero if a voltage node were to occur there. The 
amount of power coupled into the mixer for a given iris setting would 
therefore vary considerably, depending upon the amount of pulling 
by the external cavity and upon the cavity-to-antenna line length. 

Fio-. 5*5. Cavity used as frequency coutroL and source of locul-(>s(uIIii(.or power of the 
mixer, for the purpose of LO-noiso suppression. 

If a voltage node occurs near the antenna, the iris must adjusted for 
large coupling between the local-oscillator circuit and the signal (urcuit, 
mth consequent reflection of received signal power. No provision is 
included to show when the circuit is adjusted in such a way that th(^ locuiI 
oscillator is locked to the cavity. Such a provision (^ould he made by 
coupling a separate detector crystal to the cavity as in(li<*.at(Ml by the 
broken lines in Fig. 5-4. Transmission thi’oiigh the (*.avity to this 
crystal would indicate oscillation at the resonant frccjiKUK^y of tlic'. (‘uvity. 

In the circuit of Fig. 5*5 the cavity itself is iiscxl as tlu^ soure.e of 
local-oscillator signal for the mixer. Since the cavity must Ix^ tightly 
coupled to the oscillator, a large amount of energy is storcul in tlx^ (‘avity 
and the coupling to the mixer may be small. To accomplish adjustment 
of the coupling to the mixer crystal a variable exit iris must he used on the 
cavity and for this a sliding spring-metal wall between th(^ waveguide 
and the cavity can be used. Transmission of power through the (iavity 
to the mixer crystal, with consequent production of nxitificxl current by 

Sec. 5'71 



the mixer crystal, serves to indicate that the oscillator is locked in 
frequency to the cavity. The adjustment procedure, however, is com- 
plicated by the fact that no indication of oscillation is provided when the 
oscillator is not locked to the cavity. 

Neither of these circuits has been developed to the point of being 
practical for use in receivers. They have been included here only to 
show some of the difl&culties that are encountered with this kind of noise- 
suppression cii-cuit and the direction in which one might proceed. If 
an oscillator containing a built-in high-Q cavity were available, the 
mixer problem would be simpler. A separate output line from the 
resonator of the oscillator would provide the useful power and this line 
would be coupled into a mixer circuit in any of the conventional ways. 
The frequency-stabilized 10-cm oscillators earlier referred to were used 
in this way; one output loop was used to couple the oscillator tightly 
to the high-Q cavity and a second to derive the useful power. For the 
present, however, the use of these circuits for LO-noise suppression 
has been abandoned in favor of the more foolproof '^balanced” mixer 
described in Chap. 6. 

6*7. Effect of D-c Bias on the Mixer Crystal. — A slight improvement 
in over-all receiver noise figure can be obtained through the use of a 
small bias voltage across the mixer crystal, if local-oscillator noise is 
present. The effect of the bias voltage is to make the conversion loss 
at a reduced local-oscillator level almost as small as that at the normal 
level. Since the noise sidebands are proportionately reduced, an improve- 
ment in over-all noise figure results. Several additional advantages can 
be gained through the use of such a bias voltage. Accompanying the 
reduced LO power requirement is a reduction in the reaction of the 
local-oscillator circuit on the signal circuit of the mixer. The over-all 
noise figure becomes less dependent upon the amount of incident local- 
oscillator power at the crystal, because the conversion loss does not 
increase so rapidly as the local-oscillator drive is decreased. Finally, 
the i-f conductance of the crystal is less dependent on the amount of 
local-oscillator drive. 

Figure 5-G is a graphical illustration of how the conversion loss would 
be affected by a positive bias, if the d-c characteristic*, determined the 
behavior of a crystal used in a microwave mixer. For the conditions 
illustrated in Fig. 5T)a, the local-oscillator drive has been taken as 
less than enough to drive the crystal to the pai*t of the forward char- 
acteristic having the greatest slope. The addition of a positive bias 
(Fig. 5-6?0 increases the i-f current because the positive peaks of the 
envelope drive the crystal to a region in which the characteristic has a 
greater slope than before, whereas there is little change in the slope of the 
characteristic in the negative part of the envelope. There is an optimum 



[Sec. 5-7 

bias voltage for each local-oscillator level since a further increase in biai^ 
voltage would cause the negative part of the envelope to contribute an 
i-f current of increasing magnitude with increasing bias voltage. When 
this current increases more rapidly than that due to the positive part of 
the envelope, the total i-f current begins to drop, because the current 
contributed by the negative part of the envelope has the opposite phase 
to that from the positive part. The smallest conversion loss for a 
particular local-oscillator amplitude usually results from the uso of a 

bias voltage less than the amplitude 
of the local-oscillator signal. 

One method of demonstrating 
the eflFect of a bias voltage is to 
measure the elBFective over-all noise 
figure of a representative receiver 
with various values of local-oscilla- 
tor coupling and of d-c bias. Such 
a measurement is made by finding 
the available c-w input signal power 
required to give an output signal 
power equal to the output noise 
power, when the signal frccpiency is 
at the point of maximum sensitivity 
in the pass band. The effective 
over-all noise figure is the ratio of 
this signal power to kTBj where B 
is the effective noise bandwidth of 
the i-f amplifier. For relative noise- 
figure measurements, provided B is 
not changed by the parameters 
varied between measurements, it 
is not necessary to know B or 
the absolute power level. Thus, 
to demonstrate the effect of bias 

I-f component 
in rectified current 

Envelope of signal 
and local 
oscillator waves 


I-f component 
in rectified current 

Bias voltage 


Fig. 6*6. — Graphical iUustration of 
decrease in conversion loss with positive*’ 
bias, for small local-oscillator level. The 
barrier capacitance is neglected. 

voltage on the crystal it is not necessary to have an absolute calibration 
of the available signal-generator power. A block diagram of a circuiit 
for measuring the over-all noise figure is shown in Fig. 5*7. The attenu- 
ator associated with the signal generator is made to match the trans- 
mission line. A TR cavity tuned to the signal-generator frcciucncy is 
used, and a mixer with iris-coupled local oscillator. A part of the input 
circuit of the i-f amplifier is shown to illustrate the method of applying 
a bias voltage through the crystal-current metering circuit. Thc^ 
circuit shown is only symbolic, in the sense that a practical circuit 
includes, instead of the simple condenser filter on the crystal-current lead, 

Sec. 5-8] 



a low-pass x-filter of two or three sections, made up of r-f chokes and 
condensers. The bias voltage is supplied from a battery and voltage- 
divider circuit. The best values of the battery voltage and of the resist- 
ance of the potentiometer circuit, for experimental purposes, should be 
such that the series resistance introduced into the crystal-current circuit, 
for a bias voltage of one volt, is small compared with the resistance of 
the crystal. For a resistance of 50 ohms per volt, the negative bias, 
at 1 ma of rectified current, produced by the flow of the rectified crystal 
current through the potentiometer would be equal to 0.05 volts, a 
negligible quantity compared with the forward bias applied by the 

Part of i-f input circuit and 

Fig. 5*7. — Circuit for measuring the effect of crystal bias on over-all noise figure. 

battery circuit. The output power meter may be a thermocouple or 
a square-law crystal detector with a milliammeter. 

5.8. Results of Experiments on the Effect of D-c Bias. — The results 
of some experiments of the kind just described are plotted in Fig. 5*8. 
These data were taken on a 1N23 crystal having a measured conversion 
loss of 7.9 db and a noise temperature bf 1.9. The noise figure of the 
i-f amplifier was about 5 db for crystals having average i-f admittance. 
In this figure a curve of relative over-all noise figure as a function of 
crystal current due to the local oscillator alone (with the bias voltage set 
at zero) is given. The minimum of this curve is taken as the zero point, 
and an increase in noise figure from this corresponds to an ordinate 
below this point, a convention used since minimum noise figure is desired. 
There is a set of curves each having its right-hand terminus lying on the 
curve for no bias. Each of these curves gives the relative over-all noise 
figure for constant total crystal current equal to that corresponding to 
the abscissa of the right-hand terminus point and made up of rectified 
current and current due to the bias voltage in varying proportions. The 
abscissa gives, for these curves, the crystal current due to the oscillator 
alone. As the curve is traversed toward the left, the bias voltage is 



[Sbc. 5*8 

continuously increased, to keep the total current constant. The curves 
show that for any total current there is very little deterioration, and for 
most currents some improvement, if that current is produced by smaller 
local-oscillator drive and some bias, than if it is all produced by the local 
oscillator. The improvement possible varies considerably from crystal 

Fia. 6*8. — Effect, on over-all receiver noise figure, of u positivo hijiH on thocryHtnl. 
The data are for a 1N23 crystal vrith 7.9-db convorsiou loss and a iioiso tcniporaturo of 

to crystal and data on about 10 crystals showed that as miu^h as 0.5 db 
improvement may be gained or as little as 0.1 db. The liost noise figure 
was obtained in most cases with an amount of local-osc.illator drive equal 
to that which gave minimum noise figure without bias, and with enough 
bias added to increase the crystal current by a fa(^tor bctwocm 1.5 and 2. 
Almost as good results are found with bias at about half tho normal local- 
oscillator drive. 

The conclusions that can be drawn from these expciriments are 
restricted because there are many parameters that change with locah 

Sue. 5-8] 



oscillator drive which were not measured. For instance, the r-f admit- 
tance of the crystal to the signal is affe<^ed by a change in either the bias 
voltage or the local-oscillator drive, and tMs could contribute to the 
variation in the over-all noise figure. To eliminate this the mixer 
should have been tunable and adjusted for minimum noise figure for 
each point. Another source of error lies in the use of a fixed coupling 
circuit from the crystal to the i-f amplifier. Since the i-f admittance of 
the crystal depends upon the local-oscillator drive and the bias voltage, 
the effective noise figure of the i-f amplifier varies from point to point. 
Thus the only thing that this experiment does show is that for this 
combination of crystal, mixer and i-f amplifier, some improvement in the 
over-all noise figure can be obtained through the use of forward bias 
on the crystal. Of greater significance may be the fact that the range 
over which the local-oscillator drive can vary without a large increase 
in effective over-all noise figure is increased by the use of the optimum 

Fio. 6-9. — Circuit for adding bias voltage to inixor crystal. 

bias for each value of the local-oscillator drive. The noise figure can be 
kept near its minimum value with a much smaller local-oscillator drive 
with the addition of an appropriate bias voltage than without bias. 

To utilize this extension in the allowable range of local-oscillator 
drive, a fixed bias circuit has sometimes been added to the microwave 
receiver. Such a bias circuit is shown in Fig. 5*9. The bias voltage 
applied in the absence of rectified crystal current is 0.175 volts, due 
to the 1-ma current through the voltage divider. With increasing 
local-oscillator drive, the bias voltage decreases because the rectified 
current flows in the opposite direction through the 175-ohm resistor and 
thus decreases the voltage drop across it. At 1 ma of rectified current 
the bias voltage is zero. Thus the bias voltage is significant primarily 
for small local-oscillator drive, where it has the most beneficial effect. 

To evaluate completely the usefulness of the bias voltage, measure- 
ments should be made separately of the loss, noise temperature, and i-f 
admittance of the crystal. The data just quoted, showing a slight 
improvement in over-all noise figure from an added bias when the local- 
oscillator drive is optimum, could be explained by a decrease in the 
conversion loss from the addition of the bias voltage. The same decrease 
in conversion loss could be achieved with greater local-oscullator drive but 



[Sue. 6-8 

the increase of converted local-oscillator noise apparently results in a 
poorer noise figure. The advantage of increased permissable range of 
local-oscillator drive lies in the possibility of obtaining a large electronic- 
tuning range from the oscillator for AFC purposes. The addition of 
bias voltage by the circuit of Fig. 6-9 allows the tuning to be carried to a 
lower-power point in the reflector mode than without the bias. Some 
experiments were made to measure the over-all noise figure over the 

Fig. 5'10. — Effect of bias circuit of Fig. 6'9 on the conversion loss, noise temperature, 
i-f resistance, and over-all receiver noise figure as the local oscillator is olectronically tuned 
through a reflector mode. The crystal is a 1N23A, the LO tube a 723A/B, the intermediate 
frequency 30 Mc/sec, and the effective i-f noise figure 4 db. Bias voltage is supplied from 
the circuit of Fig. 5*9. 

range of electronic tuning, with and without bias. The bias circuit was 
that of Fig. 5-9 and independent measurements of loss, noise temperature, 
and i-f resistance of the crystal were made. The apparatus was similar 
to the noise-temperature test set in that it included the one-cighth-wave- 
length-line matching transformer between the crystal and the i-f amplifier. 
This made the measurement of the crystal noise temperature independent 
of the i-f resistance of the crystal. A noise diode was used to calibrate the 
apparatus and to measure the i-f resistance. With the noise diode, the 

Sbjc. 5*81 



diode current required to produce a given deflection on the output meter 
was measured with each of several resistances substituted for the crystal. 
When the crystal was in place and operating with the same amplifier 
gain, the diode current required to give noise sufficient to produce this 
same deflection was thus a measure of the i-f resistance of the crystal. 
The conversion loss was measured by use of a calibrated low-level signal 
generator. The i-f output power from the crystal was found by use of 
the noise power from the noise diode as a standard of reference, since 
the i-f resistance of the crystal was known. The i-f amplifier and output 
meter could thus be regarded as a calibrated low-level i-f power meter. 

The results of this experiment are shown m curves of Fig. 6T0. 
At the center of the electronic tuning range, the crystal used showed no 
improvement in over-all noise figure due to the bias when the rectified 
current was 0.5 ma. The over-all noise figure plotted is calculated from 
the loss and noise temperature assuming an effective i-f amplifier noise 
figure of 4 db. At the quarter-power points in the electronic-tuning 
range, however, some improvement is foimd. A crystal current of 
0.125 ma would result there without bias. With the tube tuned to 
the quarter-power point on the high-frequency side of the center of the 
electronic-tuning range, the noise figure is improved by 1.2 db by the 
addition of the bias and is almost the same as at the center of the mode. 
This is almost completely accounted for by the decrease in conversion 
loss due to the bias, since the local-oscillator noise is almost constant in 
the high-frequency part of the electronic-tuning range. On the low- 
frequency side the improvement in noise figure is not so great, however, 
because, although the conversion loss is decreased by the same amount by 
the addition of the bias voltage, the local-oscillator noise is so large that 
its effect increases significantly with the decreased conversion loss. The 
bias current must also contribute to the noise temperature somewhat 
but this is apparently small compared with the converted local-oscillator 
noise. Since the crystal used for this experiment had a noise-temperature 
of only 1.3, for about 1 ma of rectified current, small effect due to the 
bias current would be expected. 

The most marked effect of the bias voltage in Fig. 5* 10 is the change 
in i-f resistance. Whereas without bias the resistance rose from about 
400 ohms to over 650 ohms when the local-oscillator drive was decreased 
by a factor of 4, with bias the i-f resistance was between 340 and 370 
ohms for the whole range of local-oscillator drive. If the i-f amplifier 
to be used in a receiver were sensitive to the i-f resistance of the crystal, 
with respect either to noise figure or to bandpass characteristics, a 
bias-voltage circuit would be of considerable value. Provided the image- 
frequency wave is not reflected to the crystal, however, the bias voltage 
makes little difference in the percentage spread of crystal resistances 


encountered for various crystals at a fixed local-oscillator level. Hovr- 
ever, if the image-frequency wave is reflected to the crystal, by a TR 
cavity for instance, the situation is much more complicated because the 
i-f impedance varies in both resistive and reactive parts, from crystal to 
crystal, as discussed in Chap. 2. A bias voltage would probably change 
the relative spread of impedances very little. 

Both of the experiments just described were made at 3.2 cm mth a 
30-Mc/sec intermediate frequency. At 1.25 cm where the local-oscillator 
noise is somewhat greater, a larger improvement might be gained through 
the use of positive bias. No very reliable data have been taken to find 
out how much the improvement might be, largely because the balanced 
mixer was introduced as a good solution to the problem of local-oscillator 
noise. Since the balanced mixer has several other advantages besides 
that of the suppression of locfd-oscillator noise, it is often worth using, 
even if other methods of noise suppression are sufficient. A discussion 
of the balanced mixer is to be found in Chap. 6. 

In a receiver using bias voltage on the crystal, it is desirable to provide 
the usual meter for the rectified crystal current to facilitate adjustment of 
the local-oscillator coupling. The bias voltage alone produces a rather 
small crystal current but when a small amount of local-oscillator power is 
added, the crystal current increases by a considerably larger amount 
than it would without the bias voltage. For the purpose of setting the 
LO power level, it has been considered advantageous to use a meter jack 
or switch which short-circuits the bias voltage when the meter is put into 
the circuit, so that the crystal-current reading is approximately propor- 
tional to the local-oscillator power incident on the crystal. The jack 
also allows one side of the meter to be grounded, which simplifies the 


The complexity of design and of operation of mixer circuits in which 
filter cavities are used for the suppression of local-oscillator noise has led 
to considerable interest in the development of a microwave balanced 
mixer. A balanced mixer utilizes two separate mixer units driven in 
shunt by the local-oscillator signal and in push-pull by the received 
signal, or vice versa. This results in a balanced push-pull output signal 
at the intermediate frequency, and the i-f amplifier input circuit is 
designed to give response only to such a balanced signal. Any i-f output 
signals derived from noise accompanying the local-oscillator power appear 
in the same phase at the output terminals of each mixer unit and are 
therefore discriminated against by the input circuits of the push-pull i-f 
amplifier. The suppression of local-oscillator noise is thus obtained 
without resort to frequency-selective circuits. The operational com- 
plexity of the balanced mixer is no greater, and is in many respects less, 
than that of a simple mixer. The many additional properties of the 
microwave balanced mixer in its final form make it often advantageous 
even when the suppression of local-oscillator noise is not required. 

6*1. Simple Microwave Balanced Mixer. — Figure 6*1 is a schematic 
drawing of a microwave balanced mixer.* If it is assumed that the 
crystals may be treated as resistors across the microwave line and that 
the local-oscillator power can be introduced into the microwave line by a 
simple, very loosely coupled probe, it is seen that this circuit behaves as a 
balanced mixer. The TR cavity is assumed to present, in the plane of its 
exit iris, a short circuit to power at the local-oscillator frequency. Each 
crystal is therefore coupled to the local oscillator in the same way, and 
since the probe excites waves traveling in both directions and having 
the same phase at planes equidistant from the probe, the local-oscillator 
signals at the two crystals are in phase. The received signal, on the other 
hand, having passed through the TR cavity, arrives at the two crystals in 
opposite phase since the crystals are spaced a half wavelength apart. A 
consideration of the simple addition of a small signal wave and a largo 
local-oscillator wave will show that the amplitude-modulation component 
at the beat frequency, in the envelope of the sum of these two waves, 
reverses in phase if the relative phases between the local-oscillator wave 
and the signal wave are reversed. Thus the i-f voltages at the output 
terminals of the two crystals are opposite in phase. By means of the 





transformer, the push-pull i-f signal is changed into a signal that ca: 
used to excite a conventional unbalanced line or an i-f amplifier. 

The local-oscillator noise arrives at the two crystals through the s 
cii*cuit as does the local-oscillator signal. The relative phases betv 
the noise components and the local-oscillator wave are the same at 
two crystals, and therefore the noise converted to the inter, mcd 
frequency has the same phase at the output terminals of the two crysi 
The balanced transformer does not produce an output voltage f: 
equal voltages in the same phase in the two legs of its input circuit, 

thus the converted noise is 
coupled into the i-f amplifier. ' 
overfall noise figure is dcterminec 
the conversion loss of the balan 
mixer, its noise temperature j 
the noise figure of the i-f amplil 
without a contribution from lo' 
oscillator noise. If the two crysi 
have the same conversion loss i 
simple mixer circuit, the con vers 
loss in the balanced mixer is the sa 
as that of a single crystal. 0) 
half the r-f signal power is appl 
to each crystal. The available 
output power from each crystal is therefore only half what it would be 
an unbalanced mixer, but since the two powers are added, the over- 
conversion loss is that of a single crystal. The noise tempcrati 
associated with the output admittance of the push-pull transformer 
just that of a single crystal, provided the two crystals have identic 
noise temperatures. The advantage gained by this balanced mix 
therefore, is the suppression of local-oscillator noise, and nothing is lo 
The degree to which local-oscillator noise is suppressed depends up 
how closely identical are the converted i-f noise components at the outp 
termii^s of the two crystals. This is determined partially by the degr 
to which the two crystals have identical conversion losses. Since t 
available output power from the i-f transformer is proportional to t. 
square of the difference between the voltages produced by the tv 
cryst^s, a small difference in conversion loss does not destroy the su 
pression of local-oscillator noise. If the two crystals have convcrsic 
losses Li and i^espectively, the available i-f signal power is proportion 
to (VlI -1- Vi 2 )^ whereas the available converted LO noise power is pr 

portional to (VU - The factor by which the local-oscillat< 

noise is suppressed, relative to the signal, is 

(\/L~i + VX’2)V(\/Li — 



















Fig. 6-1. — Simple balanced mixer ^th 
push-pull i-f transformer to unbalanced 

Sbc. 6‘2] 



If Li - 2 L 2 , corresponding to a 3-db difference, the local-oscillator noise 
is suppressed by a factor of 34, or by 15.3 db. This factor is sufficient 
to reduce the effect of the unbalanced noise on the over-all noise figure to a 
negligible amount under most conditions; therefore an unbalance in 
conversion loss as great as 3 db could be tolerated, if this were the only 
source of unbalance in the circuit. 

A much more serious source of unbalance in this mixer circuit arises 
from the possible inequality of the r-f admittances of the crystals. The 
power delivered to the crystals, both by the signal generator and by the 
local oscillator, is divided between the crystals in a ratio dependent upon 
their r-f admittances. To the signal, the two crystals appear in parallel 
so that the ratio of the signal powers delivered to them is just the ratio of 
their r-f conductances, the crystal having the larger conductance receiving 
the larger power. To the local oscillator, the crystals appear at the ends 
of quarter-wavelength lines and these lines are connected in parallel at 
the plane of the local-oscillator probe. If the r-f admittances of the 
crystals were pure conductances, the ratio of local-oscillator power 
delivered to the two crystals would be the inverse of the ratio of their 
conductances; that is, the crystal having the smaller conductance would 
receive the larger local-oscillator power. Since the r-f admittances of 
representative crystals of a given type vary considerably, it is not unlikely 
that randomly chosen crystals might differ in conductance by a factor 
as large as 4. For example, a pair of crystals having admittances of 
27o and yo/2, respectively, would differ by this factor, and since each 
would suffer a reflection loss of only about 0.6 db in the conversion-loss 
test, they would not necessarily be eliminated by the specifications. 
This source of unbalance can be equivalent to 6 db or more of unbalance 
in output power. When this unbalance is added to the possible unbalance 
in conversion loss, it is seen that the suppression of local-oscillator noise 
might not be sufficient unless crystals were selected in balanced pairs. 
Such a selection would best be made on the basis of measurements of 
r-f admittance, since the admittance is seen to be the more serious 
source of unbalance. A mixer that requires selection of crystals is 
certainly to be avoided if possible. For the purpose of providing a 
balanced mixer that is less sensitive to inequalities of the r-f admittances 
of the crystals, the '‘magic T^' was developed. To facilitate the dis- 
cussion of balanced mixers based on this circuit, a short discussion of 
the principles of the magic T and some of its eqxiivalent circuits must be 

6*2. General Properties of the Magic T. — One variety of magic T in 
rectangular waveguide is a circuit consisting of a waveguide with two 
other waveguides connected perpendicularly to it, one in the broad wall 
and the other in the narrow wall, at a common junction plane. Each 
of the joining waveguides makes, with the original waveguide, an ordinary 



[Sec. 6-2 

T-junction. The structure formed by the branch in the broad side of the 
main waveguide and the main waveguide is called an jB-plane T-junction, 
and behaves essentially as a series-connected circuit. The arm in the 

narrow plane constitutes, vdth the 
main waveguide, an JJ-plane T- 
junction and can be described in 
terms of a parallel circuit. When 
both these side arms are present, 
and have a common junction 
plane, as in the magic T, the arms 
on the narrow side and on the 
broad side of the main waveguide 
are often referred to as the jff-plane 
and the J?-plane arms, respec- 
tively. The complete structure 
has some very special properties, 
however, because of its symmetry, 
and no simple series- or parallel- 
connected equivalent circuit can 
be used to describe it. In Fig. 6-2 a perspective view of the structure of 
a magic T is shown. 

To understand the special properties of the magic T it is necessary 
to realize the difference between the coupling of the if-plane T-junction 
and that of the JS-plane T-junction. In Fig. 6-3a and b are shown, 
respectively, the field configurations in the region of the junction for each 

Fig. 6-2. — -Perspective view of magic T. 

Fig. 6*3. — Kepresentation of coupling in simple T-junctions; (a) /f-plane T-junction; (fe) 

^-plane T-junction. 

of these simple T-structures, produced by a wave traveling into the side 
arm of each. Lines are drawn, in Fig. 6’3a, to represent the wavefront 
as it progresses down the side arm and through the junction. The 
circles with crosses represent the J?-vector pointing into the paper. 
It is seen that the waves traveling outward from the junction have the 
same phase at planes equidistant from the center of the junction, or 
from the plane of symmetry. In Fig. 6*36, which represents the jE-plane 
T-jxmction, the electric field vector is in the plane of the paper and is 


represented by lines with arrows indicating the direction. The electric 
field fringes at the junction and excites the horizontal arms with waves 
having opposite phases at planes equidistant from the plane of symmetry. 
Thus the waves in the horizontal arms of the H-plane T-junction may be 
said to possess completely even symmetry about the junction and those 
in the i?-plane T-junction to possess completely odd symmetry about the 
junction. Another way of illustrating the action of the H-plane T-jimc- 
tion is to draw the magnetic field vector, which fringes at the junction. 
The magnetic field has opposite directions at symmetrically disposed 
planes in the horizontal arms, but, since the waves are traveling in 
opposite directions, the associated electric fields must point in the same 
direction, as shown, at these two planes. In both of these T-structures, 
with each of the horizontal arms infinite in length, there would be a 
wave reflected upward in the side arm due to the discontinuity of the 

The same kind of coupling erists between the side arms and the 
coUinear arms of the four-armed structure of Fig. 6‘2. Because of the 
opposite kinds of symmetry associated with the side arms it is evident 
that a wave traveling into the jE?-plane arm excites only a wave of odd 
symmetry in the junction and cannot therefore excite the ff-plane arm. 
The result is that only waves having opposite phases at planes eqiu- 
distant from the plane of symmetry are excited in the coUinear arms, 
and a reflected wave is excited in the Ef-plane arm. Similarly, a wave 
sent into the H-plane arm excites, in the coUinear arms, only waves 
having like phases at planes equidistant from the plane of S3nnmetry 
and excites a reflected wave in the ff-plane arm. There results, therefore, 
a device that transmits power to two lines from each of two independent 
input lines but shows no direct coupling between these input lines. 

In order that the magic T may be most useful, the input arms should 
have no reflections when nonreflecting terminations are placed on 
the coUinear arms. Some kind of reflecting irises in the B-plane and the 
ff-plane arms can be provided to produce reflections that cancel the 
reflections from the junction. These arms of the T-junction wiU then 
be reflectionless when the coUinear arms are terminated with reflectionless 
loads. Provided the matching structures do not upset the symmetry 
of the junction, the lack of direct coupling between the B-plane and the 

ff-plane arms is preserved. j i, rp 

Under the condition that such matching devices are used, the T- 
structure takes on other special properties. Suppose that waves of 
equal amplitudes are sent simultaneously into the fl-plane and the 
ff-plane arms. Because of the odd and even symmetry, respectively, 
of the waves excited in the coUinear arms, the relative phases between 
the two input waves can be so adjusted that the secondary waves excited 



[Sbo. 6'3 

in one of the coUinear arms cancel. Then the secondary waves in the 
other coUinear arm are in phase and therefore add in amplitude. Thus 
the total power contained in the waves sent into the jB-plane and the 
jff-plane arms is contained in the wave traveling outward in one of the 
coUinear arms. A reversal in the direction of propagation of these 
waves then shows that a wave sent into one of the coUinear arms excites 
waves of equal amplitudes in the jB-plane and the if-plane arms, and 
does not suffer reflection at the junction, nor does it couple to the opposite 
coUinear arm. The same is true for a wave sent into the other colUnear 
arm. If planes are chosen in the ^-plane and J?-plane arms in such a 
way that the waves traveling outward in these arms, excited by a wave 
sent into one of the coUinear arms, have like phases, the waves due to 
power entering the other coUinear arm have opposite phases. Thus, 
with the matching devices in the JB-plane and the jff-plane arms, the 
structure has the property that power sent into any arm transmits only to 
the adjacent arms, and does so without reflection. Furthermore, the 
waves excited in these adjacent arms have the opposite kind of phase 
symmetry if the input wave is sent into the arm opposite to the original 
one. It is to this structure, including the matching irises, that the term 
magic T is applied. 

6*3. The Matching of the Magic T. — ^Any of the conventional kinds of 
matching structures may be used in the magic T at a single frequency. 
It has been found, however, that with inductive irises the frequency 
band over which the match is good is not large. This is especially true 
of the ff-plane arm, where the voltage standing-wave ratio to be matched 
out by the iris is larger than in the JS-plane arm. At 3.33 cm in wave- 
guide having outside dimensions of 1 in. by in., the voltage standing- 
wave ratio that must be matched out is about 3.6 in the iJ-plane arm 
and 2.2 in the j&-plane arm. In the 1.25-cm band with -J-m. by i-in. 
waveguide, it is about 7.5 in the H-plane arm and 2.8 in the JS7-plane arm. 
With an inductive iris placed as close as possible to the junction in the 
proper position to match the ff-plane arm at a given frequency, the 
voltage standing-wave ratio rises to about 2 with a change of frequency 
of less than 1 per cent. 

A structure giving a less frequency-sensitive matching effect for the 
jfiT-plane branch has been found. In the by -J-in. waveguide used at 
1.25 cm an iris in the plane of symmetry extending outward from the 
wall opposite the H-plane arm and upward into the E-plane arm has been 
used. This and an asymmetrical inductive iris for matching the E-plane 
arm are shown in Fig. 6*4. The voltage standing-wave ratio, with 
nonreflecting loads on the coUinear arms, is less than 1.10 over a plus or 
minus 1 per cent band, in the jff-plane branch. In the E-plane branch 
the voltage standing-wave ratio is less than 1.10 at the center of the band 


and rises to about 1.30 at the edges of the plus and minus 1 per cent 

For the 3.33-cm baud, a post was found to give a better match, over 
a wide band, than an iris of this kind, although a similar iris in the plane 

Fig. 6-4. — Positions of irises for matching Fio. 6-5. — Positions of post and iris for 

a magic T in Hn. hy i -in. waveguide. The matching a magic T in ^in. by i-in- wave- 
iris thickness is 0.020 in. guide. The iris thickness is ^ in., the 

diameter of the i>offt is 1 in., and the length 
is 0.650 in. 

of symmetry could be designed to give a perfect match at a single fre- 
quency. This post, again with the single asymmetrical inductive iris 
for matching the S-plane branch, is shown in Fig. 6-5. The voltage 
standing-wave ratio observed in the 12 per cent band from 3.13 to 3.53 
cm, for a magic T like that of Fig. 

6*5, is shown in Fig. 6-6. It is 
evident there that the match ob- 
tained in the ff-plane arm is al- 
most independent of frequency. 

Unfortunately no simple structure 
was found that gave a wideband 
match for the jB-plane branch. 

The voltage standing-wave ratio 
measured in the coUinear arm is 
also shown. The amount of this 
standing-wave ratio depends on 
the other two but cannot be derived from them without knowledge of the 
phases of the reflection coefficients. 

Because of the complete symmetry of the magic T, the symbols shown 
in Fig. 6-7a and b are used in illustrating its applications. The arms are 
numbered in a definite relationship to the physical structure, because 
for many applications it is necessary to know the phase I'elationships 

Fig. G-6. — Voltage standing- wave ratio 
vs. wavelength, for magic T matched as 
shown in Fig. 6*6. 



[Sbc. 64 

betw^n the waves in two opposing arms and not in the other two. In 
such cases, the coUinear arms are favored over the other two since the 
phase relationships between waves in them are completely defined by 
the symmetry of the structure. The lack of direct coupling between the 
/f-plane and the jE-plane arms (henceforth arms (3) and (4), respectivdy) 
is independent of frequency, but for arms (1) and (2) it is independent of 
frequency only to the extent that the matching of arms (3) and (4) is 
independent of frequency. Measurements could be made to determine 
the location of planes in arms (3) and (4) for which phase relationships 
similar to those holding for arms (1) and (2) could be specified, but the 
positions of these planes may vary with frequency and are dependent 
upon the particular matching structures used. 

One pair of planes in arms (3) and (4), which are useful for purposes of 
calculation, may be defined in the following way. Suppose arms (1) and 

~£f-plane arm 


fe) ^ (&) 

Fia. 6*7. — Symbols used to represent the magic T. 

(2) are both short-circuited in planes equidistant from the plane of 
symmetry. If a wave is sent into either arm (3) or arm (4), the waves 
excited in arms (1) and (2) are reflected toward the junction from the 
short-circuiting planes with the same kind of symmetry as they had in 
traveling outward from the junction. A wave is therefore excited only in 
the input arm and the standing-wave ratio in the input arm is infinite. 
For this pair of planes in arms (1) and (2) a pair of planes, in arms 

(3) and (4), at which voltage maxima (zero admittance) occur may be 
specified. It now follows that, if arms (3) and (4) are short-circuited in 
these planes, an admittance of zero will be seen in the planes which were 
short-circuited in the previous experiment, looking into arms (1) and (2). 
An equivalent four-terminal-pair network describing the action of the 
magic T in terms of voltages and currents, can now be defined, where 
the terminal pairs are understood to be located in these four planes. 

6-4. Description of the Magic T in Terms of Voltages and Currents. — 
The relationships between the voltages and currents in the terminal 

Sec. 6 * 4 ] 



pairs of any linear, passive four-terminal-pair network can be shown to be 
given by the four simultaneous linear equations 

11 = ynei + 2/1262 + 2/1868 + 2/1464 

12 = 2/1261 + 2/2262 + 2/2863 + 2/2464 

iz = 2/1361 + 2/2362 + 2/8863 + 2/3464 

U = 2/1461 + 2/2462 + 2/8468 + 2/4464 t 

where the coefficients ynm are constants depending on the properties of 
the particular network. For this particular circuit, the definition of the 
position of the planes of the terminal pairs and the fact that there is no 
direct coupling between opposite arms gives 

2/11 = 2/22 = 2/33 = 2/44 “ 2/12 = 2/34 = 0 . 

Thus Eqs. (1) reduce to 

ii = 2/1368 + 2/1464 
iz = 2/2363 + 2/2464 
iz = ^1361 + 2/2362 
u = 2/1461 + 2/2462 

It can further be shown that the coefficients 2/nm, for a network containing 
no elements capable of dissipating power, are pure imaginary. If 
matched loads are connected to arms (1) and (2) and a current is induced 
in arm (3), the symmetiy condition for the JT-plane branch and the 
conservation of power allow the relation 

iz = ± jYQ ^^ (ei + 62) 

to be written, where F 0 is the characteristic admittance of the waveguide. 

2/13 = 2/23 = ±J F 0 . 

The sign is determined by the choice of the plane of the terminals 
in arm (3), there being a plane, given by the definition above, every 
half wavelength from the first plane. Since the sign is reversed for 
consecutive planes, the definition of the terminal plane may be further 
restricted to correspond to the positive sign, and thus 

2/13 = 2/28 

Similarly, a current induced in arm (4) with matched loads on arms 
(1) and (2) gives 



[Sec. 6-4 

Again, choosing the position of the terminal plane in arm ( 4 ) that corres- 
ponds to the positive sign, there results 

Via =3 





The set of transformation equations describing the magic T thus becomes 
i^ = 3Yo^(ez+.eA) 


a /2 } (3) 

U = 3Y,^(e^ + e,) 

a /2 

u = JYq — ^ (ei — 62 ) 

transfection rdations of Eq. (3) may be used, for example, to 
C the power dehvered from a generator of known characteristic admit- 
tance on one arm to a load of known admittance on a second arm, if the 
adnaittances on the other two arms are also known. K a generator 
availaWe power P, and an internal admittance F, is connected 
inj f representing arm (3), the power dehvered to a 

load of ^ttance Y, at the terminal plane representing arm ( 4 ) is 


p ~- l- i .* .) U + y .) + (1 + r.y.) (1 + y,ir,{ P: ( 4 ) 

PM<» of T, and n, respertively, 
Fi and 7, are the load admittances connected to the terminal plani 

r^r^entang respectively, and all admittances are 

t?^' ? V “■ shows that the power transmitted 

re^A? T is therefore often 

Pi= Spiffs 

(1 + 7 , 74 ) 

P«. (5) 

Ri +J'2r,; (1 + nr a) + (i + /iF,) (i -t- 7,74) 

expression a similar equation for a load on any arm and a 
g^ator on ^ other arm may be written down simply by proper 
permutation of the subscripts. When the load and the genfratn are on 


opposite arms the equation to be used is Eq. (4); when they are on 
adjacent arms, Eq. (6) is used. 

There are many possible microwave circuits similar in behavior to 
the magic T just described. The conventional low-frequency hybrid 
coil'' circuit, used in wire telephony to isolate signals traveling in different 
directions on the same wires, behaves as a magic T if it is arranged to 
have the same characteristic admittance at all four terminal pairs. A 
microwave circuit that is coming into wide use as an equivalent to the 
magic T is shown in Fig, 6*8. This device may be made of waveguides, 
coaxial lines, or even open-wire transmission lines. The side arms may be 
connected either in series or in shunt at positions a quarter wavelength 
apart along the periphery of the circular l^-wavelength line. For the 
network to be matched, the circular line should have a line admittance 

^/2 times that of the branch lines, neglecting the effects of higher modes, 
if the side arms are connected in series, as shown. If the side arms arc 
connected to the ring in parallel, the ring should have a characteristic 
admittance ^/ 2/2 times that of the side arms. In Fig. 6*9, a coaxial-line 
circuit of this type designed for 10 cm is shown. Since this device is 
used with small cable fittings and flexible cables it is difficult to make 
as precise measurements upon it as those on the waveguide magic T. 
The measurements that have been made show that the output power 
from one of the arms adjacent to the input arm is at least 20 db greater 
than the power from the opposite arm, for wavelengths between 8 and 11 
cm. Since this small amount of coupling may be attributed to reflections 
in the cable connectors on the arms adjacent to the input arm, no attempts 
have been made to improve the balance. The standing- wave ratio in 
the input line is as small as would be expected with these connectors in the 
circuit; thus the higher-mode effects at the junctions are apparently 


Another possible circuit that behaves as a magic T is shown in Fig. 
6-10. This circuit is similar in principle to the waveguide version of the 
magic T, in that it consists of series and shunt connections, at a common 

point, to a single line, the two ends of which form the other two pairs of 
terminals. This circuit has been considered for use in the longer- 
wavdength part of the microwave region, where the physical size of 
waveguides might be prohibitive, for applications in which a ring circuit 

Sbc. 6*5] 



does not give sufficient bandwidth. Like the waveguide magic T, this 
circuit depends on the matching devices in the series and shunt-connected 
arms to obtain zero coupling between the other two arms. Like the 
magic T it derives the zero coupling between the series and shunt arms 
from its symmetry, and therefore this property is insensitive to frequency. 

For any of the applications of the magic T, any of the equivalent 
forms just described can equally well be used. In the following dis- 
cussions of balanced mixers the waveguide magic T will be used for all 


3 4 

Fia. 6*11. — An equivalent to the magio-T oirouit, made of coaxial line and waveguide in 


illustrative purposes because it has been used extensively in this applica- 
tion. The mixers can be constructed from waveguide or coaxial-line 
ring equivalents or from any of the other possible equivalent circuits 
if space or wavelength requirements make such forms preferable. One of 
the first balanced mixers to be designed using a magic-T circuit was 
made of a combination of coaxial lines and waveguide in the form shown 
in Fig. 6T1. 

6-6. The Magic-T Balanced Mixer. — In order to construct a balanced 
mixer from a magic T, two opposite arms are terminated by crystals 
in standard waveguide mounts. The signal enters one of the remaining 
arms and the local oscillator power enters the other. Although it is not 
necessary to use this arrangement, the crystals are usually mounted on 
arms (1) and (2), in the terminology shown in Fig. 6-7. Thus the 
resulting balanced mixer appears, for the 3.3-cm band, as shown in Fig. 



[Sec. 6-6 

6-12. The role of the signal-input and local-oscillator-input arms can be 
interchanged, for in either case the relative phases between the incident 
signal wave and the incident local-oscillator wave are opposite at the 
two crystals. Since there is no direct coupling between the signal-input 
circuit and the LO-input circuit, no reactive decoupling in the local- 
osciUator circuit is required. Only enough local-oscDlator power to drive 
the two crystals is needed. If more local-oscillator power is available, 
a matched dissipative attenuator can be used in the local-oscillator arm. 
The load admittance presented to the local-oscillator tube is thus well 
controlled, because the crystals themselves provide the local oscillator 
with a load that is approximately matched to the waveguide. The fact 
that the balanced mixer can be operated with a local oscillator having 
such a small output power, without the danger of loss of signal through 

To local 


Fio. 6*12. — Magio-T balanced mixer for 3.3-om band. 

interaction of the signal and local-oscillator circuits is one of the many 
advantages of the magic-T balanced mixer. 

The suppression of local-oscillator noise by the magic-T balanced 
mixer is not affected in the same way by the crystal admittance as it is in 
the simple balanced mixer earlier described. If one of the crystals 
reflects either the signal wave or the local-oscillator wave, the reflected 
power is sent only out the signal arm and the local-oscillator arm, because 
the opposite arms of the magic T do not couple directly. If there is no 
reflection of waves traveling outward in these arms, there is no way in 
which the signal power or the local-oscillator power delivered to the 
second crystal can be influenced by the mismatch of the first. If there is 
sufficient available local-oscillator power to allow some matched dis- 
sipative attenuation between the magic T and the local oscillator, the 
nonreflecting condition for the local-oscillator arm is approximated. 
If there is a bandpass TR cavity, or no resonant circuit at all, in the signal 
arm, a wave traveling outward in that arm is radiated by the antenna 
without reflection. If a resonant TR cavity must be used, that part of 

Seo. 6-5] 



the iocal-oscillator wave which, having been reflected by the crystal, 
travels out the signal arm, is reflected by the TR cavity and interferes 
with the direct local-oscillator wave coupled to the two crystals. The 
resxilt is that the division of local-oscillator power between the two 
crystals becomes similar to the division in the simpler shunt mixer. 
The power reflected from one crystal is reduced to one-half of its value 
by two transits through the magic T before it arrives at the other crystal. 
However, as application of Eq. (5) will show, the form of the dependence 
of the delivered local-oscillator power on the admittances of the crystals 
is the same in the magic-T circuit if the signal arm is open-circuited as 
in the balanced mixer with shunted crystals. A two-to-one ratio of con- 
ductances causes a two-to-one split of power. The remaining power, 
originally delivered to the mixer, is reflected into the local-oscillator 
attenuator. This imbalance in local-oscillator power delivered to the 
two crystals does not seriously affect the suppression of local-oscillator 
noise because the crystal conversion loss is not strongly dependent on 
the amount of local-oscillator drive, provided that the amount is 
sufl5.cient to produce a few tenths of a milliampere of rectified crystal 

The splitting of the signal power between the two crystals is not 
influenced greatly by the presence of a TR cavity because a reflected 
wave, at the signal frequency, coming from the mixer would not be 
strongly reflected by the TR cavity, which is txmed to pass this frequency. 
Thus the magic-T balanced mixer does not require nearly so great a 
similarity between the two crystals used as does the simple balanced 
mixer. If both the signal line and the local-oscillator line are non- 
reflecting to waves traveling outward from the mixer, the only effect of 
reflection by the crystals is an increase in their conversion loss by the 
same amount as would be found if they were operated individually from 
matched generators. With the same tuning of the crystal mounts as in 
the conversion-loss test set, and at the same frequency, the total conver- 
sion loss for each crystal in the balanced mixer, including r-f reflection 
loss, would be the same as would be measured for that ciystal in the test 
set. Under these conditions it is unlikely that more than 3 db of unbal- 
ance in conversion loss would be found, if the crystals had a small speci- 
fication value of maximum conversion loss and normal i-f admittances. 

It is desirable to employ an i-f coupling circuit, such as that shown in 
Fig. 6T3, the performance of which is not affected by a lack of balance 
in the i-f admittances of the two crystals. The transformer shown in 
the figure resonates with the mixer and tube capacitances and has 
the bandwidth and the impedance stepup from the crystals to the 
grid required to achieve a good noise figure. To reduce capacitive 
coupling between the coils, adjacent ends are made to operate at ground 



[Sbo. 6-6 

poteatial, and to achieve this the secondary is made of two sections 
wound in opposite directions. Ordinarily the inner ends of the two 
primary coils would be grounded through the current-filter capacitances, 

but in this circuit the impedances 

Fig, 6*13. — Special i-f input circuit for 
balanced mixer. C » i-f bypass, BFC = i-f 
choke, Z =* see text, MA = orj^al-ourrent 

Z are connected between the i-f 
ground and the coils. The bypass 
condenser between the inner ends 
of the two coils ensures that they 
are at the same potential. Thus, 
between the common ends of the 
primary coils and ground there 
appears an impedance equal to 
2i/2. The impedance Z is chosen 
in such a way that Z/2 is the 
complex conjugate of the imped- 
ance that would be measured be- 
tween the junction of the two 
primary coils and ground if each crystal had the i-f output impedance of 
an average crystal. 

The addition of this impedance to the push-pull input circuit makes 
the behavior of this circuit similar to that of a magic T. If a voltage^ 
were impressed from grid to ground on the secondary of the transformer, 
equal voltages in opposite phases would be produced across crystiils 
having equal impedances. No voltage would result across the imped- 
mc^ Z. A voltage across the dummy-load impedance Z/2, on the other 
hand, would produce ^ual voltages in like phases across crystals having 
equal impedances, with no voltage produced at the grid. Thus the 
tennina^ of the duinmy-load impedance Z/2 correspond to the terminals 
of arm (3) of a magic T, and the grid-to-ground terminals correspond to 
those of arm (4). The choice of a dummy-load impedance in the manner 
described corresp^ds to the use of a matching structure and a matcdied 
load m arm (3) of a magic T. If the grid admittance of the tube wen^ 
Jh! conjugate of the admittance of the secondary terminals of 

equivalence to a magic T would be complete. For 

te^ls'^Th. luismatch e.xists at these 

of a circuit that is like a magic T is that a 

of argument that was used to show the absont^c^ 

S inXoifof tuhe would 

not 1 Since the grid 

coitTlo^«^ , I independen(;e is not 

complete so far as signal transmission is concerned. 

Sue. 6-6] 



Suppose that two crystals do not have the same i-f impedances, 
but that they do develop identical output voltages when loaded with an 
impedance that matches the i-f output impedance of an average crystal. 
If these crystals were used in a balanced mixer connected to the present 
input circuit, the suppression of local-oscillator noise would be perfect 
because the equal voltages excited by the crystals would develop a 
voltage only in the dummy load Z/2, corresponding to arm (3) of the 
magic T. Because of the choice of this impedance, each crystal is loaded 
with an impedance that matches the i-f output impedance of an average 
crystal and, therefore, the equality of the developed i-f voltages is 
maintained. Because the test apparatus used to measure the conversion 
loss of crystals actually measures the voltage developed across a load 
impedance of this kind, crystals having identical conversion loss in the 
crystal test set should give perfect suppression of local-oscillator noise. 
With the magic-T-equivalent input circuit and the magic-T mixer circuit 
this suppression is assured, independently of the actual i-f impedance 
and r-f impedance of the crystals. Because of the magic T, an inequality 
in r-f impedance contributes little to the unbalance of the mixer and 
similarly, because of the i-f input circuit, which is equivalent to a magic T, 
an inequality in i-f output impedance causes little loss in noise suppression. 

If these two circuits are used, there is some significance to a calculation 
of the noise suppression realized for a given inequality in crystal conver- 
sion loss, as measured by a test set. The amount of LO-noise suppression 
may be defined as the ratio of the effective conversion loss for the signal 
to that for the local-oscillator noise, the conversion losses being measured 
from the corresponding r-f input terminals to the i-f-amplifier grid. 
If Li and L 2 are, respectively, the conversion losses of the two crystals as 
measured in a standard test set, the square of the i-f signal voltage at the 
i-f amplifier, per unit r-f signal power available at the mixer, is propor- 
tional to {^/77x + The square of the i-f noise voltage developed 

at the i-f amplifier input terminals, per unit of LO noise power available 
in the mixer, is propoi-tional, with the same proportionality constant, 
to (VXu — VX 2 )®. The suppression of local-oscillator noise is 

In Fig. 6‘14 a curve of 8j in decibels, as a function of the difference, in 
decibels, in the conversion losses of the two crystals is shown. Since more 
than 15 db of noise suppression is obtained if the difference between the 
losses of the two ciystals is less than 3 db, it is reasonable to assume that 
no selection of crystals would be required under ordinary circumstances. 



ISbo. 6*5 

A magic-T balanced mixer for 1.25 cm, with an i-f amplifier equipped 
with an input circuit such as that of Fig. 6-13, was tested in the following 
way. A group of 30 randomly selected 1N26 crystals were measured 
for r-f impedance, conversion loss, and noise temperature. The r-f 
impedances scattered in a random fashion, within the impedance circle 
corresponding to a voltage standing-wave ratio of 3. The conversion 
losses ranged from 6 to 8.5 db and the noise temperature from 1 to 2. 

Pairs of crystals having almost identical r-f impedances and losses were 
used and the effective over-all noise figure of the mixer and i-f amplifier* 
was measured. With pairs of crystals matched in this way, the result 
corresponded, within the probable error of measurement, to the calculated 
value, if local-oscillator noise was neglected and if the effective crystal 
noise temperature was assumed to be equal to the arithmetic mean of the 
values for the two crystals. Other pairs were formed, representing the 
diametrical extremes in r-f impedance and the smallest and largest 

SBC. 6-61 



conversion loss. For these pairs the measured effective over-aJl noise 
figure agreed closely with the calculated value assuming a conversion 
loss midway, in decibels, between the two and, again, the arithmetic 
mean of the noise temperatures. Thus the measurements showed that 
the suppression of local-oscillator noise was sufficient to reduce to a 
negligible amoimt the contribution, from that source, to the over-ail 
noise figure. 

An independent measurement, for the various crystal pairs, of the 
actual LO-noise suppression was made in the following way. A test 
fli gnal was added to the local-osciUator signal, and the output voltage 
from the receiver was measured. The result of this measurement was 
compared with the output voltage from the recdver when the same test 
signal was sent into the signal arm of the magic T of the mixer. The 
noise suppression was found to vary from about 13 db to over 30 db 
depending on the pair of crystals used. The results correlated reasonably 
well with what would be expected on the basis of the data on the indi- 
vidual crystals. There is, however, an additional factor depending on 
how well the input transformer is balanced; consequently, the crystal 
pair appearing to be the most nearly balanced with respect to conversion 
loss did not give the greatest noise suppression. 

6-6 Additional Features of the Magic-T Balanced Mixer.— The 
magic-T balanced mixer has been found to furnish a very satisfactory 
solution to the problem of local-oscillator noise. It has, moreover, 
certain features that make it useful even in the absence of such noise. 

One of these features is the smaE LO power requirement, which makes 
possible the use of a well-matched attenuating pad between the local 
oscillator and tho mixer, as already discussed Tim attenuation becomes 
very important in the 3- and 1-cm bands if a mixer must be operated 
without the assistance of a resonant TR cavity. The power available 
from most small local-oscillator tubes is insufficient in these bands to 
aUow the reactive coupling circuits to be used without involvmg a 
significant interaction of the local-oscillator circuit on the signal circuit, 
with an accompanying deterioration in noise fipire. With the 
duction of the wide-band fixed-tuned TR switch in the 3.3-cm band, me 
balanced mixer became the only avaUable mixer satisfactory from this 
viewpoint. Because the effect of local-osciUator noise on the over-all 
receiver noise figure is increased if no resonant filter is used in the signal 
line of a simple mixer, the balanced mixer has an additional advantage. 

Another feature of the magic-T balanced mixer is that radation of ffie 
local-oscillator wave by the antenna of the receiver is reduc^. Tffis 
is because the only power coupled into the antenna circuit from the 
local-oscillator circuit is a part of the power reflected by the crystals. In 
an ordinary single-crystal mixer, with nondirectional local-oscillator 



[Sbc. 6-6 

coupling, as much local-oscillator power is sent to the antenna as to the 
mixer crystal unless there is a resonant filter in the signal line. With 
the balanced mixer, a resonant filter still attenuates the local-oscillator 
power that is coupled into the signal arm of the magic T. If the radiation 
of local-oscillator power must be minimized for any reason, the use of a 
balanced mixer, with one of the crystal mounts made tunable, would be 
worth while. Since the scatter of crystal impedances is so large, it 
could hardly be expected that the local-oscillator power sent to the 
antenna, in the absence of a resonant filter, would always be more than 
10 db below the input level to the mixer, unless the crystal impedances 
were equalized by tuning. If one crystal were matched to the waveguide, 
for instance, and the other had a voltage standing-wave ratio of 2, the 
power sent to the antenna would be it oi that sent into the mixer by the 
local oscillator. If each of the crystals had a voltage standing-wave 
ratio of 2, but with reflection coefficients having opposite phases, i of the 
power sent into the mixer by the local oscillator would be radiated by 
the antenna. With a timing adjustment on one crystal such that the 
reflection coefficients could be equalized, the radiation by the antenna 
could be kept at least 40 db below the input level of the mixer, at the 
frequency for which the tuning was made. 

The balanced mixer discriminates against i-f signals arising from 
beats between two frequencies present m the signal channel, for the 
same reasons that it suppresses local-oscillator noise. This discrimination 
is of value because it reduces the susceptibility of the receiver to inter- 
ference from signals that are not at the signal- or image-frequency 
sidebands of the local oscillator. Interference can be produced, in a 
receiver having an ordinary mixer and no resonant preselecting filters, 
by beats between any two signals that differ in frequency by the inter- 
mediate frequency and that can propagate down the transmission line of 
the receiver. The discrimination against interference of this kind is 
about the same as the discrimination against local-oscillator noise and 
may, xmless selected crystals are used, be as small as 13 db. If such 
discrimination is deemed important in view of the application of the 
receiver, provision may be made to achieve an exact balance in the mixer 
circuit by addition of a small adjustable r-f attenuator, for example, 
between one crystal and the junction. The crystal having the smaller 
conversion loss should be used on the side that has the attenuator, and the 
adjustment would have to be made on an actual set of interfering signals. 
Whether the balance would be sufficiently good over the whole band in 
which interfering signals can occur, however, is questionable. 

If a resonant TR cavity is used in the signal line of a balanced magic-T 
mixer, the i-f admittance of the crystals is influenced, as in the single 
mixer, by reflection of the image frequency by the TR cavity. It is 


dijficult to make the line length between the cavity and the crystals so 
short that the phases of the reflected image-frequency waves arriving 
at the mixer crystals do not change very much over a wide frequency 
band. A considerable variation in i-f admittance and some variation in 
conversion loss over a wide band might therefore be expected. With 
the input circuit that is equivalent to a magic T, the variation of i-f 
admittance does not seriously affect the balance of the mixer but it does 
affect the pass band of the input circuit and the i-f-amplifier noise figure. 
For a single-frequency receiver, as with the 
single mixers, the length of line between the 
cavity and the crystal can be chosen to give 
the best noise figure. For most purposes, how- 
ever, this has not been considered worth while 
and instead, consideration has been given to a 
special change in the balanced mixer to allow 
the effect of the image-frequency wave to be 
eliminated at all frequencies. 

Since the phase relation between the signal 
and the local-oscillator waves results from the 
symmetry of the magic T, the line lengths from 
the T-junction to the crystals may be made 
unequal. A change in the line length, very 
small compared with a wavelength at the 
intermediate frequency, makes a very small 
change in the phase of the i-f voltage produced 
by the crystal, because both the local-oscillator 
wave and the signal wave are delayed by 
almost the same phase angle. It is therefore 
possible to make the distance from the junction of the magic T to one 
crystal a quarter of an r-f wavelength different from the distance from 
the junction to the other crystal, as shown in Fig. 6T5. The result of 
adding a quarter wavelength to one side of the magic T is that, if image- 
frequency waves of equal amplitude are developed by the crystals, 
their phase relation, as they converge on the junction, is such that they 
are transmitted entirely into the local-oscillator arm of the magic T. The 
way in which this comes about is illustrated graphically in Fig. 6-16. 
The vectors of Fig. 6T6a represent the waves that are excited in the 
crystal arms of the magic T by the local oscillator and the signal genera- 
tor. The phase of the local oscillator is taken as a standard of reference 
and the vector representing it therefore remains fixed. The relative 
phases between the signal wave and the local-oscillator wave, in each 
arm, are determined by the angle between the local-oscillator vector and 
the small vector representing the signal. Since the frequency of the 

Fig. 6*15. — Balanced 
mixer so arranged that the 
image-frequency wave is 
transmitted into the local- 
oscillator attenuator. 

278 BALANCED MIXERS [Sec. 6-6 

signal differs from that of the local oscillator by an amount equal to the 
intermediate frequency, the small vectors rotate at the intermediate 
frequency, in the direction indicated by the curved arrows. Because 
the local oscillator is connected to arm (3) of the magic T, the vectors 
representing the local-oscillator phases at points equidistant from the 

junction in the two crystal arms point 
in the same direction. The vectors 
representing the signal are oppositely 
directed, since the signal enters the 
mixer from arm (4). 

At the two crystals, the relative 
phases are changed because one line 
is longer, by a quarter wavelength, 
than the other. If the vector repre- 
senting the phase of the local-oscil- 
lator wave at crystal (2) is directed 
upward, that at crystal (1) is directed 
toward the left because it is retarded 
by 90°. A Kke change in the relative 
phases between the two signal vectors 
occurs, and the situation is therefore 
like that represented in Fig. 6- 166. In 
this diagram the phases of the two 
image-frequency waves generated by 
the action of the crystals are indicated 
by the dashed-line vectors. Because 
the image frequency differs from the 
local-oscillator frequency by the same 
amount as does the signal frequency 
but in the opposite sense, these vec- 
tors rotate at the intermediate fre- 
quency in the direction opposite to 
that of the rotation of the signal vec- 
tors. The relative phase between the 
image and signal waves is not unique- 
ly determined at the planes of the crystals, since the effective line 
l^gths within the crystals may not be negligible. However, the rela- 
tive phases between the two image vectors must be as shown, if the 
crystals are identical, because the phase of each is determined by the rela- 
tive phases of the signal and local-oscillator voltages. A reversal of the 
phase of the signal wave relative to that of the local-oscillator wave 
must reverse the phase of the image. The relative phases have been 
drawn on the basis of two assumptions. It is assumed first that the 


( 1 ) 


f x ^ LO 
( 1 ) 


( 6 ) 


( 2 ) 




( 2 ) 

( 1 ) 


( 2 ) 

Fig. 6-16, — Oraphioal illustration of 
relative phases of waves at the LO 
signal, and image frequencies, when the 
crystal arms differ in length by one 
quarter wavelength, (a) Vectors show- 
ing the relative phases of the incident 
signal and loc^-oscillator waves in 
arms (1) (2) at planes equidistant 

from the junction. (6) Vectors repre- 
senting the relative phases between 
signal, looal-oscillator, and image waves 
at the two crystals, (c) Vectors show- 
ing relative phases of the two image- 
frequency waves as they converge on 
the junction of the magic T from the 
two crs^stals. 

Sec. 6*7] 



image-frequency wave is produced entirely by modulation from the i-f 
voltage, and second, that the signal voltage arising from the i-f voltage is 
such that the admittance of the crystal to the signal wave is reduced 
by the presence of the i-f voltage. 

The image-frequency waves travel from the crystals back toward the 
junction of the magic T. Because the line on the left side is a quarter 
wavelength longer than that on the right, the relative phases of the two 
image-frequency waves are changed by a 90° retardation of the vector 
representing the image wave on the left. These waves therefore have like 
phases, as shown in Fig. 6T6c, as they converge on the junction, and if 
they have the same amplitudes, all of the image-frequency power is 
transmitted into the local-oscillator arm of the mixer. A matched 
attenuator pad in this arm allows the image-frequency power to be 
absorbed without reflection, and both crystals behave as they would in a 
mixer without a resonant signal circuit. The i-f admittance and the 
conversion loss of each crystal are not strongly dependent on the operat- 
ing frequency. A large percentage change in frequency can be made 
before the difference in length of the two crystal arms becomes so different 
from a quarter of a wavelength that most of the image-frequency power 
is not sent into the local-oscillator arm. 

It is not known how well this treatment of the image-frequency wave 
can be achieved in practice. Its success depends on the equality of the 
amplitudes of the two image-frequency waves generated, and on the 
validity of the assumption that the effective line lengths contained within 
the crystals are identical. Since the production of the image-frequency 
wave by the crystal is a second-order effect, a greater inequality would 
be expected in the production of image power by various crystals than in 
their conversion efficiency. It is also possible that the effective line 
length contained within the crystals, especially at 1 cm, would vary too 
much, from one crystal to another, to allow the assumption about the 
relative phases of the two image-frequency waves to hold. Again, it 
would be possible to add a tuning adjustment, in the form of a line of 
variable length on one side of the magic T, so that the correct relative 
phases of the image frequencies could be obtained. Measurement 
of the output admittance of the i-f coupling circuit as a function of the 
line length between the TR cavity and the magic T shows how well the 
image-frequency wave is being disposed of. If all the image-frequency 
power is being transmitted to the local-oscillator attenuator, the i-f 
admittance should be independent of the distance between the cavity 
and the magic T, unless harmonic frequencies have an effect. 

6-7. Special Crystal Mounts for the Balanced Mixer. — ^For some 
receivers, the push-pull transformer of Fig. 6T3 is not suitable. For 
example, because mutual inductance is used and because it is not easy to 



LSbo. 6*7 

obtain large coupling coefficients in transformers for high frequencies, 
some difficulty is encountered in making such a circuit with a very wide 
pass band. It would be much simpler if the two i-f voltages could 
be made to have like phases so that the output voltages of the two 
crystals could be added in parallel. 

If the pin end of one crystal and the base end of the other are grounded, 
the crystals can be made to produce i-f voltages in like phases from the 
input signal and voltages in opposite phases from local-oscillator noise. 
For the ceramic cartridge crystals used in the 3-cin band, an inverted 
crystal mount has been designed which allows the i-f voltage to be 
taken from the large end of the cartridge, with the pin end connected 
directly to the waveguide. This mount is similar to the 10-cm coaxial- 
line mount, ha that it has a polystyrene-supported choke on the large end 
of the crystal. To obtain flexible fingers for making contact with the 
pin end of the crystal, a half-wavelength coaxial line is used The 
position of the crystal in the waveguide, and its r-f admittance, are 
identical with those in the ordinary 3.3-cm crystal mount. 

The disadvantage of using crystal mounts of opposite polarities in a 
balanced mixer is that an i-f input circuit equivalent to a magic T is 
difficult to achieve. Direct connection of the output terminals of the two 
crystals in parallel does not secure the independence of noise suppression 
from the i-f admittance that is achieved with the push-pull circuit. It is 
possible to devise a shunt circuit that contains a dummy load for the 
imbalance signal hut such a circuit has not been tried. With a non- 
resonant signal circuit connected to the mixer, however, there is not a 
great variation in i-f admittance from crystal to crystal, and the unbal- 
ance caused by inequality of the i-f admittances may not be serious. 

It is impossible to achieve TR-aided tuning of the crystal mounts 
over a wide band of frequencies because the distance between the crystals 
and the TR switch is too great. Because of this fact, and because the 
balanced mixer is peculiarly suitable for use in systems that have no 
resonant TR switch or preselecting cavity between the antenna and the 
mixer, a crystal mount that has an r-f admittance characteristic less 
frequency-sensitive than that used in the simple mixers is desirable. 

For the band from 3.13 to 3.53 cm, an improved crystal mount has 
been designed. It was first attempted to increase the bandwidth of the 
simple crystal mount by adding a resonant iris across the waveguide, a 
quarter wavelength ahead of the crystal. Since the susceptance of a 
crystal in the simple mount increases with frequency, whereas the con- 
ductance remains approximately constant, the crystal in its mount is 
approximately equivalent to a shunt-tuned resonant circuit, as discussed 
in Chap. 3. If a resonant shunt-tuned iris is placed a quarter wavelength 
from the center line of the crystal, toward the generator, the combination 

Sbc. 6-71 


behaves as a double-tuned coupled circuit. The response may be double- 
peaked or single-peaked, depending on the Q of the resonant iris. The 
resonant iris may be made up of a symmetric inductive iris and a capaci- 
tive post in the plane of the iris, and the Q of such a structure is pro- 


M \m 

0*17. — Crystal mount with ins for broad pass band. 

3.499 cm ^ 

— 3.330 cm 

— 3.139 cm 0.10 0.15 

Fiu. 0*18. — Adniittaiioos of representative crystals in broadband mount. 

portional to the susceptance of the inductive iris at resonance. Such a 
structui-o can be made to give, for a given crystal, less than about 
0.5-db reflection loss in the 12 per cent band, but this structure does not 
represent a significant improvement in the bandwidth of the crysta 
mount for many crystals. The tuning and the effective coup mg are 



changed if the admittance of a crystal does not match the waveguide 
admittance at the center frequency, and the compensation of the iris for 
the frequency sensitivity of the crystal is not so good as for a crystal that 
is matched at the center frequency. It has been found that there is no 
iris Q that gives significantly improved results with crystals representing 
all r-f admittances to be encountered. 

A more satisfactory means of improving the bandpass characteristic 
of the simple crystal mount was found in the form of a simple inductive 
iris. The final design of this crystal mount is shown in Fig. 6T7. An 

Fia. 6*19. — Perspective view of 3.3-om magic-T balanced mixer using one inverted crystal 


average crystal in the mount shown in detail in Fig. 3.6 has, at the center 
of the frequency band, a conductance slightly above the line admittance. 
The susceptance of the inductive iris, and its position, are such that the 
area covered by the admittance plot for representative crystals is centered 
at the characteristic admittance of the Me at the midband frequency. 
The combination of the frequency sensitivities of the line length from 
crystal to iris, of the iris susceptance, and of the crystal admittance is 
such that the total spread of admittance is reduced from that for a simple 
mount. Curves showing the admittances measured at 3.14 cm, 3.33 cm, 
and 3.50 cm are given in Fig. 6-18. Almost all of the representative cry- 
stals fall within the circle of voltage standing-wave ratio equal to 2.66 


Sue. 6*8] 


and, therefore, the reflect on loss for almost all crystals is less than 1 db 
at any wavelength in this band. 

Figure 6*19 is aperspective view of a magic-T balanced mixer designed 
for the 12 per cent band centered at 3.33 cm. Included in the figure are 
crystal mounts in opposite polarities, the band-broadening irises, the 
matching structures for the magic T, and a variable matched attenuator 
for the LO coupling adjustment. 

6*8. A Double Balanced Mixer for Separate-channel AFC. — Because 
the local-oscillator circuit for a magic-T balanced mixer is simple, the 
addition of a second mixer for separate-channel AFC is straightforward. 
A simple single-crystal mixer could be coupled to the local-oscillator 

waveguide, on the high-power side of the local-oscillator attenuator, with 
any of the circuits described in Chap. 3. The two-channel balanced 
mixers have been made with a balanced mixer for each channel, however, 
rather than with a simple mixer for the AFC channel. Although the 
suppression of local-oscillator noise is not significant in the application of 
the balanced mixer as an AFC mixer, some of the other features are 

A two-channel balanced mixer is constructed from three magic T's. 
One T is used for each mixer and the other to split the local-oscillator 
power between the two balanced mixers, in the manner indicated sym- 
bolically in Fig. 6-20. Although the fourth arm of the center magic T, 
containing only a dummy matched load, is not essential, it docs serve a 
useful purpose. If the attenuator in the local-oscillator arm is reflection- 
less, no local-oscillator power reflected from one mixer is coupled into the 
other. For this reason all four crystals receive power depending upon 
their admittances in the same way as if each were connected to a matched 



[Sue. 6*8 

waveguide generator independently. It is therefore possible to use a 
single adjustment of the local-oscillator power for all four crystals, 
since their reflection losses will not be large. 

Another advantage of the center magic T over a simple T-structure 
for splitting the local-oscillator power is that an increase in the cross 
attenuation between the two mixers is obtained through its use. If 
power that leaks past the TR cavity enters the signal-input arm of the 
left-hand mixer, none of this power is sent into the local-oscillator arm 
of this mixer, provided the two crystals have identical r-f admittances 
at this power level. Under ordinary circumstances the two crystals are 
sufficiently alike to allow not more than 10 per cent of such power, sent 
into the mixer, to be coupled out the local-osciQator arm. To travel into 
the AFC mixer this power must be coupled from arm (1) to arm (2) of 
the center magic T. If the reflection coefficients for waves traveling 
outward in arms (3) and (4) are both zero, the coupling between arms (1) 
and (2) is zero and, therefore, the cross attenuation is infinite. In 
practice the dummy load in arm (4) can be made to have a very small 
reflection coefficient, but the reflection coefficient in arm (3) is determined 
by the amount of attenuation used. Even in the worst case, when the 
local-oscillator tube delivers only sufficient power to drive the crystals 
with no attenuation and completely reflects the signal frequency, 6 db 
of cross attenuation is gained through the use of the center magic T. 

The balanced AFC mixer provides additional effective cross attenu- 
ation. The signal arriving from the receiving mixer by way of the local- 
oscillator circuit, because it arrives with the local-oscillator signal, 
is discriminated against by the combination of mixer and i-f input 
circuit in just the same way as is local-oscillator noise. Even if the 
conversion losses of the crystals differ by as much as 3 db, the equivalent 
of 15 db of cross attenuation is obtained. Thus a total of at least 31 db of 
cross attenuation can be obtained with this double mixer, even with 
a local oscillator having just sufficient available power to drive the 
four crystals. With more lodal-oscillator power and well-balanced 
crystals, the cross attenuation would be very high and an ordinary 
leakage signal from the TR switch would certainly not interfere with the 
functioning of the AFC circuit. 

The balanced AFC mixer serves also to reduce the effect, on the AFC 
circuit, of the video pulse produced at the output terminals of a crystal, 
when the AFC signal is too large. Such video pulses may contain 
frequency components in the intermediate-frequency region and these 
are sometimes large enough, relative to the beat-frequency signal, to 
cause some interference with the AFC action. With the balanced mixer, 
if the rectification efficiencies of the two crystals are equal, the video 
pulses produced by the two crystals will also be equal. With an i-f 

Sec. 6-8] 



input circuit arranged to transmit the beat-frequency signal, the i-f 
components of the video pulses cancel. Video components due to stray 
signals or to harmonics of the transmitter signal are similarly canceled. 

One diflSiculty often encountered with an AFC circuit is that the circuit 
locks when a harmonic of the beat frequency passes through the i-f 
amplifier. With an intermediate frequency of 30 Mc/sec, for instance, 
the AFC circuit might lock with the local-oscillatbr frequency only 16 
Mc/sec away from that of the transmitter. To prevent this, the har- 
monics of the beat frequency must be kept below the threshold level 
of the AFC circuit. The balanced mixer assists in this because even- 
order harmonics, arising from beats between an even-order harmonic of 
the local oscillator and a harmonic of the signal of the same order, are 
balanced out. This may be shown to occur because a reversal in phase 
of a fundamental frequency does not alter the phase of an even-order 
harmonic generated from it. The cancellation of such even-order 
harmonic voltages is probably not very complete, because the effi- 
ciency of generation of harmonics by different crystals probably varies 

A further attractive feature of the balanced mixer for the AFC 
channel is that the*. signal-input arm can be provided with a matched 
dissipative attenuator without affecting the coupling of the local oscil- 
lator. If such an attenuator is used, the crystals receive signal power 
from a matched generator, which is not true if a cutoff attenuator, or 
small hole, alone is employed. From a matched generator, the power 
delivered to the crystals is not strongly dependent on their admittances 
and, therefore, the range of input power for which the circuit must be 
made to operate is considerably reduced. A dissipative attenuator made 
of polyiron, cut with matching transformers at both ends and having 
20 or 30 db of attenuation, has been used in the signal-input arm of the 
magic T that forms the AFC mixer. This attenuator also reduces the 
danger that stray leakage signals may get into the signal circuit at a 
connector on the signal-arm waveguide. Interference with the operation 
of the AFC circuit from this source is therefore reduced. Harmonics 
of the AFC signal coming from the transmitter tube are also effectively 
attenuated and should therefore cause no trouble. Thus it is apparent 
that the balanced AFC mixer solves practically all of the problems 
encountered in the two-channel mixer, and the improved performance is 
well woi-th the added complexity of one extra crystal. 

A perspective view of a double balanced mixer used in the 12 per cent 
band centered at 3.33 cm is shown in Fig. 6*21. This mixer represents 
only one of many possible arrangements of the magic T's and was chosen 
only because it gave the most convenient physical arrangement for the 



[Sbc. 6-8 

A double balanced mixer for the 1.25-cm band is made from a die-caSt 
block containing all of the waveguides and matching irises. Once the 
dies have been made, this part of the mixer can be inexpensively repro- 
duced with very high precision and in large quantities. The remaining 
parts, associated with the crystal mounts, the i-f attenuator, and the 
waveguide choke joints, may be added later or machined into the din-cast 
block. For the block to be die-cast, it has to be made in two halves and 

Pig. 6-21. — double balanced mixer for 3-cni band. 

thCTe has to be a small taper in the waveguide heights to allow the pio(K« 
to be p^ed off the dies. The mixer is split in a plane through the center 
of the broad wall of most of the waveguides so that no current linos arc 
^ regions of the junctions of the magic T’s. 
caused by leakage or poor contacts in this split. 
The adtoonal precaution has been taken, however, to have the adjacent 
ac^ of the two halves honed flat. The tapers in the waveguides cause 
their heights to change from 0.171 in. at the center, in the plane of the 

Sbc. 6*9] 



split, to 0.169 in. at the side walls. There is no detectable effect on the 
standing-wave ratios in the mixer from this small taper. A perspective 
view of the double balanced mixer, with the two halves separated to 
show the internal structure, is shown in Fig. 6-22. 

Cut away to reduce weight 

Fig. 6-22. — A die-cast double balanced mixer for 1.25-cm band. 

6-9. Other Special Circuits. — It is very simple to adapt the double 
balanced mixer to satisfy other, special, circuit requirements. If, for 
instance, a separate local oscillator for beacon reception is desired, such 
an oscillator may be connected to the dummy arm of the center magic T. 
The dummy load may be replaced with a variable attenuator and this 
arm becomes equivalent to the input arm of the first local oscillator. 
Either of the oscillators may be used, with a switch provided to select the 
desired one. For beacon reception, the AFC mixer is not used, but no 
harm comes of supplying local-oscillator power to it. 

If beacon AFC is desired, a reference cavity and detector crystal 
may be added to the LO-tube mount in place of the short circuit normally 
used behind the tube antenna. The same requirements must be met 
by the circuit, to avoid frequency discontinuities, as by the circuit 
described in Sec. 4*13. 

If a resonant TR cavity is used with a mixer for a radar system, it 
may be desirable to use a beacon-tuning device. This device can be 
placed, just as in the single mixers, in the signal input arm a half-wave- 



[Sbo. 6-9 

length behind the TR cavity. Shutters for protection of the crystals 
during shutdown and turnon periods can also be added to the signal input 

Because the magic-T balanced mixer is especially suited for use with a 
broadband nonresonant TR cavity, the 3-cm-band versions have usually 
been used in combination with a TR system of that type. As a conse- 
quence beacon tuners have not been required. In conjunction with 
systems using the bandpass TR cavity, in the desire to eliminate as many 
of the manual tuning controls as possible, the electronically controlled 

Fig. 6-23.— Double balanced mixer with beaoon-AFC cavity and detector. In this mixer a 
single thermally tuned oscillator is used for both radar and beacon reception. 

thermally tuned local oscillators have usually been used. In the 3 -cm 
band, for instance, the 2K45 tube, which can be tuned electronically from 
3.13 to 3.53 cm, is useful for this purpose. With such an oscillator 
tube it is not necessary to add a second oscillator for beacon reception. 
Instead, the single oscillator is tuned electronically to receive either the 
beacon signal or the radar signal depending upon which AFC circuit is 
operative. When the AFC circuit is actuated by the balanced AFC 
mixer, the oscillator is controlled at the correct frequency to receive 
radar echoes. On the other hand, a beacon reference cavity and detector 
crystal may be added and used to control the oscillator at the right 
frequency to receive beacon signals. Such a reference cavity may be 

Sbo. 6 * 9 ] 



added in place of the short circuit behind the tube antenna in the ordinary- 
tube mount, as for a separate beacon oscillator. It is also possible to add 
the beacon reference cavity by means of another magic T, as illustrated 
symbolically in Fig. 6*23. The magic T provides independence between 
the two circuits in such a way that reflections in the cavity circuit do not 
affect the power delivered to the mixers. A pad between the magic T 
and the cavity reduces the interaction between the cavity and the 
oscillator. Consequently, the load on the beacon cavity need not be so 
heavy as in the application without the input-K5ircuit pad. In this circuit 
the steepness of slope in the transmission characteristic of the cavity is 
sacrificed to some extent to gain decoupling in order to reduce pulling 
of the resonant frequency of the cavity by the external circuits. The 
formulas of Sec. 4T1 still apply, since the magic T between the oscillator 
and the cavity is equivalent to 3 db of matched-attenuator padding. 



By Eric Durand 

In the first chapter (Sec. 1*2) it was shown that the allowable percent- 
age frequency drift is much smaller in microwave receivers than in those 
designed for lower frequencies. Furthermore, many microwave oscil- 
lators are inferior in percentage stability. In some cases radar gear 
must be operated by the pilot of a plane, who cannot spare the time to 
maintain correct tuning manually. For these and other reasons, the need 
for automatic frequency control (AFC) became apparent early and at 
present AFC is used in nearly all equipments. This chapter^ will 
consider the causes of frequency drift and methods for minimizing its 
ill effects through AFC. 

74. Sources of Frequency Drift. — In most microwave receivers, the 
pass band of the r-f components is much wider than that of the over-all 
receiver. The center frequency of the pass band of the i-f amplifier is 
very stable compared with the beat note at intermediate radio frequency. 
Consequently, a receiver once tuned will operate at full efficiency as long 
as the frequency difference between local oscillator and transmitter has 
the correct value. 

Oscillators of three types are in common use at microwave frequencies : 
the magnetron, the velocity-modulation tube, and the triode lighthouse 
tube. Each is governed by a resonant circuit having effective inductance 
and capacitance. Although lumped constants are not used, as in the 
case of low-frequency oscillators, the same fundamental criterion for 
operating frequency applies, namely, that the over-all impedance around 
the feedback loop shall be equal to zero. Changes in resistance produce 
changes in amplitude, while changes in reactance cause a shift to a new 
frequency at which the net reactance is again zero. 

For practical purposes, factors affecting circuit reactance may be 
divided into three classes: 

1. Geometric factors, in which the effective inductance and capaci- 
tance of the oscillatory circuit are changed directly through 
mechanical motion. 

2. Pulling factors, in which reactance is coupled into the oscillatory 
circuit from the load. 

^ See also Vol. 23, Chap. 3. 


Sbc, 7*1] 



3. Pushing or electronic-tuning factors, in which reactance is intro- 
duced by changes in electrical conditions, such as voltage, current, 
or magnetic field. 

Here we are concerned with geometric factors deliberately introduced 
through a tuning mechanism only in so far as the mechanism is affected 
by the ambient conditions of temperature, pressure, and vibration. 
Magnetrons, whose resonant circuits are carved of solid copper blocks, 
are geometrically stable except for a drift of a few megacycles per second 
during warmup. They are, however, affected by both pulling and 

The 'pulling figure of an oscillator (see also Vol. 7) is defined as the 
maximum change in frequency when a load having a voltage standing- 
wave ratio (VSWR) of 1.5 is presented in all possible phases to the tube. 
Pulling figures in the 10- and 3-cm bands range from 10 to 16 Mc/sec, 
while at 1 cm, values lie between 25 and 30 Mc/sec. At low frequencies, 
pulling may be avoided by the use of a buffer amplifier. High-power 
microwave amplifiers, however, do not exist, and the microwave trans- 
mitter is therefore coupled directly to the antenna line. Consequently, 
pulling may occur during scanning because of reflections in the line caused 
by off-center rotary joints, reflections of energy into the antenna from 
radomes or other nearby objects, lobe switches, or variable antenna- 
feed devices such as wobbled feeds or variable-width leaky-waveguide 
antennas. The last-named antennas are very troublesome because the 
standing-wave ratio often suffers large fluctuations when the reflections 
from the individual radiating elements all add in phase. 

The amount of transmitter pulling is variable. Low-gain antennas 
are particularly troublesome since their diffuse pattern makes reflection 
back into the line almost unavoidable. Thus, in the 1-cm band, in 
spite of the large pulling figure, pulling is usually negligible because of 
the high antenna gains commonly used. 

The pushing figure of a magnetron is defined as the frequency shift, 
in megacycles per second, per ampere change in magnetron current. 
The figure is negligible in the 10-cm band, around 1 Mc/sec per amp in 
the 3-cm band, and 2 Mc/sec per amp in the 1-cm band. With reason- 
ably well-regulated primary supplies, pushing offers no AFC problems. 

The resonant frequency of the caWty of a velocity-modulation tube 
is altered by changes in either the cavity volume (inductance) or the 
space between the grids (capacitance). For our purposes, only the 
capacitance change is significant. Geometric changes in grid spacing 
are caused by thermal expansion and, in the case of airborne gear, by 
changes in barometric pressure. The magnitude and polarity of thermal 
changes depend on the detailed design used; in some cases, excellent 
compensation is possible. Tubes in which the tuning range is covered 



by the use of a thermal strut (see Sec. 7*2) are likely to show large drifts 
caused by temperature changes. Tubes such as the 2K46 and the 2K50, 
which have built-in triodes to energize the thermal strut, are very sensi- 
tive to triode heater voltage. The end effect here is geometrical, although 
the immediate variable is a voltage. 

Pulling, in local oscillators, is seldom a problem since the r-f geometry 
is fixed. A special dfficulty arising from the use of precision reference 
cavities as AFC standards has been treated in Chap. 4. 

Pushing, in local oscillators, is commonly referred to as electrical or 
electronic tuning. In triodes very little electronic tuning is available 
without serious deviation from optimum conditions. Velocity-modula- 
tion tubes, however, may be tuned many megacycles per second by varia- 
tion of either accelerator or reflector voltage. This property offei’s 
little difficulty as a source of drift since well-regulated power supplies 
may be used. In fact it is a means of tuning well suited to either manual 
or automatic control of frequency. 

7 * 2 . Properties of Local Oscillators for Frequency GontroL — ^As was 
pointed out at the beginiiing of the previous section, control of tho 
frequency difference between the local oscillator and the transmitter is 
sufficient to maintain correct tuning of a microwave receiver. Beciaiisc 
it is usually far easier to tune a local oscillator than a transmitter, tho 
former is usually chosen for control purposes. ’ 

Corresponding to the three mechanisms for producing freciuency 
cha,nges, there are three types of control that may be applied to the local 
oscillator. Geometric control may be exercised either by straight 
mechamcal devices operating through motor-driven tuning mochanisms 
or by the use of thermal expansion. Pulling control can be used by locu- 
li the oscUlator to a stabilizing cavity. In such a system there is no 
AFC per se, but only frequency stabilization. The use of roactanc-,o 
tubes, which is common at low frequencies and perhaps possible in tlu^ 
10-cm re^on, m a means of utilizing the principle of pulling since th<i 
reactance tube injects reactance across the tuned circuit in much the same 
manner as does a r^ctive load. Electronic tuning is commonly effectet 1 

T o' » volodty-m«luU.ti.,n 

£11! O“ai»*ore My b« tuiKicl anywho™ 

^ Mo/m to ±» Mc/boo before the output pmvor ie cut in half 
The ea^itmty of euoh tabee rouge, from 1 to 4 Mo/m per volt 

riven tvue '‘^’teneiee, with large variations within any 

£ Vol. ? ' ^ discussion of electronic tuning will be found 

Geometric control is relatively slow whereas response in electronic 

luSiff acoorfMy 

quite different as will be seen in later sections. ^ ^ 

SBC. 7 - 2 ] 



A number of thermally tuned reflex oscillators are now available. 
One example of the type is the 2K50, which operates in the 25,000- 
Mc/sec band. The essential features of the tuning mechanism are shown 
in Fig. 7-1. It operates in the follomng manner. When the bias on the 
tuner triode grid 0 is reduced, current flows to the plate P, causing its 
temperature to rise. The resulting expansion of P distorts the triangle 
abc, causing the apex a to pivot downward about c. Since the apex is 
welded to a metal sleeve 5, which, in turn, is welded to the upper plate D of 
the resonant cavity, this motion is transmitted to the cavity, and causes 

7 . 1 ^ — Thermal-tuning mechanism of the 2K60 oscillator. 

the upper grid G\ to approach the lower grid G%. This reduces the opera- 
ting frequency. It will be noted that the reflector P, which is inside 
of a ceramic cylinder cemented inside of jS, maintains a fixed distance 
from (?i. 

The 2K50 will tune from 1.21 to 1.29 cm (about 2000 Mc/sec) with 
6 watts of triode plate dissipation. The thermal time constant is about 
1.7 sec; consequently the maximum tuning rate at either end of the band 
toward the other end is 1300 Mc/sec per sec, and at band center, 650 
Mc/sec per sec. 

The 2K45 operates in the 10,000-Mc/sec band. The tuning mecha- 
nism is somewhat different from that of the 2K50 but gives the same 
results. The tube also covers a 2000-Mc/sec range with 6 watts of 



triode power, but the time constant is about 8 seconds, giving a maximum 
tuning speed at band center of 125 Mc/sec per sec. 

Two properties of these thermal tubes introduce new problems in 
AFC and have necessitated the introduction of new circuits radically 
different from those previously used for reflector AFC. The first of 
these properties is the time delay that occurs between the application of a 
control voltage to the triode grid and the attainment of equilibrium of the 
oscillator frequency. This delay jflxes an upper limit to the rate at 
which the AFC can foUow a disturbance, and even this limit cannot be 
reached unless the strut power is turned fully off or fully on when a 
frequency shift is required. The new circuits utilize this ‘^on-off'' 
principle. The second property is the wide tuning range afforded. 
The tubes will oscillate over a range of several hundred megacycles per 
second at a single value of reflector voltage. This introduces the problem 
of possible locking to the '‘wrong sideband’^ as will be shown in Sec. 7-10. 

A particularly troublesome feature of thermal tubes with built-in 
triodes is the dependence of the frequency on the triode heater voltage. 
Because of thermal inertia, changes in frequency from this cause are 
always slow and can be readily compensated for by the AFC. If, how- 
ever, one wishes to have manual tuning, for instance (to allow operation 
in the event of AFC failure), it is necessary to regulate the heater voltage 
closely. Ballast tubes are of some help, but for good regulation an 
electronic device is necessary. One scheme is to drive the heater by 
means of a stable oscillator operating from the electronically regulated 
LO accelerating voltage. 

7-3. Classiflcation of AFC Systems. — There are two TYiain classes of 
AFC systems: difference-frequency (D-F) systems and absolute-frequency 
(A-F) systems. D-F systems are those which maintain a constant 
frequency difference between local oscillator and transmitter, and A-F 
systems are those which hold the local oscillator to a fixed radio frequency. 

The conventional AFC of a home broadcast receiver^ is an example of 
a D-F system, since the comparison between local oscillator and received 
signal is made at the intermediate frequency, and errors in the frequency 
of the resultant i-f beat are used to control the local oscillator. 

The crystal-controUed flxed-frequency receivers used in commercial 
communications are examples of A-F systems. In microwave receivers, 
the function of such crystals is performed by precision cavities, and 
complex control circuits are required. 

The type of system required depends on the problem involved. In 
normal radars, samples of the transmitter signal are at hand, and varia- 
tion in transmitter frequency is expected. A D-F system is therefore 

1 F. E. Tennan, Radio Engineer* s Handbook, McGraw-Hill, New York, 1943, Sec. 9, 
p. 654. 

Sbo. 74] 



clearly necessary. On the other hand, for the reception of beacons, no 
signal is available until the beacon transmitter has been triggered. 
Therefore, the receiver should be always in tune. Tuning can be main- 
tained only by the accurate control of beacon transmitter frequency 
coupled with A-F stabilization of the locai oscillator. 

Again, in home recdvers any one of many carriers must be received, 
•which eliminates the possibility of A-F control; in fixed-frequency 
recdvers, the signal shordd not be lost during a fading spell or a noise 
burst, so that A-F control is desirable. 

In addition to classification according to the frequency to be controlled 
(that is, intermediate frequency or radio frequency), classification 
according to control circuit is useful. In particular, each of the specific 
systems mentioned above requires that the local oscillator be tuned 
very close to the desired frequency before control is established; that is, 
these systems have a small “pull-in” range. Once locked, a much 
larger drift tendency may be overcome; that is, the systems have a large 
“hold-in” range. These, then, &ie nonhunting systems. 

It is possible in either D-F or A-F systems to cause the local oscillator 
to sweep over a large band of frequencies in order to find the correct 
operating point. When the local oscillator is used in such a way, the 
system is known as a hunting system, and the pull-in range may approach 
or even equal the hold-in range. Hunting systems become useful when 
two conditions exist: (1) the expected drifts are large compared with the 
receiver bandwidth, and (2) there is no possibility of signal confusion 
(locking to wrong transmitter, etc.). Since both of the conditions 
usually apply, most AFC systems developed for radar receivers have the 
hunting feature. 

The balance of this chapter will treat himting and nonhunting 
difference-frequency systems, and absolute-frequency hunting systems. 
Corresponding to the greater effort spent in their development, emphaas 
is placed on D-F hunting systems suitable for pulsed transmittera ra^er 
t.ha.Ti on A-F and nonhunting systems for c-w transmitters. It is recog- 
nized, however, that the latter will play an increaangly important role 
in postwar work. 


7-4. The AFC Feedback Loop.— The basic operating principles of a 
difference-frequency AFC system are illustrated in the block diagr^ of 
Fig. 7-2. Samples of the transmitter signal /r and the local oscill^r 
signal /io are appUed to a mixer. The resultant i-f signal is ampMed 
and applied to a discriminator. This produces an error voltage w ose 
polarity depends on whether the intermediate signal frequency is above 



or below the crossover frequency and which is zero at crossover, as shown 
in Fig. 7*3. The error voltage is amplified and applied to a control 
circuit which transforms it into a control voltage^ suitable for changing 
the LO frequency. Polarities are such that any deviation from crossover 
produces a correction voltage tending to offset such deviation. It can 

JPiG. 7’2, — Block diagram of AFC loop. 

be seen that such a circuit is essentially an inverse feedback loop, and 
therefore, the Nyquist theorem^ applies. 

In particular, if the loop is broken between the discriminator and the 
control circuit, an alternating voltage applied to the control circuit will 
reappear, modified in both phase and amplitude, at the discriminator 
output terminals. By Nyquist's theorem, the system will be stable 
provided the over-all gain is less than unity at each frequency for which 

the two voltages are in phase. For 
the normal operating frequencies, the 
I frlSnl^ncy will be large for high stability, 

and the phases 180® apart corres- 
ponding to the negative feedback. 

Most of the differences between 
hunting and nonhunting systems are 
in the control circuits. The next 
sections treat in detail those features 
common to both. Most of the em- 
phasis is placed on systems with near-by pulsed transmitters, partly 
because these are more complex than those with remote or c-w trans- 
mitters, and partly because much material on the latter systems is already 
in the literature. 

7-6. The Transmitter Sample. — When, as in a communications 
receiver, the transmitter is remote, the normal received signal must be 



Fig. 7*3. — Discriminator characteristics. 

^ See Sec. 7*7 for a more general definition of these terms. 

* Nyquist ‘‘Regeneration Theory,” Bell System Technical Journal 11, 126 
(January 1932). 

Sec. 7-6T 



used. It is customary to utilize the main receiver channel, up to and 
including the last i-f stage, without modification. The simple detector 
is replaced by a discriminator (Sec. 7-7) which generates the necessary 
error voltage. Normally, no changes in the r-f, mixer, and i-f stages are 
required although, occasionally, a separate i-f channel is used to obtain 
greater bandwidth. 

In a radar set the transmitter is near by. At first glance this would 
seem to simplify the problem since a constant source for sampling is 
available. It proves, however, to add a whole new set of problems 
brought about by the excessive power which may reach the receiver unless 
special care is taken. 

Experience has shown that in pulsed-radar sets an overwhelming 
majority of AFC failures result from improper r-f conditions. Usually 
they take the form of an improper quantity and quality of transmitter 
sample reaching the AFC crystal (which may be either the main receiver 
crystal or a separate crystal). 

When a very large signal is applied to a silicon rectifier, it begins to 
pass current in the backward direction. The ‘'back resistance^' falls 
until it approaches the value of 
the “forward resistance." Conse- 
quently, the rectification eflBlciency 
of the crystal approaches zero. If 
we observe the rectified cun’ent as 
a function of a-c input power we 
obtain a curve such as is shown in 
Fig. 7*4, which has a real maximum, 
with decreasing output current for 
very large input powers. 

A typical radar pulse is really 
more or less trapezoidal in shape, as 

shown in Fig. 7*5a. The effect of impressing such a pulse on the char- 
acteristic of Fig. 7*4 is shown as a function of pulse amplitude in Figs. 
7-6c, d, and c. 

It can be seen from a Fourier analysis that this video pulse from the 
crystal, even if it has the simple shape shown in Fig. 7-5c, will contain 
energy components at the intermediate frequency. The amount of 
energy at this frequency is, however, 30 db or more below the normal 
i-f level. Under overload conditions, the pulse will have the form shown 
in curve d or even curve e of Fig. 7*5. In this case, there will be large 
amounts of energy at the intermediate frequency, which in some cases 
will exceed the desired energy and result in the continuous generation of 
error voltage, even when the local oscillator is completely dead. This 
spurious error voltage can be regarded as being produced by a shock 


i’la. 7*4. — Typical rectification charac- 
teristic of a silicon crystal-rectified current 
vs. input power. 


excitation of the i-f circuit. It has sometimes been referred to as “video 

There are also found, in the output voltage from the crystal, com- 
ponents whose frequencies are integral multiples of the difference between 
the frequencies of the local oscillator and transmitter. Such harmonic 
signals, or “harmonic hash," may be generated by the nonlinearity of the 
crystal, or they may be caused by the beating between 
harmonics of the transmitter and the local oscillator. 
Spurious control information results when the fre- 
quency difference between the two oscillators is a 
submultiple of the intermediate frequency. 

If the local-oscillator frequency is swept through 
the region around the transroitter frequency, a series 
of pulses is obtained. Figure 7*6 shows how these 
look with and without spurious control signals of each 
of the kinds mentioned above. One may produce 
these characteristics experimentally by applying a 
linear sweep voltage to the frequency-control elec- 
trode of the local oscillator and to the horizontal 
plates of an oscilloscope, and by applying the dis- 
criminator output voltage to the vertical plates 
through a suitable amplifier. 

The relative importance of each type of spurious 
signal increases with increasing transmitter-sample 
power. Experiments with crystals at 10,000 Mc/sec 
and 25,000 Mc/sec show that they both become 
troublesome if the r-f power at the crystal exceeds a 
few milliwatts. Also, the desired signal increases but 
slowly at these levels. An operating level between 
1 and 2 mw is therefore desirable. The partial satu- 
ration at this level makes the signal output voltage 
fairly independent of input power. On the other 
hand, spurious signals are at least 20 db below the 
desired signal. Furthermore, if one tries to operate 
below 1 mw, the spurious signal decreases but 
slowly whereas leakage soon becomes intolerable, and extra i-f gain is 

Accurate control of gain up to the error-voltage generator is cleai’ly 
needed. If the gain is too low, locking occurs, if at all, near the peak of 
the discriminator curve, well away from crossover (see Fig. 7*3). If it is 
too high, spurious signals will cause locking either completely out of the 
band (transient response) or at one half, one third, etc., of the inter- 
mediate frequency (harmonic response). 

(a) Transmitter pulse, 
positive envelope 

(6) I-f pulse 

(c) Norma! “video pulse" 

(d) Saturated “video 


^ n 

(e) “Video pulse" under 
.extreme overload 
Fig. 7-5. — Genera^ 
tion of shock excita- 


Leakage is particularly troublesome in. automatic frequency control. 
There are tvro sources: (1) bad joints (choke joints, backs of crystals), 
and (2) inadequate cross attenuation, which allows TR leakage power to 
reach the A.FC crystal through the common coupling provided by the 
local oscillator. Leakage power and the sample power introduced 
deliberately are coherent and add vectorially in amplitude. Thus if 

Fio. 7'0. — Output BiKnal from a discriminator at radio frequency! fv is the transmitter 
frociuoiicy; /% is tho intermediate frequency. 

the two arc equal, the not power may range from zero to four times the 
desired power, according to the phases. 

The impoi-tance of leakage becomes apparent when one considers 
that the power in the main transmitter line may be as high as 1 mega- 
watt, while the amount allowed to reach the crystal through leakage 
should be less than -J mw, a difference of 96 db. 

7.6. Mixers, Local Oscillators, and I-f Amplifiers. In early radar 
sets a single mixer was used, and the transmitter sample was the power 
leaking past the TR switch. The first two stages of the mam receiver 
served as i-f amplifier, and only three or four additional tubes were 



need^: one or occasionally two i-f amplifier stages, and two control 
tubes. A typical AFC chassis . circuit of the “d-c amplifier’^ type is 
shown in Fig. 7-15. The use of a gas-discharge-tube control circuit 
(Fig. 7-18) was also common. 

In its simplest form, single-mixer AFC suflEers three serious drawbacks. 
First, the power reaching the crystal is much too high (20 mw or more), 
giving rise to spurious signals caused by shock excitation. Second, the 
20-mw “flat’’ is preceded by a short high-energy “spike” which gets 
past the TR tube before it has had a chance to fire. This generates 
transients. Moreover any harmonic energy present in the transmitted 
signal may be passed by the TR switch in the fired condition. Finally, 
the system is subject to control by energy reaching the antenna between 
transmitter pulses. In practice, this results in echoes from nearby 
objects (“ground clutter,” and so forth) producing control information. 
The effective gain of the system therefore depends on whether the antenna 
points toward the horizon or toward the sky. Also, the AFC may 
lock to the wrong transmitter either accidentally from a friendly system 
or as a result of enemy jamming. 

By the use of more elaborate devices, some of these difficulties may be 
overcome. Bell Telephone Laboratories have developed a “spike- 
blanking” circuit in which the leading edge of the video pulse at the 
primary of the transmitter pulse transformer is differentiated and applied 
to the cathode of one of the i-f stages. The positive pulse thus pro- 
duced cuts off the stage during the time of the TR spike, but allows it to 
recover for the balance of the transmitted pulse. Bell Telephone 
Laboratories have also used an “enabling” circuit to reduce the effects 
of echoes. Again the primary video pulse is used, undifferentiated. It 
is reduced to about -|-120 volts in amplitude and applied to the screen 
and plate of one of the i-f stages. Since this stage has no other source 
of d-c power, it is dead except during the transmitted pulse, so that the 
signals entering the antenna between pulses are ineffective. Figure 
7T6 shows how these triggers are introduced. 

With these modifications, reliable operation may be achieved in some 
cases. No control over the flat part of the TR leakage power is possible, 
however, and many system designers have gone over to double-mixer , or 
separate-channel AFC. 

In the separate-channel system, a small fraction of the transmitted 
pulse is coupled out to a separate crystal which drives a separate i-f 
amplifier. Thus, the power reaching the crystal may be adjusted to the 
optimum value and will be “spike-free.” Because of the high attenu- 
ation, signals entering the antenna cannot reach the AFC crystal. The 
design and operation of the r-f components involved in separate-channel 
AFC have already been discussed in Chaps. 4 and 6. 

Sac. 7-6] 



Further improvement in AFC reliability may be obtained by the use 
of a balanced mixer (Sec. 6*8). Since a balanced mixer is customarily 
used in conjunction with a similar mixer for the main receiver, the 
resulting unit is commonly called a ‘^four-crystal mixer.’’ In the four- 
crystal mixer, TR leakage power and the resultant transients, and all 
harmonics of even order generated in the crystals are balanced out. 
Only stray leakage and harmonics generated by the oscillators remain as 
problems. Harmonics of third and higher orders are normally negligibly 

The method of obtaining the transmitter sample in a separate-channel 
system is important. Usually, a small coupling hole in the side of the 
transmitter line is used, although occasionally directional couplers 
(Vol. 11, Chap. 14) are used to make the sample-power level independent 
of standing waves in the antenna line. Only part of the necessary 75 to 
90 db of attenuation may be thus provided Often, from 20 to 40 db 
more is obtained from a dissipative pad inserted directly in the mixer. 
This pad serves to provide a matched line looking out from the mixer, 
and to reduce the effects of leakage into the line in front of the pad. 

The coupling hole is a waveguide beyond cutoff and may be a wave- 
guide within cutoff for harmonic frequencies. Thus, a small percentage of 
harmonic content in the transmitter output may become a large or even a 
dominating fraction of the power in the AFC line. Because this hamionic 
energy may be so large as to generate transients, its elimination is most 
important. To attenuate the harmonics, a resistance strip or a polyiron 
plug may be inserted in the coupling hole. 

Little need be added about local oscillators. Many of their properties 
were discussed in Sec. 7*2, and the problems of coupling them into 
mixers are covered elsewhere (Chap. 4). The amount of power that 
should be applied to the AFC crystal from the local oscillator is governed 
by the fact that it should differ from the power from the transmitter by at 
least a factor of 3, in order to reduce the amount of harmonic generation 
by the crystal. It is clear that the local-oscillator power should be the 
lesser of the two. First, there is seldom any power to spare in reflex 
oscillators; and second, the higher the transmitter power at the crystal, 
the less important is a given amount of leakage power. Thus, in normal 
parlance, the transmitter serves as local oscillator, and the real local 
oscillator serves as signal. 

A local-oscillator power level of about ^ mw is desirable and also 
convenient, since it is also the approximate power required for a main 
receiver crystal and so the two crystal currents may be set to the same 
value. If a magic T is used to divide the power among the crystals, 
as in a four-crystal mixer, a single adjustment will suffice, and all crystals 
will receive equal power. 



The i-f output signal of an average crystal operating under the con- 
ditions outlined above lies between 0.25 and 0.60 volt rms. Since 
this is inadequate for a discrmhnator, one or more stages of i-f amplifica- 
tion are used. The bandwidth requirement of the i-f amplifier is gov- 
erned by the discriminator bandwidth, which should be slightly less than, 
or equal to, the over-all receiver bandwidth. The receiver bandwidth, 
in turn, is governed by the system pulse-length or modulation require- 
ments. Since typical radar bandwidths lie between 1 and 8 Mc/sec to 
the half-power points, the gain per stage is usually low. Furthermore, it 
is now considered good practice to make the AFC i-f channel considerably 
wider than the discriminator peak-to-peak separation to remove the 
necessity for complete realignment when the discriminator crossover 
frequency is shifted. This makes possible the adjustment of the AFC 
locking frequency with a single control. With the system locked to 
AFC, this control may be timed for maximum performance. 

Gain at the intermediate frequency is expensive, whereas gain after 
detection is cheap, since, in most cases, the video pulses have been 
greatly “stretched,’^ and hence the video bandwidth requirements are 
low. It does not pay, however, to overwork this idea. The video input 
signal should be approximately 1 volt in order to be large compared with 
stray pickup. For pulses longer than 1 or 2 jusec, a single i-f stage 
preceding a conventional dual-diode discriminator will suflfice. For 
pulses between i /xsec and 1 jitsec, two stages may be needed, while still 
shorter pulses may require three or more. In the latter case, extra band- 
width may be obtained by staggering the center frequencies of the first 
two stages (Vol. 18). A voltage gain of four or more is possible in the 
circuit between the crystal and the first amplifier grid. This extra gain 
involves extra alignment problems, however, and a single-tuned circuit 
with unity gain may be preferable. 

Symmetry in the i-f amplifier is far more important in the AFC 
channel than in the signal channel. The i-f spectrum of a short pulse 
contains sideband energy on either side of its center frequency. If the 
amplifier is asymmetrical, the over-all discriminator characteristic will 
likewise be asymmetrical, and the sidebands will not be canceled out at 

7*7. Discriminators. — ^The characteristic curve of a discriminator 
shown in Fig. 7*3 is not of the most general possible type. For one thing, 
the zero referred to may be at some d-c level other than ground potential. 
For the purposes of this chapter, the zero to which polarities are referred 
is the d-c voltage existing at the output terminals w'hen there is no signal at 
the input terminals. Crossover frequency is that frequency lying between 
the two output peaks for which the output voltage is zero. If the i-f 
input signal consists of continuous waves, the output voltage will be d-c; 

SBC. 7-7] 



if it consists of a series of short pulses, the output voltage will consist of 
a series of pulses whose amplitude and polarity follow the scheme shown 
in Fig. 7-3. In the special case of the beacon AFC described in Sec.7-18 

the output voltage varies sinusoidally. Change of polarity is replaced by 
a 180® reversal of phase, but if plus and minus are taken to mean one or 
the other phase, Fig. 7*3 still applies. 



Three types of i-f discriminators are shown in Pig. 7-7.^ 

The Travis circuit depends on the action of two resonant circuits, 
one tuned above the desired crossover frequency and one tuned below it. 
Detectors across the two circuits are connected back to back. The 
individual and sum voltages developed by the detectors are shown in 
Fig. 7*8. It should be noted that the individual resonant elements 

are double-tuned. Hence, if close 
coupling is used, each side of the 
discriminator characteristic may be 
double-humped. This is not possi- 
ble in either of the other circuits. 
If the peak-to-peak separation is too 
great for the circuit Q's in any of the 
circuits, the characteristic will have 
a “chair,” as shown in Fig. 7-8d. 

Three factors must be adjusted: 
the crossover frequency, the peak- 
to-peak separation, and the sym- 
metry. In the Travis discriminator 
the crossover is shifted by tuning the 
two resonant elements in the same 
direction, while separation is changed 
by tuning them in opposite direc- 
tions. The other circuits, on the 
other hand, have separate, indepen- 
dent crossover and separation ad- 
justments. The characteristic is 
symmetrical if the i-f amplifier pass 
band is symmetrical, and if the dis- 
criminator primary is tuned to the 
Fig. 7-8.-Operation^of Travis disorimi- crossover frequency. In addition, 

the Travis circuit requires that the 
individual circuit bandwidths be equal. The adjustment of the primary 
circuit of the discriminator is commonly called the symmetry control. 
It may be used to offset the slight inherent asymmetry which arises from 
the unbalance of the discriminator with respect to ground potential (see 
Sec. 7*8). 

The Foster-Seeley discriminator of Fig. 7-76 has been well covered 

1 D. E. Foster and S. W. Seeley, “Automatic Tuning, Simplified Circuits, and 
Design Practice,” Proc, I.R.E., 26, 289, March 1937. 

Hans Roder, “Theory of the Discriminator Circuit for Automatic Frequency 
Control,” Proc. I.R.E., 26, 590, May 1938. Charles Travis, “Automatic Frequency 
Control,” Proc. I.R.E.j 23, 1125, October 1935. 

Sec. 7-7] 



in the literature and will not be treated here beyond noting that the 
mutual inductance determines the peak-to-peak separation and that the 
crossover frequency is the resonant frequency of the secondary circuit. 
At the frequencies commonly used for i-f amplifiers in microwave receiv- 
ers, little if any lumped capacitance is added. The distributed capaci- 
tances of the diodes, in series, comprise the bulk of the tuning 

The Weiss discriminator of Fig. 7-7c was developed at the Radiation 
Laboratory in an attempt to reduce the detrimental effect of stray 
capacitances by making them serve a useful function. It is essentially 
the capacitance-coupled analogue of the Foster-Seeley circuit. It has 
been shown experimentally that the two discriminators have sub- 
stantially identical electrical performance (gain-bandwidth product, 
susceptibility to stray capacitance, and so forth). The Weiss dis- 
criminator, however, requires accurate control over the small difference 
between the coupling condensers required for a narrow-band char- 
acteristic. On the other hand, the 
Foster -Seeley discriminator suffers 
at large bandwidths from the large 
variation in mutual inductance + 
with small displacements of the _ 
coils. An analysis of the action + 
of the Weiss discriminator is given ^ 
in the next section. 

The term ' ‘discriminator eflSici- 
ency ’’ is commonly applied to the 
ratio of the maximum available 
output voltage (d-c or pulse) to discriminator, 

the peak voltage of the i-f signal 

at the input terminals. Since voltage stepup is possible, resulting in 
“efficiencies^' greater than unity, such usage is improper. We shall use 
the term “discriminator voltage gain" to express this factor. 

As in a conventional detector with transformer coupling, discriminator 
gain is affected by a variety of factora, including diode conductance, 
transformer design, and video load resistance. In addition, when one of 
the detectors is producing a maximum signal, the other is absorbing 
some of the available power, and this power, when rectified, balances 
out pait of the signal from the fii-st detector. It can be shown that this 
balance causes a 30 per cent reduction in discriminator voltage gain 
under optimum adjustment. 

Figure 7-9 is the equivalent video circuit of a discriminator. Consider 
the action of one of the diodes alone. If a step-function i-f signal is 
applied to the discriminator, the voltage across the bypass condenser will 



rise exponentially with the time constant RintCa^ Rise times of the 
order of 1 /zsec are common. When the step function is removed, the 
voltage across Cb will immediately start to decay with a time constant 
RbCb. FuU voltage is reached, therefore, only if the i-f pulse is long. 
In a typical design the amplitude of the output pulse for a i-zisec input 
signal will be about one third that for a long pulse. 

Increasing RbCb results in a stretching of the pulse. If Cs is increased, 
there will be a corresponding reduction in amplitude unless the original 

Sue. 7'7] 



equal. Since the two generator impedances are equal, the effective 
bypass capacitances should be equal. It should be noted that the total 
capacitance across the lower detector iacludes both the coupling con- 
denser Co of Fig. 7'9 and stray capacitances. Consequently, the actual 
value of condenser Cb should be 15 to 20 fi/d greater than that of C^. 

Figure 7-10 shows the effect of a moderate video unbalance. Curves 
(a), (b), and (c) show the waveforms observed across the individual 
detectors and at the output terminals when a pulse of length t, at cross- 
over frequency, is applied to the discriminator. The capacitance across 
the upper detector is assumed to be 30 per cent too large. Because 
of the difference in the time constants for charging, the peak voltage 
reached across the upper detector is less than that reached across the 

Fio. 74 1. — Fostor-Soeloy diBcriminator with Straudberg detectors. 

lower detector. At the end of the i-f pulse, therefore, the net output 
voltage is negative. Because of the difference in the discharge time 
constants, however, the voltage across the lower detector falls toward 
zero more rapidly than that across the upper detector. Consequently, 
after a time, the voltage across the upper detector dominates, and the 
total output voltage Ix^comes positive. Finally, all charge leaks off, 
and the voltage becomes zero. 

If the signal from a pulsed signal generator (see Fig. 7*6), the fre- 
quency of which is varied from pulse to pulse, is applied to such a dis- 
criminator, the pattern of Fig. 7-10(1 will be seen on an oscilloscope 
connected to the output terminals. Near the crossover frequency every 
pulse will extend on both sides of the axis, and the crossover frequency 
will no longer 1)0 shai-ply defined. Such a broadening of the crossover is 
not serious unless the unbalance is severe, in which case the output voltage 
of one polarity is markedly reduced. A nominal figure of 20 per cent 
unbalance toloraiuie is usually stipulated for discriminators that are to 
be manufactured in quantity. This is readily achieved if the original 
design is good. 

From the foregoing, one might assume that only diodes are used as 
detectors. Actually, triodes are often used. For instance. Bell Tele* 



phone Laboratories have used a pair of plate-circuit or “anode bend” 
detectors. Since both output voltages are positive, one of them is 
inverted to give the correct over-all characteristic. A circuit of this 
t3rpe is found in Fig. 7‘ 16. Strandberg* has used a plate-circuit detector 
for one branch and an “infinite impedance” or cathode detector for the 

(a) (6) 

7*12. Circuit and OQuivalexit circuit for Weiss discriminator. 

other, the two being coupled by a common cathode connection. The 
circuit is shown in Fig. 7*11. 

The great advantage of these detectors is that they supply the 
energy necessary to charge the bypass condensers from the power supply 
instead of from the i-f amplifier. Much greater pulse stretching is 
possible. Thus, in the circuit of the Bell Telephone Laboratories, the 
pulse is stretched out until the next pulse arrives, so that almost d-c 



Fig. 7-13. — Equivalent circuit for 
Weiss discriminator after -Tr-to-T trans- 

control signals are obtained. With 
smaller bypass condensers, the rise 
time may be made so low that the 
output voltage is independent of 
pulse length even for pulses less than 
0.1 A*sec long. 

7-8, Discriminator Theory.® — A 
simplified theory for approximate 
calculation has been developed for the 

Weiss discriminator. Figure 7*12 
shows the basic circuit of the discriminator, its equivalent circuit, and the 
important voltages. Ci and C 3 represent the diode capacitances, and 
the circuit Q’s are assumed to be infinite. The first step is the trans- 
formation of the TT-network Ci- Ct-L into its equivalent T-network, 
shown in Fig. 7-13, where 

* M. W. P. Strandberg, “A Video-Frequency Modulation Detector,” RL Internal 
Group Report S3, Apr. 1, 1945. 

» W. Sdove, “Frequency Discriminator Analysis,” RL Internal Group Report 61, 
Jan. 1, 1945. 

Sue. 7-8] 



and where 


f., _ CxCz 

( 1 ) 

At some angular frequency «i, Zi will resonate with C, so that all of 
the current will flow in the upper branch, making Ei large, and Et zero. 
Similarly, at an angular frequency «2, E2 will be large and Ei zero. 
The frequencies «i and «2 are very close to that of the peak response. 
At «i 




LC'cof _ Cl 

«fLC' - 1 " C ’ 

1 - wlLC' _ C 
<otLC' ~ Cl 



LC' = 





If, for the sake of argument, it is assumed that Ci > C2, then cji > 6)2. 
For angular frequencies decreasing from coi, the impedance of the upper 
branch increases from zero and is inductive. Similarly, raising the 
angular frequency from (02 causes the impedance of the lower branch 



to iD crease capacitively. Therefore, there exists an angular frequency 
a>o at which the two impedances are equal in magnitude but opposite in 
phase. At this frequency the currents in the branches are equal in 
magnitude, so that Ei = £? 2 , and the error voltage is zero. This is the 
crossover frequency. At coo 

2fi + Zc = —(Z 2 + Zc)j 


Zi Z 2 — — 2-Zc. 

Substituting the values for these impedances given in Eq. (1), 


Equation (4) shows that the crossover frequency is that frequency at 
which L resonates with C' and C/2, that is, with the total capacitance 
across L. 

An expression for the peak-to-peak separation can be obtained from 
Eqs. (2), (3), and (4): 

COi — CO2 


Ci + C 


In some cases, a simplified expression is possible. 
Eqs. (2), (3), and (4), we have 

Cl C 2 

Cl + C C 2 + C 

^1 - 





Starting again from 

-(l\ C(Ci~C2) 

\ ^2Ci/(Ci + C)(C2 + C) 

( 6 ) 

Now if the percentage peak-to-peak separation is small, we may 



^1 “ “2 _ (^1 W2)(c0i + CO2) ^ 2 (c 0 i — CO2) 

* — ~ ~ . ■ 



Equating this to the right-hand side of Eq. (6), we obtain 
<oi — ti>2 ^ 0(01 "b C's) 

(Dc 20i0i 


The voltage at each peak can easily be calculated. For example, 
at coi the current in the upper branch is E/Z$ and the voltage across the 
diode is Ei = (E/Z^Xo- 


- «iC0 


ojf A _ Cl + C2 

co?V "^cJ Ci + C‘ 

{E2\ Cl + C2 
\EU^ C2 + C‘ 

These equations indicate that peaks of equal amplitude are possible 
only if Cl + C = C2 + C, for which condition Ei = E 2 for all frequencies, 
and the error voltage from the discriminator is zero. The branch having 
the smaller coupling condenser will have the larger current, and we have 
already seen that this will be the low-frequency branch. If we make 
Cl < C2, then El < £2. We can, 
however, by restricting the size of 
the bypass condensers of Fig. 7-12, 
arrange matters so that not all of the 
voltage El in the theoretical expres- 
sion appears across the upper diode. 

By proper selection of these con- 
densers the two peaks may be made 
equal. With the diodes connected 
as shown and Ci < C2, the upper 
branch will give positive output 

1 , . 1 i* Tr xi. Fig. 7-14. — Circuit for hum reduction. 

voltage at low frequency. If the 

characteristic is to have the opposite sense, then for the equality of the 
peaks to be maintained, the diodes themselves must be reversed. 

In any event, the dissymmetry is usually not serious and approximate 
compensation may be secured by a slight detuning of the resonant 
circuit normally associated with the primary voltage source E of Fig. 7-12. 

It may be noted here that most miniature tubes have a certain amount 
of leakage conductance between heater and cathode resulting in the 
appearance of a hum voltage at the cathode of the upper diode, which 
carries the desired signal. The amount of such hum is variable from tube 



to tube and depends on the resistance from cathode to ground. If this 
resistance is i megohm, a common value, the hum may amount to a large 
fraction of a volt. Fortimately, a bias of either polarity between cathode 
and heater will cure the trouble. Positive bias on the cathode is partic- 
ularly effective. If the amount of such bias slightly exceeds the peak 
value of the heater voltage, the hum will be completely eliminated. 
This condition may be readily attained by the use of a separate negatively 
biased heater winding, or by the circuit of Fig. 7T4, which may be 
applied to any of the discriminators of Sec. 7*7. 


7-9. Control Circuits for Nonhunting Systems. — Control circuits for 
nonhunting systems with c-w transmitters are very simple. Since the 
characteristic of a discriminator is linear near crossover, the output 
voltage is a pure d-c voltage whose level and polarity are determined 
by the frequency error of the local oscillator. As a rule the only require- 
ment is a direct connection between the discriminator and the frequency- 
control electrode; that is, the grid of the reactance tube, or the reflector of 
the reflex oscillator. Descriptions of many such circuits are to be found 
in the prewar literature.^ If the frequency-control electrode is insensi- 
tive, a d-c amplifier, preferably push-pull, may be required. 

When the transnadtter output power consists of short pulses separated 
by long intervals, as in a radar set, it is necessary to provide only for the 
stretching out of the pulses that appear at the discriniinator, so that their 
peak amplitude is maintained between pulses. 

Figure 7*15 shows the circuit used for AFC in a radar set designed at 
Bell Telephone Laboratories. This represents a highly developed 
nonhunting, single-mixer system (Sec. 7*5). It is seen that the output 
terminals of a conventional Weiss discriminator (Secs. 7*7 and 7*8) are 
connected to a pair of plate or anode-bend detectors. The plate load 
resistors are very high and are bypassed by large condensers, giving a 
time constant of 3.2 X sec. Since the interval between pulses in 
this set is only 2.5 X lO—^ sec for the lowest pulse recurrence frequency, 
most of the charge developed during the pulse will be sustained until the 
next pulse. What little ripple remains is filtered out by a large con- 
denser at the reflector of the local oscillator. 

The plates of the detectors are connected directly to the grids of a pair 
of push-pull d-c amplifiers which have a large common cathode resistor. 
Because this resistor is degenerative for everything except signals on 
either grid, it increases stability. Control voltage is taken from one of 
the amplifier plates, the operating range being selected by adjustment of 
the plate supply voltage. 

^ Tenn^, Uc, cit. 



Ail capacities are in umi 
Fig. 7-15. — “ D-c-amplifier 



The output voltage of this amplifier will swing at least 25 volts above 
or below the no-signal level, and is adequate to control a refiex oscillator. 

It will be noted that the ‘^enabling'* feature discussed in Sec. 7*5 is 
provided by energizing the first i-f amplifier stage only during the initial 
transmitter pulse. The trigger for the screen and plate supply of this 
tube is taken from the primary of the transmitter pulse transformer. 
Other BTL circuits have also contained the “ spike-blanking feature 
already considered (Sec. 7-5). The leading edge of the video pulse at the 
pulse transformer is differentiated to produce a sharp, very short positive 
pulse, which is applied to the cathode of 7i, cutting this tube off during 
the first part of the transmitter pulse, during the time when the TR 
spike comes through. The point at which such a trigger is introduced is 
also shown in Fig. 7-16. 

Other nonhunting systems have been used successfully by the British. 
An interesting feature of one of their circuits is the '' reflexing of a par- 
allel pair of output i-f amplifier tubes to serve as push-pull d-c amplifiers. 

With reference to Fig, 7-6 (a), if the connections are so chosen that a 
positive error voltage tends to reduce the local-oscillator frequency, it is 
then clear that locking is possible where and only where the discriminator 
characteristic has a positive slope. In the main pass bands, there are 
three such regions: one near crossover at the low-frequency sideband and 
two on the outer skirts of the high-frequency sideband. The latter pair 
are too far from crossover for satisfactoiy operation. In this case, then, 
the high-frequency sideband is the wrong ddehand. Other types of 
operation on the wrong sideband will be noted later. It is also possible to 
lock incorrectly at any one of three places on each pair of harmonic 
sidebands if the gain is too high. With adequate r-f selectivity, of course, 
these dangers could be avoided^ in nearly every microwave receiver, how- 
ever, they must be considered. 


7*10. Basic Theory. — The ^^drift-in^^ theory of operation is illustrated 
in the block diagram of Fig. 7-16. During the hunting cycle, only the 
shw-sweep generator need be considered. This generator impresses a 
sawtooth voltage on the frequency-control electrode, which results in 
a sawtooth frequency modulation large enough to allow for all possible 
tuning errors. At some time duiing the sweep, the crossover frequency of 
the desired sideband will be passed. Information generated at this time 
will actuate the search stopper which will halt or reverse, as needed, 
the progress of the slow sweep. There is a perpetual tendency for the 
frequency to drift off; this tendency is offset by the search stopper. A 
“walF' may be thought of as existing at the point A in Fig. 7-17 and 
inhibiting the sweep. Note that here too there is a wrong sideband, 


Sbc. 7-11] 


smce a similar “wall” exists at B. Each harmonic likewise offers a pair 
of “walls” for possible locking. 

The system is stable, for, if the oscillator frequency tends to drift 
to the right, the rising discriminator output voltage will develop extra 

To local oscillator 

Fia. 7*16. — Drift-in AFC. 

Right sideband 

Wrong sideband 


Tuning error 

Direction of slow sweep 
Fig. 7*17. — Hight and 'sili'ong sidebands. 

Tuning error 

search-stopping power, pulling the frequency back. Similarly, a shift 
to the left results in a diminution of search-stopping power, and the 
normal slow-sweep drift mil resume. 

7*11. Standard Gas-discharge-tube AFC. — ^The first AFC for pulse 
radar developed at Radiation Laboratory used the gas-discharge-tube 
control circuit of Fig. 7-18. Although this circuit has certain inherent 

Fio. 7-18. — Standard gas-dischargo-tubo AFC circuit. 

limitations which have necessitated the development of new hard-tube cir- 
cuits, it is still in wide use and is likely to remain so for some time to 
come. Because of this, and because no adequate report on it has yet been 
issued, this circuit will be considered in detail. 

Fi is a gaseous tetrode having the characteristic that the grid voltage 
necessary to cause breakdown is nearly independent of plate voltage 



It is so biased as to remain nonconducting in the absence of a positive 
pulse or trigger from the amplifier that follows the discriminator. 

7® is a gaseous triode so biased as to fire whenever the plate voltage 
reaches a critical value (usually about 200 volts for a 300-volt supply)* 
7j is the slow-sweep generator discussed in the previous section. 
Current flows throu^ iZi and Bj, charging 0% imtil the ciitical voltage 
is reached. 7s then breaks down, discharging Cs abruptly. Because 
of the large number of ions formed in 72 (or later in 7]) during the 

I^G. 7*19; — ^Voltage-time reLationships in gas-disohargo-tubo AFC. 

breakdown, and because of the finite ion-recombination rate, ep^ is 
carried well below the critical voltage for ion production. Before Ri 
and J ?2 can recharge C 2 to this voltage, all ions will have recombined. 
Therefore, the tube will remain nonconducting and the slow upwai'd 
sweep will resume. This sawtooth sweep voltage, divided down by 
Rb and 2?4, is applied to the reflector of the reflex local oscillator, causing; 
it to execute a corresponding sawtoothed frequency sweep. Ci, being 
much smaller than C 2 , plays an insignificant role in modifying the sweep. 

If the range^set control Rb is properly adjusted, the local oscillator will 
be swept through the correct operating frequency. At first, negative 
pulses appear, but as crossover is reached and passed, these disappear 


and are replaced by positive pulses. The first pulse of sufficient ampli- 
tude will fire the search stopper Vi. When this happens, Cp^ abruptly 
drops to some 11 volts above the cathode potential. The flow of current 
in R 2 is reversed, and starts to fall. This causes the local-oscillator 
frequency to move back from the threshold, so that one of the next few 
pulses to appear will be too small to fire Vi, or may even be negative. 
Because Ci is small, however, jRi and 222 quickly restore the charge, and 
the forward sweep resumes until another pulse large enough to fire Vi 
comes through. 

These effects are shown in Fig. 7T9. The potentials of the two plates 
at any one time are shown, one above the other. The time scale after 
locking (to the right) has been expanded manyfold for clarity. 

This circuit is an example of the frequency-control principle. The 
control voltage applied to the reflector is determined by the frequency 
with which Vi is triggered and is unaffected by the trigger amplitude as 
long as it exceeds the threshold deteiinined by the bias on the Vi control 
grid. Later (Sec. 7-13) we shall consider circuits employing amplitude 
control^ in which eveiy pulse is effective, the amount of the effect being 
proportional to pulse amplitude and thus to the amount of deviation from 
the crossover frequency. 

7-12. Design Theory for Gas-discharge-tube Control Circuits. — In 
pulsed systems, since control information is available only for short, 
widely separated intervals, it is necessary to limit the amount by which 
the LO frequency can shift between successive pulses. This restriction, 
in turn, limits the speed with which the control circuit can readjust itself 
to meet new conditions. 

In Sec. 7*1 the causes of frequency drift were considered. Of the 
effects discussed, pulling during the antenna scan is usually the only one 
that takes place so rapidly as to constitute a following-rate problem. 
When rapid pulling occurs, the local-oscillator frequency may lag behind 
its proper place, resulting in mistiming, or it may drop back so far that 
control information is lost, ca\ising the system to become unlocked. 

With reference to Fig. 7-17, pulling may be thought of as causing a 
displacement of /o to the left or to the right, with the discriminator 
characteristics exccuiting a similar shift. If/o shifts to the right, control 
information will disappear and the local-oscillator frequency will start 
to drift to the right as the slow sweep resumes. No matter how great the 
shift in/o (within the limits of the control range) nor how fast the shift 
takes place, the local oscillator will ultimately reach the threshold 
frequency A, and control will be restored. 

If, on the other hand, /o shifts to the left, the firing rate of the search- 
stopping tube (Fi of Fig. 7T8) will increase up to the limit of one per 
transmitter pulse, causing the local-oscillator frequency to shift to the 



left. If the rate of shift of Fq is too great, the oscillator will fail to keep 
up with it and presently will be so far out of tune that the positive pulse 
from the discriminator amplifier will fall below the threshold, and Vx 
will cease firing. Then the slow sweep to the right will resume and the 
system will be unlocked. This one-sidedness is a characteristic of all 
drift-in systems. 

It might be mentioned here that the “push-pull’' systems discussed 
in Secs. 7T4 to 7T6 can become unlocked as a result of fast shifts in 
either direction. Nonhunting systems may also become unlocked if a 
fast frequency shift exceeding the system pull-in range occurs (see 
Sec. 7-3). 

Maximum following rates determine the ability of a system to follow 
fast frequency shifts. They are usually expressed m megacycles per 
second per second. They are functions of the value of the oscillator 
frequency within its control range and are, in general, different for the two 
directions of frequency shift. 

The control circuit determines the maximum rate at which the fre- 
quency-control electrode (here, the reflector) voltage may be changed. 
The corresponding frequency follomng rate is then determined by the 
electronic-tuning sensitivity of the oscillator, that is, by the shift in 
frequency in megacycles per second per volt change on the frequency- 
control electrode. 

In any pulse-operated hunting type of AFC, there is an inherent 
ripple in the local-oscillator frequency. This is due to the tendency 
of the oscillator to resume the hunting sweep during the interval between 
successive pulses and can be reduced only at the expense of reduced 
following rates. Ripple is usually expressed as the peak-to-peak ampli- 
tude of the frequency modulation (in megacycles per second) where the 
system is in equilibrium and depends, as do the following rates, upon 
the value of the local-oscillator frequency within the control range. 

In a practical design, ripple is usually the factor that limits the 
following rates. Sometimes, however, it is found that while the hunting 
sweep is traversing the discriminator characteristic, the control informa- 
tion received is insuflB.cient to stop the sweep although, once the sweep is 
stopped, locking is possible. The speed of the hunting sweep would then 
be the limiting factor. The maximum permissible ripple can be calcu- 
lated from receiver bandwidth and similar considerations, and from this 
the amount of voltage ripple that can be tolerated on the reflector may be 
computed. With these data, the following theory may be applied to 
determine optimum circuit constants. 

For the rest of this section, following rates and ripple will be referred 
to in terms of the reflector voltage. Two voltage following rates are 
defined: the maximum “down- pull” rate, the rate at which the reflector 

Sbo. 7-12] 



voltage becomes more negative when the search-stopping tube is fired at 
each transmitter pulse; and the maximum “up-puli'’ rate, the rate 
at which it becomes less negative when the search stopper does not fire at 
all. These rates are expressed in volts per second. Ripple will be 
referred to as the peak-to-peak amplitude of the ripple voltage at the 
reflector when the system is in equilibrium. 

(c) Effective and equivalent circuits for charging C 2 
Fio. 7-20. — Equiviilcut circuittt for gsiH-tlwcsliiu-gc-tubo APC. 

N. Rochester^ has dovolopod a theory giving the precise behavior of 
gas-discharge-tube control circuits, from which the following rates and 
ripple may be derived. The only assumption involved is that the time 
constant for charging the sweep condenser C2 is much larger than that for 
charging the search-stopping condenser Ci. This is always true in prac- 
tice since the slow swoop must bo such that several ])ulseH appear during 
the transit of the receiver pass band, whereas the search stopper must be 
fully recovered within a few pulses. 

^ Sylvania Electric Products Co., Boston, Mass, 



For the notation of this discussion, the reader is referred to Fig. 7-20. 
In this figure capital letters denote J&xed quantities; lower-case letters, 
variable quantities. Average values are differentiated from instanta- 
neous values by the presence of a superscribed bar. Fi and Vz are repre- 
sented by switches which close only long enough to discharge their 
respective condensers. To simplify the calculations, all voltages are 
referred to the plate voltage of either tube when conducting (about 
10 volts above the cathode potential). The resistance of the potentiom- 
eter from which Ez is derived is neglected. One can allow for it by 
replacing it with an equivalent voltage and resistance, using Th 6 venin's 
theorem, and including the resistance in pyR. In practice such a cor- 
rection is small. 

Because of the difference in time constants, may be considered 
constant during any one firing cycle of Ti. Hence ei may be computed 
as a function of time. When ex has been determined, the instantaneous 
current in pR flowing into Cz may be computed for one cycle. From 
this, the change in ez may be computed. Figure 7*20& shows the circuit 
for charging Cx and the equivalent circuit derived from Th^venin's 
theorem. The charging voltage and resistance are 

= P-^O 4" ^2 

1 + P 

Ra = 

1 + P 


( 10 ) 

When, after a trigger, the tube Fi is momentarily made conducting, 
the voltage across Cx will bi^d up exponentially from zero, with a time 
constant R^Cx, approaching 64 . The equation is 

ex = 64 (1 - ( 11 ) 


PT — R^Px = ( 12 ) 

and r is the interval between pulses. 

When the AFC is in equilibrium, control pulses will be applied to the 
grid of Ti at more^or less regular intervals so spaced as to maintain the 
required value of Cz. Let us assume this interval to be nr. Because 
of the linear relation between voltage and current, the average current 
flowing in pR may be computed from the difference between the average 
voltage ex across Cx and the voltage ezi 

hL «.* - 5 [i - i (1 - a-i)] - (13) 

A plot of F(x) ve. X, where x = fi/n, is shown in Fig. 7-21. 

Sbo. 7-121 



To compute the ripple, we observe that when Ci = ei, the instanta- 
neous current in pR equals the average current so that the instantaneous 

slope de 2 /dt is zero. This is the 
Tnfl.TriTnnTw excursion downward 
between triggers, and the time at 
which it occurs may be foimd by 
equating the right-hand sides of 
Eqs. (11) and (13), with the result 

= JUT In 

We next note that, as shown in Pia. 7-2i.— F (®) vs. a. 

Fig. 7-20c, Th4venin’s theorem 

can be applied to reduce the influences on the voltage across Ci to that 
of a single variable voltage source 6$ with internal resistance Be where 

_ Ra + y6i 
~ 1 + T 

Ra = 


l + y 



Now 66 is made up of a steady component cj and a ripple component e* 
We may obtain es by replacing ei by ei in the first of Eqs. (IS) 

62 = 

^ Ba -f 761 

1 + 7 

The ripple is then given by 

3 = «. - a - 


Taking ei and ei from Eqs. (11) and (13), we obtain 

62 = 



The current flowing out of (72 is 

(1 - F - 6 I"). 






This may be integrated from zero to the time of the maximum excursion 
tij of Eq. (14), to give the flow of charge. Dividing by C 2 gives the 
maximum excursion, or 'peakAo-peah ripple, Ae 2 B. 




-- F) In 


1 -F 

( 20 ) 


We may solve Eqs. (10), ( 13 ), and ( 16 ) for 62, eliminating 64. This gives 

r* = + (1 + p)Ez 

(l+p)(l + 7) -yF 

( 21 ) 

The maximum down-pull rate occurs when Ti is fired by every pulse. 
This is computed in the same way as the ripple except that the integration 
interval is simply r. The result is 

(Ae2)D = 



Fq = F(fi) ~ 1 — /z(l — e '*). 

The up-pull rate is simply the free charging rate of C2. Again by 
Th6venin’s theorem, we can combine the influences of Eo and Es on C2 
into a single voltage E^ acting through a resistance Re. The circuit is 
similar to that shown in Fig. 7 *200 except that ei is replaced by Eq, and 
pR by (1 + p)JJ. Thus 

= (1 + p)Fz + pyEp 


1 + P + PT 

R, == Tpd + p) 

1 + P + PT 


( 23 ) 

( 24 ) 

The current flowing into Ca is 

% = 

Et — 6% 
Ri ’ 

( 25 ) 

giving rise to a voltage change per interpulse interval of 
('Ae.'lir = (1 + p)E» + ypEp — (1 + p + Tp)e2 

These equations, although accurate, are inconvenient to use. A 
simpler form that is directly related to quantities easily measured in a 
practical circuit may be obtained as follows: 

Set ^ 


Fb = £2, when n = 1, 

Et = Cs, when n = 00 . 

After prolonged operation with no triggers, will equal Et, and wiW be 

From Eq. ( 26 ), then, 

(1 + p + 7 p)£?r = (1 -f- p)jS8 + ypEa. ( 26 ) 


This may be substituted back into Eq, (25), giving 

From Eqs. (16) and (13) 

For n = 1, this becomes 

These quantities may be substituted in Eq. (22) to give 

No such simplification of the expressions for the ripple voltage is possible. 

Eb and Et may be measured with a vacuum-tube voltmeter at the 
plate of 72 by the application of triggers to 7i at the pulse recurrence 
frequency and by the removal of all triggers from 7 1 , respectively. They 
may also be computed from Eq. (21) by the substitution of Fo and 

= 1 respectively for F. These values depend on Ez, which is 
determined by the range-setting potentiometer. 

The general principles that must guide the designer are fairly clear. 
The highest possible following rate consistent with allowable ripple 
should be sought. Eb and Er should be well outside the control limits 
between which is to operate in order to provide residual following speed 
at the limits. 

It appears that the choice of p is not critical. All values between 
i and 2 will give substantially the same ratio between ripple and maxi- 
mum down-puU rate. A large value of p tends to make the up-pull and 
down-pull time constants (not following rates) equal, and provides better 
filtering of the sawtooth voltage on Ci by the p/JC- network. The 
extra filtering is precisely offset, however, by the reduced down-pull 
rate and meanwhile 7i will become harder to extinguish. A similar 
effect is observed if p is made small. The compromise value p = 1 
should be satisfactory in nearly every case. 

The choice of Ci should be such as to make cl have its midrange value 
for n « 3.6. If n is much smaller, there will be inadequate control range 
for down-pull, whereas if it is larger, the ripple will become excessive at 
the upper end of the control range, for which n will become greater than 
10. Equilibrium at different parts of the range will occur for values of n 
between 2 and 10, the range below 2 and above 10 being for extra following 



rate at the ends of the range. At n * 10, the ripple will be almost 
exactly twice the maximum down-pull, and this will be the limiting factor 
in the choice of C 2 . Ripple is normally limited to a peak-to-peak value of 
about one fourth of the receiver bandwidth to the half-power points. 

The peak current allowable for tubes used for Fi is usually 0.6 amp- 
This fact makes necessary the use of a limiting resistor of at least 600 
ohms (for a 300-volt supply), or a limiting choke in series with Ci and C%. 
With such limiting, Vi will not extinguish reliably if R 4 ., the parallel 
resistance of R and pjB, is less than about 600,000 ohms. The lowest 
value consistent with reliable performance should be used. A common 
value is JS = pJB = 1 megohm. The current through the bleeder prfR 
reduces Et, particularly when Ez is made large and negative. To reduce 
this effect, pyR should be as large as possible, consistent with the leakage 
and runaway^ possibilities of the controlled reflector. Values in excess 
of 6 to 8 megohms are dangerous. 

One serious problem faces the designer of a gas-discharge-tube control 
circuit. It is necessary to ensure proper operation with any tube ful- 
filling JAN-IA specifications. The specifications for a type 884 gas- 
discharge triode, for instance, are such that if the bias is set for nominal 
firing at, for example, +200 volts, various tubes may fire an 3 rwhere 
between 160 and 240 volts. Added to this variation is an uncertainty 
of at least ± 10 per cent in the bias if 6 per cent resistors are used. The 
tube is required to fire at a plate voltage appreciably less than Et for any 
setting of the range-set control. In a reasonable design, with a 300-volt 
supply, Et must be as low as 260 volts when the control is at its most 
negative end. 

On the other hand, the tube must be capable of covering the entire 
sweep demanded by the local-oscill^or reflector. When the control 
is at its most positive end, the value of €2 at the positive end of the hunting 
sweep is fairly high. In fact it has not been found possible to find any 
set of constants that will ensure firing at the end of the sweep with the one 
setting and simultaneously ensure nonfiring within the control range 
at the other setting for all JAN-approved tubes. The addition of a 
bias adjustment for V 2 will cure this dijSSculty but no simple procedure 
exists for making such an adjustment in the field. 

It may be pointed out here that the effects of tube variation may be 
greatly reduced by feeding back part of the d-c plate voltage to the control 
grid. The effect is similar to the use of invers,e feedback with high- 
vacuum-tube amplifiers. If one plots a graph of the grid voltage at 

^ If the reflector of a reflex oscillator becomes positive, from an accidentally applied 
potential, it may draw sufficient current to heat up and emit electrons, and secondary 
electrons will be produced. In this event, if the external resistance in the reflector 
circuit is too high, the control of the reflector voltage may be lost . 


which the tube will fire as a function of the plate voltage, it will be seen 
that a triode such as the 884 has a “gain'' of about 10, in that if the 
plate potential is increased by 10 volts, the grid firing potential becomes 
more negative by 1 volt. The corresponding curve for a tetrode such 
as the 2050 shows a “gain" of around 200, the grid firing potential being 
almost independent of plate voltage. The feedback factor is the ratio 
between Ri and Ri + R 2 in Pig. 7*22. 

Using these definitions, the usual equations for feedback apply, 
effective “gain" is given by 

0 = 


1 - AP 

and the improvement by 



(Firing-voltage variability with feedback) 

(Firing-voltage variability without feedback) 

Using the constants shown in Fig. 7-22, and taking A = 200, we find 
that 0 = 19, and the variability reduction factor is 1/12.5. It should be 
noted that a fairly large negative supply is required. If the feedback 
is achieved through the use of a cathode-biasing resistor, the control 
range is reduced by the reduction in available cathode-to-plate supply 
voltage. Also, the feedback loop draws current and reduces Et in the 
same way as did pyR for negative settings of the range-set control. 
Much of the benefit of such stabilization is thus offset. 

It will also be noted that there is considerable variation (up to 3 to^ 1) 
in the maximum iip-pull and down-pull rates, depending on the position 
of the range-set control and the position in the sweep, because of the 



exponential nature of the C 2 charging curve. Since the conditions which 
limit following rate apply to the maximum case, the following rate is 
unpleasantly low in the minimum case. Many of these difficulties are 
reduced to tolerable proportions if the supply voltage is increased. Thus, 
the circuits may be suspended between the --300-volt and the -f- 105-volt 
supplies. This results in considerable improvement. 

Some workers claim that gas-discharge tubes are not sufficiently 
reliable for these applications. One claim is that the firing conditions 
are affected by past history, age, and temperature. Another claim 
is that, in those circuits where the entire control unit is required to 
operate at the -2000- volt level, the tubes are subject to erratic firing 
caused by electrostatic influences. Neither of these claims has been 
conclusively verified, but both add weight to the argument that only 
high-vacuum tubes should be used in the control circuit. The following 
sections deal with a circuit that contains only hard tubes and is therefore 
free from the above objections, including the one resulting from nonlinear 
sweep rates. 

7-13. Diode-transitron Control Circuits. — ^The new hard-tube control 
circuit is shown in Fig. 7*23. The block diagram of Fig. 7T6 is still 

applicable, the diode detector Vi serving as search stopper, and the 
transitron oscillator 72 as the slow-sweep generator. The transitron 
oscillator is a modification of a precision, ranging circuit used extensively 
in radar indicators (Vol. 22). ,, its operation, which will be explained in 
detail below, depends essentially on the negative transcoiiductance 
which exists between the suppressor grid Gz and the screen grid Gz of a 
pentode. As used in the control circuits it is a free-running sawtooth 
oscillator whose plate voltage sweeps slowly from just below the plate 
supply voltage to a point not far from the cathode voltage, after which. 



it snaps back rapidly, and starts the downsweep again. The down- 
sweep part of the cycle is used as the hunting sweep. Thus the local- 
oscillator frequency sweeps from low to high frequency, whereas, when 
the gas-discharge-tube circuit is used, it sweeps from high to low. 

If, during the downsweep, the grid-return resistor is tied to a point 
suitably negative with respect to the cathode, the sweep action will 
stop, and the tube will act as a normal d-c amplifier with a gain of approxi- 
mately 50. Such a negative bias, supplied by the diode detector when it 
receives control information from the discriminator, is the basis of locking. 

Let us consider the sequence of events which takes place in this 
circuit, starting at the beginning of a downsweep. Assume, for the 
sake of argument, a plate supply of +160 volts measured from the cathode 
potential. The plate voltage Bp is about +140 volts, the plate current 
ip being therefore 20 /xa. Gz will be at groimd or positive potential 
(see below, also Fig. 7*24) . As the division of the cathode current between 
plate and screen is normally in the ratio of about 4 to 1, the screen 
current ig^ is 6 iua, causing a drop in the screen resistor of only 0.25 volt. 
Since the cathode current io is only 25 /la, the control grid Gi must be 
nearly at cutoff potential, about —10 volts. At the beginning of the 
downsweep, the local oscillator is far off tune, and no control information 
appears at the output terminals of the discriminator amplifier. Ci, 
being small, plays no part at this time, nor does the diode, since its plate 
will be at —5 volts because of the division between Ri and 22 2 . Because 
of the 10-volt drop, a current of 5 jua fiows along 22 1 and 222 into the 
condenser C 2 . Consequently, the voltage across C 2 , which is (sg^ — O, 
changes at a rate 

The grid voltage does not approach ground potential at this rate, for, 
as it rises, the plate voltage is approaching ground A times as fast, where 
A is the gain of the stage. Thus 

dt dt' 


Substituting in Kq. (33), we have 

deg^ e,, 

'W ~ iRi + /e2)(l + A)Ci 


There is, therefore, an apparent input capacitance (1 + >1) times as 
great as the actual feedback capacitance O'*. This capacitance ampli- 



fication makes possible very slow sweeps with small condensers. It is a 
manifestation of the well-known Miller effect.^ 

The downward rate of change of the plate voltage is 

dt ~ (J2i + Bs) (1 + A)C^ (Ri + R^)C, ^ ^ 

since > > 1. The sweep rate is nearly independent of tube character- 
istics. In practice, swings from about —10 to —8 volts as the plate 
covers its sweep. The sweep is therefore linear to within about ± 10 per 
cent, a great improvement over the gas^discharge-tube circuit (Sec. 7-12). 

This then is the picture that we see during the downsweep, up to the 
time the discriminator crossover frequency is reached. As soon as the 
crossover frequency is passed, positive pulses appear at the plate of 
the discriminator amplifier and are coupled through Ci into the diode 

The action of the detector is straightforward. During the positive 
pulse the diode is conducting, and charge flows into Ci. When the pulse 
is removed this charge remains, and the potential across the diode 
becomes negative. After a few pulses the average potential across 
the diode is sufficiently negative so that the charge leaking off Ci through 
jBi between pulses equals the charge transferred to Ci by the pulses. 
The system will reach a stable equilibrium in which the oscillator rides 
far enough up on the discriminator characteristic to supply pulses whose 
amplitude is just right to maintain the bias which holds the transitron, 
and thus the reflector, at the correct voltage. If the oscillator frequency 
were to increase, the pxilse amplitude would increase, causing an increase 
in bias and hence of transitron plate voltage. This would cause the 
oscillator frequency to decrease again. Lowering the oscillator frequency 
would be compensated for in a similar way. 

To complete the picture, we have only to show how the system is 
recycled if no control information is received during the sweep or if 
the system becomes unlocked. The effects are illustrated in Fig. 7*24, 
with reference to the circuit of Fig. 7-23. When control information is 
lost, the charge on Ci quickly disappears, so that, the downward sweep 
of the plate is resumed. This is illustrated in region A, 

At first, the voltage drop across the screen-supply resistor Rg is 
negligible both because most of the cathode current reaches the plate and 
because of the low value of Rg^, As the plate potential approaches 
ground, however, an increasing fraction of the increasing cathode current 

^ J. M. Miller, "Dependence of the Input Impedance of a Three-electrode Vacuum 
'rube Upon the Load in the Plate Circuit,” Bureau of Standards Scientific Paper 
No. 361, Terman, op. cii., Sec. 5, p. 468. 

Sec. 7-18] 



is diverted to the screea Gs whose potential therefore starts to fall. 
Because of the condenser Cg, this fall is coupled over to the suppressor Gt. 
Soon, the process becomes regenerative, at B. As the suppressor voltage 
is carried bdow groimd potential, it diverts current from plate to 
screen, causing e, to rise and to fall farther. The rise in ep is coupled 
through Cg to Gi, causing an increase in cathode current most of which 


Fig. 7-24. — Transitrou wavofonrm. 

now flows to the screen, further accelerating the process described above. 
Since this process involves no change in the charges on C2 and C3, only 
interelectrode and sti*ay capacitances slow it down. The entire transition 
actually takes place in a few microseconds. 

When has been carried by the plate to a slightly positive voltage, 
grid current will be drawn, preventing further rise. At this instant the 
cathode current is large, and all of it flows to the screen, the plate being 



cut off by the suppressor. Consequently, is close to ground potential, 

is far below ground potential, and Cp is perhaps 15 volts above its 
value at the end of the slow downsweep. 

During the next period (region C of Fig. 7-24) C 2 is charged, with a time 
constant RpC^, toward Eb> Meanwhile, the charge on Cz leaks off 
through Rg^, so that approach^ ground potential with a time constant 
Rgfiz. Presently, Bg^ comes close enough to ground potential to allow 
some of the current to reach the plate, which by this time is practically at 
Eb- This flow of plate current, by causing Bp to drop, starts the second 
regeneration at D, in the following manner. 

The downward trend of P, being transmitted by C 2 to Gi causes a 
reduction in the cathode current, and hence in the scre^ current. The 
resultant rise in Bg^, because of Cz, causes a similar rise in Bg^, which in 
turn allows more current to reach the plate. Thus, the original effect is 
accelerated both by the increased drop in Bp and by the decreased screen 
current. Again there is a fast transition, which stops only when Bq^ 
has been carried so far negative that only a little cathode current flows, 
an amount consistent with the plate current flow necessary to maintain 
Bp some 10 volts below Pj*. At this point the slow sweep downward 
repeats, starting the new cycle. This sawtooth sweep, then, will recur 
until control is again secured. 

Before the idea of -the diode search stopper was conceived, a circuit 
was developed using a gas-discharge tetrode search stopper, as in the 
standard gas-discharge-tube AFC, and a transitron control tube. Essen- 
tially, the plate of 7i of Fig. 7*18 was attached to a potential divider 
whose lower end was at —*300 volts, and the divider tap was connected 
through a resistor to the control grid of the transitron. 

A new type of miniature tube, the 6AS6, was developed for use in 
transitron ranging circuits. In that application, a sharp cutoff of plate 
current by the suppressor was desired. When this tube was tried in the 
circuit described above, it was found that the regeneration at the end of 
the downsweep occurred while the plate was still far above ground poten- 
tial. In order to prevent this, the circuit was modified by coupling only 
about one sixth of the screen wave to the suppressor by tying the coupling 
condenser Cs of Fig. 7-23 to a tap on the screen-dropping resistor 
The change is shown by dotted lines. 

An examination of the diode-transitron circuit shows a number of 
advantages some of which, such as linearity of sweep and the obtaining 
of long sweep times with relatively small condensers^ have already been 
cited. Others include the possibility of using a high-voltage condenser 
between the video amplifier and the diode, enabling the circuit to operate 
at a voltage far fropa ground potential. A further increase in sweep 
time may be obtained by the use of high resistances, in the grid circuit; 

Seo. 7-14] 



this is not possible when the charging resistance is in the plate circuit. 
Since the output voltage is taken from the plate at relatively low imped- • 
ance, it is possible to apply voltage to the reflector from a divider of lower 
impedance than that used in the gas-discharge-tube circuit, without 
having the sweep seriously affected by the range-set control. By proper 
choice of constants, the range covered by the sweep may be made nearly 
independent of tube selection and resistor tolerances. One final point 
to be noted in connection with reflector circuits is that the control 
tubes are often connected between the negative power supply and ground, 
since the reflector voltage is usually below ground. 


7*14. Background and Basic Theory. — When the thermally tuned 
tubes, the 2K45 and the 2K50, became available, it was necessary to 
develop new circuits for controlling their frequency. One of the normal 
drift-in systems (Sec. 7-10) could be used by connecting the output of the 
control tube to the grid of the tuner triode through a suitable potential 
divider. If a system of this kind were used, however, the sweep period 
would have to be made long compared with the time constant of the 
thermal assembly in order to avoid hunting or even oscillation over 
the feedback loop. For instance, when such a system was applied to the 
A5022A,^ the complete hunting cycle had to be set at 90 sec. Further- 
more, because of the wide tuning ranges involved, locking to the wrong 
sideband (Sec. 7-9) became a serious problem. 

Circuits were therefore devised in which the tuner power is either 
fully on or fully off, so that hunting and following speeds are limited 
only by the thermal inertia of the tuning strut. In some of the circuits, 
the wrong sideband is inherently rejected; in others, it is arranged so that 
there is no wrong sideband — ^that is, these systems will lock on frequency 
on either sideband. In the present state of the art, these circuits repre- 
sent a considerable increase in complexity; control circuits with four to 
seven tubes must be used to replace the two-tube drift-in circuits. 
There are compensating advantages, however. Foremost is the fact 
that fully automatic following of a tunable magnetron over a wide range 
becomes possible. This fact may be of primary importance in enabling 
the operator of a radar set to escape from jamming, either by the enemy or 
accidentally by friendly systems. In peacetime applications this prop- 
erty may be less important. 

A second point is that, with the advent of the balanced mixer (Chap. 6), 
local-oscillator noise in the receiver has been practically eliminated, and 

1 The A5022A was an early 1-cm oscillator which did not have a tuning triode; 
however, the external power supply used for heating the tuning mechanism was grid- 



the major reason for the use of high intermediate frequencies with the 
poor receiver noise figures which they entail is thereby removed. The 
trend is toward the use of a 30-Mc/sec intermediate frequency for which 
the sidebands are only 60 Mc/sec apart. When a 60-Mc/sec receiver 
is used, the local oscillator stops oscillating before it reaches the wrong 
sideband. At 30 Mc/sec, this is not true, and locking on the wrong 
sideband is a problem even with the limited tuning range afforded by the 

A final point is that, at least in the mechanically tuned 25,000-Mc/sec 
2K33 oscillator, a large imgainly tuning mechanism is required. Also, 
the temperature drifts to be expected are so great that a remotely con- 

Fiq. 7*26. — Operation of thermal AFC systems. The direction of the frequency drift 
after a pulse of a given polarity is given at the top of the figure for the various cases. Note 
the possibility in the Whitford system of being trapped between the negative trigger wall 
at C-C' and the search-reversing point B-B\ In the Nibbe-Duraiid AFC, Case A repre- 
sents the condition existing after a heat-control reversal at A- A'; Case B, that existing 
after a reversal at B-B'. 

trolled tuning motor is required to enable the operator to select the 
operating range for the AFC. This motor adds considerably to the 
weight and volume of the local oscillator. 

In spite of their complexity, the circuits about to be described are 
reliable, and are not critically dependent on tube selection or component 
tolerance for satisfactory operation. In view of the advantages cited, 
therefore, their use is justified for some applications. 

The ‘'on-off” feature described at the beginning of the section makes 
possible reasonable following rates. This feature is combined with 
push-pull operation to obtain locking and wrong-sideband rejection. 
In the Whitford AFC system, the operation (see Fig. 7-25) is the fol- 
lowing. If the circuit is an*anged in such a way that positive triggers 
from the discriminator turn the strut power on, causing the oscillator 

Sbo. 7-16] 



frequency to decreaae (move to the left) and negative triggers turn it off, 
causing the frequency to increase (move to the right), then it is possible 
to lock on frequency at the left-hand sideband, and locking at the other 
sideband is excluded. If, furthermore, provision is made for causing 
this cycle to repeat once every few seconds when the system is not locked, 
the frequency will hunt back and forth over a band whose hmits are 
shown at A- A' and B-B' in the figure, until the desired locking frequency 
is reached. The AFC system as described can be trapped between the 
right-hand end of the sweep B-B' and the negative “trigger wall” 
C-C' at the high-frequency side of the right-hand sideband. This 
trapping is overcome by desensitizing the video amplifier during the 
heating part of the hunting cycle so that the frequency has to sweep all 
of the way to the left and start back before any pulses can come through. 
In the Nibbe-Durand system described in Sec. 7T6, a form of “lazy man” 
reversing switch is used, which, in essence, inverts the relation between 
trigger polarity and the tuning-strut-heater control in such a way as to 
make it correct for locking to the first sideband encountered during 
hunting. The next two sections treat in detail the circuits actually used. 

7-16. The Whitford AFC. — A block diagram of the control circuit is 
shown in Fig. 7-26 and a circuit diagram in Fig. 7-27. The balance of the 

7-20.- - (Jonirol ciimiit for Whitford AFC. 

feedback loop is similar to those already discussed in Secs. 7*4 to 7*8 
and shown in Fif?. 7*2. 'The only dilTerence is that the discriminator 
must be designed to produce a ]>ulsc with a short rise time (Secs. 7*7 and 
7*8) ; stretching the pulse is unnecessary. 

The circuit operates in the following manner. The power in the 
tuning strut of the local oscillator is controlled by a reversing multi- 
vibrator, or Ecclos-Jordan “trigger” circuit (Va in Fig. 7*27). This 
circuit has two stable conditions of equilibrium. In the first condition, 
the left-hand section, is conducting heavily, with its grid potential 
at the grid-current point, while the other section, Vu, is completely 
cut off. The plate potential of section a is therefore close to 5-|- , and the 
tuner triode grid is close to ground potential. Stnit power is therefore 
high, and local-oscillator freciuency low or falling. Tn the other position, 



Vib is cut off and Via conducts. The plate of section a is now close to 
cathode potential, the tuner grid is negative, strut power off, and fre- 
quency high or rising. 

Hunting is accomplished by switching Vi alternately between these 
positions at intervals somewhat longer than the thermal time constant 
of the local oscillator (from 2 to 10 sec). Locking is accomplished by 


switching at a rate so high (50 to 200 per sec) that thermal inertia keeps 
the strut temperature substantially constant. The average temperature 
is determined by the ratio of the time spent at full power to that spent at 
zero power. 

It was shown in the previous section that a one-to-one relation 
between trigger polarity and the application or removal of strut power 
was sufficient to provide locking of one sideband and rejection of the 
other. A simple capacitance coupling between the video-amplifier plate 

Sue. 7-161 


and the grid of produces such a rdation, but it is unreliable A 
smaU negative pulse is capable of turning an “on-tube” off, but a laree 
positive pulse is required to turn an “off-tube” on. This is because 
the grid of an on-tube is held, by grid current, close to cathode potential 
where the mutual conductance gm is high, whereas, to provide an adequate 
margin of safety against tube variations, the grid of an off-tube must be 
held far below the pomt of complete plate-current cutoff. The serious 
effect of such asymmetiy is that if the gain of the system is adequate to 
^ure operation on the positive pulses of the fundamental sideband 
it may allow operation on transients or on the negative pulses of a 
harmonic sideband (see Sec. 7 - 6 ). 

Complete symmetry is assured by using a phase inverter (Fj) and 
applying the two equal but opposite output voltages to the two grids of 
F4. Thus, positive pulses at the plate of Fi result in negative pulses 
at the plate of Fs, which wUl turn F^ off if it is on. Similarly, negative 
pulses at Fi produce negative pulses at the cathode of F*, which can 
turn F4« off. 

In principle, the positive pulses appearing at the plate or cathode of F* 
might be used to aid the negative pulses on the opposite dectrode. If 
such aid is permitted however, another ill effect causing unreliability- 
may occur. Suppose two positive pulses appear in sequence at the plate 
of Fi. The first produces a negative pulse on the grid of Vn, which is 
therefore turned off. The second produces, in addition, a poative pulse 
which would roach the grid of F4« if it were not for the diode Fjo. Since 
F40 is now conducting, with its grid drawing current and acting as a 
diode, this positive pulse would charge the coupling condenser. When 
the cathode end of this condenser returned to its quiescent voltage, 
the grid end would become negative. This overshoot, caused by differ- 
entiation of the pulse, would be quite capable of turning F4a off a gflin and 
producing an undesired reversal of the heat-control circuit. Adding the 
diodes of Fs is a complete cure for this trouble. This special coupling 
circuit gives satisfactory operation independent of tube selection and 
component tolerance, lleturning to the main argument, then, we see 
that Fi through F4 provide precisely the type of coupling between 
discriminator output voltage and thermal triode power that was specified 
in Sec. 7 - 14 . 

Hunting and the desensitizing discussed in the pre-vious section are 
accomplished by means of a slow timing multi-vibrator Fb. The cycle of 
the grid potential of a multivibrator is such that during one phase the 
grid is very close to ground potential, whereas during the other phase it 
is negative and rising. One of the grids of Fb is tied directly to the 
suppressor grid of the video amplifier Fi. When these grids are close to 
ground potential, F 1 acts as a normal amplifier. When they are negative. 

+ 150v 12 ma 


Fig. 7-2S. — Nibbe-Durand thermal AFC. 

Sec. 7-161 



however, the plate current in Fi is completely cut off, providing the 
required desensitizing. Furthermore, the transition between the two 
conditions produces a sharp voltage rise at the plate of V\ when this tube 
is cut off. This abrupt voltage change is differentiated in the coupling 
condenser, proceeds through and Fs, and acts as a trigger to cut 
F 46 off. The multivibrator that governs strut power is thus reversed, 
and the desensitized recovery sweep of the local oscillator is started. 
Similarly, when the multivibrator switches to the other phase, turning Fi 
on again, the negative wavefront thus produced turns F 45 on again, and 
institutes the active hunting sweep. 

The only problem remaining is to stop the action of the multivibrator 
when the system is locked. For this purpose, the audio-frequency 
square wave at one of the plates of the heat-control multivibrator is 
differentiated and rectified by Fb. The negative voltage thus produced is 
applied to the grid of Fr,?,, effectively holding the multivibrator fixed. 

7-16. Nibbe-Durand AFC System. — This system, shown in Fig. 7*28 
is arranged to lock on whichever sideband is first encountered after the 
heat-control reversal marking the end of a hunting sweep. Both direc- 
tions of the sweep are active, and the video amplifier is always sensitive. 
The heart of the system is a pair of reversing-multivibrator circuits 
similar to that \isod in the ^^itford system described in the previous 
section. The coupling into the first circuit and the coupling out of the 
second arc respectively identical to the input and output couplings of 
the rcversing-multivihrator circuit in' the Whitford AFC. In addition, 
there is a coupling l)ot\veon the two multivibrators such that whenever 
the first one revci’s<^s, the sec.ond will likewise reverse. Thus, with a given 
phase relationship Ix'-twoen the two, the system can lock on one sideband 
just as it docs in tlie systcun previously discussed. The triggered reversals 
of the first trigger-sign selector, or TSS, circuit are transmitted to the 
second ]icat-<'.ontrol, or HC, circuit. If the relative phases are changed, 
the system will loc.k in a similar manner on the other sideband. This is 
illustrated in Fig. 7*25. 

A transitron osc-illator Ft that has a period of one to two times the 
time constant of the thermal assembly of the local oscillator to be con- 
trolled is provided (see Sec. 7T3). The transitron generates triggers 
which op(u-ato the TSS and IK- circuits. The triggers are obtained by 
differentiating the voltage wave at the screen grid (see Fig. 7*24c). 
The differential output wavefinm consists of a sharp negative trigger 
followed by a sharj^ positive trigger. These triggers are introduced to 
the grid of a triode Fh that is luased beyond cutoff. The negative trigger 
therefore has no effect, l)ut a positive trigger brings the grid into the 
conducting region and r'esults in a small positive trigger at the cathode 
and a large negative trigger at the plate. Because of a connection from 



the cathode of this tube to the cathode of the video amplifier V i, the small 
negative trigger is applied to the signal channel leading to the TSS. It is 
equivalent to a negative trigger at the grid of Fi and therefore -presets the 
TSS in such a way as to make it ready to accept only positive triggers from 
the discriminator. 

Simultaneously, the negative trigger at the plate of Fs is coupled 
throu^ small condensers to the grids of the HC and cuts off whichever 
section of the HC is conducting at the time. The heat control in the 
tuner triode is reversed and a reverse sweep is started. 

To restate, in the absence of control information from the discrimin- 
ator, the oscillator frequency is swept up and down over the band, the 
reversals occurring at each cycle of the transitron. At each reversal, 
provision is made to ensure that the TSS is ready to accept positive 
triggers from the discriminator. Exammation of Rg. 7-25 shows that, 
after each HC reversal, the first discriminator triggers that are capable 
of causing a TSS reversal, and hence a locking reversal of the local oscil- 
lator, come only after the crossover frequency has been passed. Conse- 
quently, if control iuformation appears, the frequency will pass crossover, 
and then the drift will be reversed. When the crossover frequency is 
again passed, the negative triggers from the discriminator will cause a 
second reversal of frequency drift, and soon. The system will be 

If the transitron were allowed to continue operation, there would be 
,an even chance that a given reversing trigger would disturb the phase 
relation between the TSS and the HC, making a shift to the other 
adeband necessary. For, althou^ every trigger would cause a reversal 
of the HC, reversal of the TSS would occur only if it happened to be 
prepared to receive negative triggers at the time, which would be true 
on the average only half of the time. 

Therefore, the transitron trigger generator must be stopped. This is 
accomplished by a detector, 7», whose input voltage is the differentiated 
waveform at one plate of one of the reversing multivibrators. The 
pulses that appear every few seconds from the hunting-cycle reversals 
are too infrequent to generate appreciable voltage, but when the system 
is locked, pulses appear at an audio frequency, and 7$ develops a large 
negative bias. This bias is applied to the suppressor grid Oz of the 
transitron. Since the bias does not affect phases A, B, and C of Fig. 7-24, 
after due time the transitron screen voltage suffers its abrupt drop. 
It does, however, prevent the completion of phase D of the wave on Gi 
(Fig. 7-24:g), with the result that the plate remains completely cut off 
and the transitron cycle is stopped. 

Application of the stopping bias voltage in this manner permits a 
valuable “second chance” feature. The time required for the voltage 

Sbc. 7-16] 



to leak off, should the system become unlocked, is set to be somewhat 
greater than the time required for the frequency to sweep from one side- 
band to the other and back (about i sec in a typical case) . Suppose that, 
because of transmitter sparking, for example, the discriminator output 
signal disappears long enough to allow the system to become Tinlocked. 
If, at that time, the oscillator frequency is approaching the transmitter 
frequency, it will drift over to the other sideband, where a pulse will 
appear that sends it back to its original position. The bias voltage will 
have held the transitron off long enough to allow this to happen and lock- 
ing will be restored. If triggers have not been restored when the other 
sideband is reached, the frequency will continue to charge for a short titYia 
at the end of which the bias voltage will leak off, the transitron will 
begin to oscillate, and the drift will be reversed by the first trigger. The 
system now will lock on the other sideband. If the oscillator frequency 
were moving away from the transmitter frequency at the time of the 
original unlocking, it would simply continue until the release of the 
trigger generator, at which time it would reverse its direction of frequency 
change, move back, and lock to the original sideband. 

In a typical case, the interval between unlocking and the second- 
chance trigger is about i sec. Locking is therefore resumed within a 
second. This speed of locking represents a great improvement over the 
Whitford AFC in which, with equal probability, locking may be restored 
quickly by the pulse from the other sideband, or a complete recycling, 
which may take two full transitron periods (20 sec, in some cases) may be 

It may seem that fairly complex methods have been adopted to 
secure simple ends. When the circuit was originally conceived, Fj, 
Vz, Vz, and Va were not included, yet locking was obtained. The 
system was unrelialile, however; to provide positive action, all of the 
above tubes are required. The necessity for the phase inverter Vz and 
the dual diode F* has already been discussed in connection with the 
Whitford circuit (Sec. 7T5). The identical problem exists here. 

Originally, the coupling to the HC was taken from a single plate of 
the TSS. The negative wavefront of one reversal turned the on-tube off, 
and the positive one f rom the other reversal turned the off-tube on. This 
arrangement worked satisfactorily except for the special case where the 
input pulse to the TSS was slightly below the voltage necessary to produce 
a reversal. With such a trigger, the plate voltage of the on-tube of the 
TSS would rise part of the way, reversing the HC, and then fall again, 
leaving the TSS unreversed and destroying the correct phase relation. 
Under these conditions, the plate potential of the TSS off-tube remained 
fixed. The slightest lowering of this voltage sufficed to ensure TSS 
reversal. Therefoi'e, the negative triggers from both plates were coupled 


to the HC, and the diodes Fs were added to decouple the plates from 
each other and to eliminate the effects of the positive wavefronts. 

The main purpose of the tube V% was to make possible the use of the 
positive portion of the transitron screen wave, which provides the second- 
chance feature, and at the same time to utilize the sensitivity of the 
reversing multivibrators to negative triggers. Coupling without the tube 
Vs was unreliable and used the negative part of the screen wave. Most 
of the difficulties resulted from spurious reversal from overshoot on the 
positive part of the wave and from the loading of the HC by the coupling 
circuit, which made reversal of the HC by the TSS difficult. 

One further point should be noted. In the firfet model of the final 
circuit the two sections of a 6J6 twin triode were used for Vi and Vs, which 
have a co mm on cathode connection. No troubles were encountered. 
In a second model, similarly constructed, it was found that the TSS 
reversed on the negative trigger from the transitron screen. This caused 

a reversal of the HC when, shortly, 
the positive trigger came along; the 
TSS was preset properly, but the 
HC was reversed a second time, 
leaving no net reversal for the hunt- 
ing sweep. The trouble was traced 
to the capacitive coupling between 
the grids of the two sections. The 
sharp negative dip in the grid of 
Vs produced a similar, smaller dip 
in that of V i. The use of separate 
tubes, of course, solved the prob- 
lem. Other solutions may be possi- 
ble. For instance, if the wavefronts 
were slowed down by an RC circuit, a combination might be found which 
would be slow enough to reduce the capacitance coupling to a negligible 
value, yet fast enough to ensure the desired triggering. 

Other reductions of circuit complexity may be possible. One tube 
can clearly be eliminated by the use of a combination phase inverter 
and amplifier; the so-called ^^cathode-coupled push-pull amplifier used 
in the Dumont Model 208 oscilloscope. A circuit for this device is shown 
in Fig. 7-29. 

Since overshoot is caused by differentiation of the pulse, it may be 
that it could be reduced below the danger point by stretching'' the 
pulse from the discriminator (see Sec. 7-7) and making the negative 
slope at the end of the pulse small. The elimination of Vz might thereby 
be possible. If the capacitance of the cross-coupling condenser C (Fig. 
7-28) of the TSS were increased (which would pose new problems in the 

Fig. 7*29. — ^Phase inverter with amplifica- 

Sec. 7-17] 



triggering of the TSS), the wave at one of the plates would have the form 
shown in Fig. 7-30a. The downward trend of the plate voltage is inhibited 
only by interelectrode and stray capacitances. The voltage rise is 
likewise fast until the giid of the opposite section begins to draw current. 
After that, it is slow, as the plate load resistor charges the cross-coupling 
condenser. If tliis wavefoim were differentiated by an RC circuit of 
very short time constant, the 
pulses of Fig. 7*306 would appear. 

The sum of these pulses would be 
a smaller negative pulse which 
might be adequate to reverse the 
TSS, eliminating the need for Vb. 

It is doubtful if the phase inver- 
sion can be eliminated. 

The circuit in its present form 
is fairly reliable. It will operate 
with any tubes meeting JAN-IA 
specifications and with any re- 
sistors or condensers within + 10 
per cent of design value, including 
the most unfavorable combina- 
tions, 'svith the exception that the 
resistors in the reversing multivibrator circuit should be + 5 per cent if 
limit tubes are to be used. 


7*17. The Beacon Problem, — The nature of absolute-frequency, 
A-F, AFC systems and their application to the radar-beacon problem 
were briefly considered in Sec, 7*3. Beacons are treated extensively 
elsewhere in this series,^ but a brief review of their operation will be 
given here. 

A i-adar bea(*,on is a device which enables a radar operator to determine 
the range and bearing of the point at which the beacon tninsponder is 
located. When the operator throws the swit(?h to beacon, the length 
of the transmittei- ])iilse is changed to a value that will allow the pulse to 
pass through the*, beacon receiver and operate the coding circuits. As a 
result, the beac.oii transmitter issues a series of coded pulses which 
identify it from other beacons, and the first of which appears on the radar 
indicator at a ])ositiun that shows the range and bearing of the beacon. 

If bcac.on signals were rec.eived continuously, one of the AFC systems 
described in the previous section could hunt for and lock to the signals. 
But because of antenna scanning, only a few sets of pulses are received 

^ Volume 3, lladiation Laboratory Series. 

Fia. 7*30. — Effect of waveform on overshoot. 



at each rotation. Therefore, the beacon receiver must be in tune when 
the first beacon pulse is received. 

The problem of manually tuning a receiver to a beacon, with no 
^.reference frequency available to the operator, is almost insuperable, 
since the receiver must be in tune at the instant at which the antenna 
points to the beacon. Either a manual tuning aid or AFC is highly 
desirable. Either requires that the beacon transmitter frequency be 
known to the operator. Therefore, all beacons for a given class of service 
operate at a single fixed frequency. 

The manual tuning aid consists of a precision reference cavity whose 
response peak differs from the transmitter frequency by an amount equal 
to the center frequency of the i-f amplifier. Power from the local 
oscillator is applied through the cavity to a crystal, the current from 
which is read on a nulliammeter. The operator tunes the local oscillator 
until he gets an indication on the meter, at which time his receiver is in 

If AFC is used, the same type of reference cavity and crystal are used. 
The r-f problems associated with the cavity have been discussed in 
Chap. 4, and the circuits for control will be treated in the rest of this 
chapter. Most of the control circuits for beacon AFC have had provision 
for hunting (Sec. 7*3). These will be described in Secs. 7T8 and 7*19. 
A nonhunting d-c amplifier system operating with a microwave discrimin- 
ator and capable of very precise control is discussed in Vol. 11 Chap. 2, 
of this series. 

A tunable wavemeter cavity may be used in any of these systems to 
provide a stable tunable receiver with a precise calibration. Such a 
combination would be useful for multichannel communication. 

7-18. Reflector-modulation Schemes for Reflector AFC. — These 
systems employ the drift-in control circuits described in Secs. 7-10 to 7T2. 
The problem is to convert information coining from the beacon AFC 
crystal to a voltage capable of operating the search stopper. The block 
diagram of Fig. 7*31 shows the method used when a diode transitron 
(see Sec. 7T3) is used. When a standard gas-discharge-tube control 
circuit (see Sec. 7T1) is desired, the coincidence tube itself is the search- 
stopping tube, the rest of the circuit being as in Fig. 7T8. 

The nature of this circuit is such that when the local-oscillator fre- 
quency is on one side of the cavity resonance peak, the gas-discharge tube 
will not fire, but after the peak is passed (analogous to passing the cross- 
over frequency), the tube starts to fire 1000 times per second. But this is 
precisely what happens when a conventional discriminator is used. On 
one side of the crossover frequency, the negative signal from the discrimin- 
ator amplifier is ignored; on the other side, the positive signal triggers a 
gas-discharge tube or operates a diode detector as the case may be. 

Sec. 7-181 



(a) Crystal output (D-C) vs 
Input frequency 




^ \ / 

fo V/ 

(6) Modulation voltage 


(c) LO frequency 

(d) Generation of a-c output voltage (6) 

I'lu, 7*32,- -Wavef onus iix coiuoidence detection. 



It should be noted that when the gas-discharge tube fires, since the voltage 
across C cannot change instantaneously, the first effect is that the 
cathode voltage rises toward the plate potential. Only later, as C is 
discharged through the tube and R (a low resistance of about 2000 ohms) 
does the plate voltage fall to mark the start of the sawtooth sweep. 
This positive pulse at the cathode acts precisely as did the positive signal 
from the discriminator in developing a negative search-stopping voltage 
across the diode. All of the explanations of Secs. 7T1 and 7T3 therefore 

It remains, then, to analyze the action of coincidence detection, which 
is illustrated in Fig. 7*32. A 1-kc/sec oscillator^ provides a modulation 
voltage (b) of about 0.5-volt peak, which is superimposed on the LO 
reflector voltage. This causes a frequency modulation (c) to appear on 
the LO output signal. In (d) and (e) are shown the output voltage of the 
crystal when the frequency-modulated signal is applied to the cavity 
with the indicated pass band. To show the relative phases, the time at 
which the modulation voltage crosses zero with a positive slope is denoted 
by to. 

Figure 7-32a shows the output voltage from the beacon AFC crystal 
as a function of local-oscillator frequency. Since the LO output power 
is nearly constant over the narrow range involved, this is essentially the 
cavity resonance curve. It may be noted here that the cavity is loaded 
by the local oscillator and the crystal until its bandwidth at the half-power 
points approximates the locking accuracy desired; that is, it is nearly 
equal to the peak-to-peak separation of the discriminator that would be 
used were the AFC of the difference-frequency type. 

If now the center frequency of the local oscUlator is on the low-fre- 
quency side of this response curve, the frequency modulation will cause a 
voltage component at 1 kc/sec to be superimposed on the d-c output 
voltage from the crystal. As is shown in Fig. 7-32d this voltage is 180° 
out of phase with the original modulating voltage. If, on the other hand, 
the center frequency is above the resonance peak, the a-c component of 
the crystal output voltage will be in phase with the original modulation 
voltage, since on this side the slope of the resonance curve is negative. 
Figure 7*32/ shows this a-c component as a function of frequency and 
is drawn so that amplitude is proportional to the magnitude of the 
ordinate and phase is indicated by its polarity, a positive ordinate indi- 
cating that the crystal voltage is in phase with the original modulating 
voltage. It is seen that this curve has the appearance of a conventional 
discriminator response curve. 

If the amount of frequency modulation is large, there will be some 

^ A phase-shift oscillator with a four-section tapered phase-shifting network has 
been found excellent for the purpose. 

Sec. 7-181 



output voltage from the crystal at the crossover frequency. It will 
consist only of even harmonics of second and higher orders of the 1-kc/sec 
voltage, and can be removed by a suitable low-pass filter if desired. 

The crystal output voltage is applied to a high-gain amplifier with 
negligible phase shift at the modulation frequency. Either two stages of 
resistance-coupled amplification may be used, or a low-impedance 
microphone-to-grid transformer (such as the TJTC type 0-14) driving a 
single stage. 

The output voltage from the amplifier is applied to the control grid 
of a gas tetrode (2050 or 2D21) and, simultaneously, a 10-volt peak 
signal from the 1-kc/sec oscillator is coupled to the shield grid. Each 
grid has a bias of about —10 volts with respect to the cathode. 

Measurements on gas tetrodes show that if either grid is biased to — 10 
volts, the tube will not fire even if as much as +76 volts is applied to the 
other grid. Therefore, if the a-c signals on the grids are 180° out of phase 
with each other, firing is impossible. When they are in phase, however, 
and of adequate amplitude, the tube will fire once each cycle if the plate- 
circuit time constant permits adequate recovery between cycles. Thus, 
the condition stipulated at the beginning of the section is fulfilled, 
and the AFC system will lock. The phases must, of course, be selected 
so that during the hunting sweep the phase condition for firing will not be 
encountered until the resonance peak has been passed, or else the system 
^vill lock far out on the skirt of the response cuiwe. 

Some of the earlier beacon AFC systems used a pentode coincidence 
tube in place of the gas-discharge tetrode. The amplified crystal 
output voltage was injected at the control grid and the direct signal from 
the audio oscillator at the suppressor grid, both being biased beyond 
cutoff. Tinder coincidence conditions the pentode put out broad negative 
pulses. An additional amplifier was therefore required to obtain the 
positive output pulse necessary to fire a gas-discharge tube. 

This arrangement operated successfully in conjunction with the 
standard gas-disc, hiirge-tubc AFC, although two more tubes were required 
than are uschI in the circ.uit described at the beginning of this section. 
It was completc^ly unsuccessful in conjunction with the diode-transitron 
c.ontrol circuiit, however, and this failure led to the circuit of Fig. 7-31. 

The cause of the failure was essentially the onoimous variation in the 
effective gain of the system. In addition to tho normal factors of tube 
variability, TjO output power, crystid recjtification, and so foi-th, three 
potent effe(‘.tR exist: 

1. For constant modulation voltage, the amplitude of the frequency 
excursion, and hence of the crystal output voltage, is proportional 
to the electronic-tuning sensitivity, d?//dV. In xisual reflex 
oscillators this factor varies by a factor of 3 among tubes of a 



given type. In addition, unless very loose coupling is used, the 
pulling effect of the cavity on the local oscillator may cause a 
further increase by a factor of 3; that is, tubes with a high normal 
dv/dV are readily pulled, and the effect is such as to increase the 
effective di^/dV, but tubes with a low dv/dSf are little affected. 
These two factors of 3 combine to give an uncertainty in the gain 
of a factor of 9. 

2. The bias on the control grid must be enough to ensure cutoff for 
every tube. If it were not, the signal on Gz would give rise to plate 
output voltages capable of operating the control circuits even 
when no signal was present on Gi. If tube variability is such that 
cutoff ranges from —4 to —8 volts, then —10 volts is a reasonable 
design figure. If, moreover, one of the tubes whose cutoff is —4 
volts is used, then a signal having a peak amplitude of 7 volts wUl 
cause a 1-volt excursion into the conducting region, but an 8-volt 
signal (14 per cent larger) will produce a 2-volt excursion. 

3. Not only is this excursion twice as large, but the upper half of it 
occurs in a region of higher tube Om] the output voltage might 
therefore be three or four times as large. 

From the foregoing discussion, it can be seen that a mere change of 
local oscillator and coincidence tube, may cause a system in which the 
maximum available output voltage is barely adequate for the generation 
of control voltage to become one in which a slight deviation from the 
crossover frequency will produce the maximum effect. In practice the 
output voltage of the coincidence tube, under the high-gain condition, 
changes, between two successive cycles of the audio oscillator, from zero 
or a small value to one so great that a large potential is developed across 
the detector of the diode-transitron circuit. This large potential causes 
the local-oscillator frequency to be driven back a long way, so that an 
interval of perhaps 10 to 20 cycles will occur before the next crossing of 
the resonance peak. It will be foimd that the ripple in the local-oscillator 
frequency will amount to many megacycles per second. 

It is felt that this difficulty is inherent; that the cavity-modulation 
scheme must always be applied to a control circuit which operates on the 
frequency principle (Sec. 7T1), and which is not affected by amplitude 
variations as large as 100 to 1. 

Another problem peculiar to a circuit of this type should be noted. 
Let us ignore, for the moment, the audio-modulation voltage, and considei* 
only the slow-sweep voltage of the hunting cycle. As the frequency is 
swept through the resonance curve, a positive transient voltage appears at 
the crystal output terminals. A badly distorted reproduction of this 
voltage — ^the distortion depending on the low-frequency amplitude and 
phase response of the amplifier — will appear at the grid of the coincidence 

Sec. 7-19] 



tube. At the time coincidence information should appear, for instance, 
the potential of this grid may be more negative than its fixed bias, 
and hence it may be necessary for the local-oscillator frequency to 
pass somewhat beyond the resonance peak before the gas-discharge tube 
starts to &-e. On the other hand, after the gas-discharge tube does fire, 
the transient may cause a reduction in bias such that the firing will 
continue for several cycles after the reversal of the drift direction. The 
g^eration of an excessive search-stopping voltage results, so that the 
frequency is pulled back in much the same way as when a pentode 
coincidence tube is used. When the output pulses from the coincidence 
tube are obseiwed, groups of 5 to 15 consecutive pulses followed by a long 
interval without pulses are seen instead of a more or less uniform dis- 
tribution. A large ripple appears in the reflector voltage, and a spectrum 
analyzer shows large excuraions in the oscillator frequency. 

This effect can be eliminated by so designing the am plifiAr that it has 
poor response to low frequencies. On the other hand, its phase shift at 
the modulation frequency must be small if fibing in the “anticoincidence” 
position is to be avoided. One solution is to admit the considerable phase 
shift in the amplifier which occurs when short-time-constant coupling 
networks are used, but to offset it by an equal phase shift in the line 
canying the oscillator signal to the shidd grid. In practice, the phases at 
the two grids should be compared when the whole system is in place, 
including any sranll bypass condensers at the reflector. Such a com- 
parison may bo ojisily made with an oscilloscope, and a suitable phase- 
correcting cir<!uit may be installed. This is a design test, and normally 
should not have to bo made on each individual system. 

7-19. Beacon AFC for Thermally Tuned Tubes. — At the time of the 
writing of this section, no fully engineered circuit for the absolute- 
frcciucncy AF(1 of thermally timed oscillators has been developed. The 
circuits to bo described have been built and operated but are not yet 
known to be fully satisfactoiy. 

The first approach to the problem was a circuit designed by M. W. P. 
Htrandberg,' who, following the lines of development described in 
Secs. 7- I I to 7- 10, used push-pull, on-off control with reversing multi- 
vibrator. The circuit is shown in Fig. 7-33. 

The r-f jiart of the circuit is identical with that described in the 
previous sec'tion. Suico no modulation is applied to the reflector, the 
response (uirvo of Fig. 7-32a applies. A sweep mechanism which will be 
described later causes the local oscillator to sweep back and forth across 
the baud just as it docs in the thermal AFC circuits described in Secs. 
7- 14 to 7-1 6. 'Phe crystal output voltage is applied through an amplifier 

' M. W. P. Hlr!in(ll)(>rK, “Automatic Frequency Control Circuits for Thermally 
Tunoil Uedex Oscillators,” ItL Report No. 965. 



Fig. 7-33. — Beacon AFC for 2 . 

Sbc. 7'191 



having very good low-frequeacy response to a “trigger shaper,” TS. The 
TS is essentially a reversing multivibrator sim ila r to those previously 
described, except that one of the gnd-plate crosscoupling resistors is 
replaced by the coupling of the common cathode. 

The first output voltage from the crystal, as the operating frequency 
approaches the cavity resonance, is positive. This voltage actuates the 
TS in such a way as to preset it to a definite position. The TS Hi enal at 
this reversal is ignored by the subsequent circuits. 

As soon as the resonance peak is passed, the crystal output voltage 
starts to decrease. This negative wave causes the TS to reverse again, 
but this time the reversal is effective in operating the subsequent circuit, 
which is a heat-control reversing multivibrator similar to those described 
in Sec. 7- 15. Thus, immediately after the frequency has passed the peak, 
the power switch in the tuning triode is reversed so that the frequency 
once more approaches the peak, resulting in a positive output voltage and 
the presetting of the TS once more, so that it can again operate from the 
negative signal received on the other side of resonance. Thus, the system 
is trapped between the two sides of the response curve. 

The preset feature is important for, if it were not present, 
fluctuations due to hum or microphonics would cause two or more suc- 
cessive negative impulses to appear, which would result in an extra 
reversal of the heat-control switch that would carry the oscillator away 
from the peak. 

On the other hand, the sensitivity of the TS to a presetting ai gnai 
must be appreciably greater than its sensitivity to a heat-control signal; 
otherwise the frequency might ride back over the “hump” without the 
TS being preset, and the next reversal of the heat-control switch would 
not occur. It is this extra sensitivity, apparently, that introduces the 
troubles which at this stage make the circuit seem impractical. For if, 
immediately after receiving the HC signal, the frequency should vary 
rapidly, as from hum or microphonics, there is a chance that a small aignai 
adequate for presetting may be followed by a larger signal adequate 
for heat reversal while the oscillator is still on the same side of the peak. 
This extra reversal would then send the frequency away, and the system 
would be unlocked. Whether this difficulty can be overcome without 
basic circuit change is not known. 

The sweep mechanism referred to in the foregoing material is Rinni1a.r 
to that used in the radar AFC circuits. A transitron (see Sec. 7T6) 
simply triggers the hcat-control multivibrator at suitable intervals. 

A circuit was devised,^ which, it was hoped, would not be sensitive to 
microphonics. It is shown in Fig. 7-34. This circuit combines many of 
the features discussed in connection with several of the previous circuits. 

* Strandberg, loc. cit. 

+150 V 

Fig. 7-34. — Second form of beacon AFC. 

Sec. 7 - 19 ] 



It is essentially of the drift-in type (Sec. 7-10). The reflector-modulation 
coincidence-tube scheme of Sec. 7*18 is used to provide the search- 
stopping information, but control is of the on-off type. 

The circuit, up to the gas-discharge-tetrode coincidence tube, is 
identical with that used for reflector beacon AFC (Sec. 7-19). The plate 
voltage of the gas tube is, however, supplied from a multivibrator Va, 
which provides the hunting sweep. The “ ground point for both the 
multivibrator and the gas-discharge tube is at a negative potential 
(usually — 105 volts). The tuner-triode grid is tied directly to the plate 
of the gas-discharge tube, while the plate supply is the real ground (at 
chassis potential). The following action occurs. 

During the desensitized or return portion of the sweep, the left-hand 
section of the multivibrator is conducting. Its plate potential is therefore 
close to catliode potential, and thus the potential of the tuner-triode 
grid is far below ground potential and the strut power is zero. After a 
suitable interval, the multivibrator reverses spontaneously, initiating the 
active portion of the sweep. At this time, the left-hand section is cut off. 
As a result, its plate load resistor acts as part of the plate load of the gas- 
discharge tube, whose plate is therefore at ground potential. Conse- 
quently, the strut power is high, and the oscillator frequency starts to 
sweep downward. As the frequency approaches the cavity resonance, 
the audio signal from the crystal is in the wrong phase to fire the gas- 
discharge tu])c (see 7*18), but as resonance is passed, information 
of the correct phase appears and fires the gas-discharge tube. The 
plate potential of tlic gas-discharge tube therefore is brought momentarily 
close to the pokjiitial of the cathode, cutting off the tuner triode and caus- 
ing a reversal of the frequency drift. The oscillator consequently sweeps 
back over the hump. Presently, however, the gas-discharge-tube 
condojiser is ixH^harged through its plate load resistor so that strut power 
reappears. The strut power causes the frequency to drift back into the 
coincidc^iKu^ n^gioii, siiid another firing of the gas-discharge tube ensues. 
The (circuit is locked. 

To stoi) furtluM- a(d.ion of the multivibrator when the system is locked, 
positive pulses dovc^lopcjd across a small resistor in the cathode lead of the 
gas-(lis(^harg(^ tiib(^ ar(^ impn^ssed on the detector Fs, the left-hand section 
of the multivibrator, clToctivcly preventing the completion of its cycle. 

This circ.uit should not be sensitive to microphonics, since micro- 
phonic.s, l)y ])r(Klucing a few extra firings of the gas-discharge tube would 
merely (*auso i.ho Icxtal-oscillator frequency to back away somewhat from 
the cavity p(«ik without becoming unlocked. The one test model of this 
circuit that has be(ui built showed some tendency to unlock when the’ 
local oscillator was tapped. The cause of this unlocking has not yet been 



The purpose of this chapter is to outlme some of the special measure- 
ment techniques that have been used in conjunction with the design and 
testing of microwave mixers. There are many microwave and low- 
frequency techniques that have had general use in the microwave-radar 
development program. These will not be discussed here because they are 
well described elsewhere. For discussions of such subjects as admittance 
measurements, power measurements, and the design of signal generators, 
power meters, and standing-wave detectors, the reader is referred to 
Vol. 11 of this series. Only those techniques and pieces of apparatus 
which have been used primarily for the design and testing of mixers, 
because of peculiarities of the problem not encountered in other micro- 
wave problems, will be discussed here. 

8-1. Production Tests for Losses of Signal Power.— A mixer cannot 
be tested, in production quantities, for correct dimensions and good 
electrical contacts so simply as can many other pieces of microwave 
equipment. In the design of a mixer, the tuning of the crystal mount 
is one of the most important features, and this is determined by making 
standing-wave-ratio measurements for large numbers of crystals. The 
work is reduced by using crystals representative of the extremes in admit- 
tance, sdected from a large number of crystals on the basis of admittance 
measurements. For production tests, admittance measurements by 
standing-wave-ratio methods are tedious and do not necessarily reveal 
losses due to such causes as poor contacts. 

As discussed in Chap. 3, the r-f tuning of a mixer should be based on 
measurements of the admittance for a small signal, with the local oscillator 
operative and coupled to the proper degree and with a matched i-f 
load and any preselecting r-f components that are to be used in place. 
In practice, however, it has been found that the admittance measured 
in this way is almost identical with that found if a signal at the local- 
oscillator level is applied to the mixer, without a local-oscUlator voltage 
being present. This leads to a simple test involving only admittance 
measurements for such a signal^ but the fact that the mixer crystal is 
also a detector can be utilized to make an even simpler test. 

This test is a comparison of the rectified crystal current produced 
in the mixer by each of a set of crystals representing the extremes in 
admittance of a large group at a signal strength equal to the optimum 



local-oscillator level, to that produced in a tunable crystal holder by the 
same signal when the tunable crystal holder is tuned for Tnfl.iriniiiTn 
rectified crystal current. The apparatus used for such a test is illus- 
trated in Fig. 8T. The signal generator is padded with a matched 
variable attenuator and this combination provides a signal source that is 
matched to the waveguide and adjusted to deliver power at the required 
level. Figure 8' la shows the necessary arrangement of apparatus for 
testing a single mixer with an iris-coupled local oscillator designed for 
operation with a TR switch. The TR switch must be used in the test 
since it provides some tuning of the mixer and changes the dependence of 
the power delivered to the crystal on the r-f admittance of the crystal. 
Each of four or five borderline crystals are put into the mixer and the 
maximum crystal current obtainable by tuning the TR cavity is noted. 
Then the mixer and TR switch are replaced by the tunable crystal holder, 

( 6 ) 

Fkj. 8*1.-- 'AppjinitUH for production toeting for r-f tune and loss in mixer. 

and for eiich crystal the mount is tuned to give maximum crystal current. 
At this level (0.5 to 1.0 ma), the crystal current for most crystals is 
approximately propoi-tional to the power absorbed and, therefore, the 
ratio of the crystal currents produced by the same crystal in the two 
mixers shows approximately the transmission loss and reflection loss due 
to mismat(^h in the tested mixer. Experience shows how much loss can 
be expcct(Hl for a properly constructed mixer. A badly constmeted 
mixer will show up as having a large loss for some of the crystals. A poor 
electrical (jontact will show up as a large loss for all of the crystals. A 
limit of 2 dh can usually l)e set on the sum of the loss in the TR cavity and 
the loss due to mismat(di, iind the crystal current in the tested mixer 
should therefore be at least 63 per cent of that in the tunable mount for 
each crystal. 

If the mixer is to be used over a wide band, it is well to make this 
test at each edge of the band. For testing a large number of mixers, 
the tunable crystal holder need be used only frequently enough to ensure 
that the signal-generator power level has not changed, and that all of the 



[Seo. 8-2 

crystals are unchanged in rectification efficiency. To avoid burnout, 
care must be taken, in inserting the crystals, not to allow an electrostatic 
discharge to pass through them from the body. 

A test of the refiected power alone could be made almost as simply 
by means of a directional coupler on the signal-generator waveguide 
adjacent to the mixer, so arranged as to couple to the reflected wave only. 
This method would eliminate the need for a comparison with the tunable 
mixer, but it would not necessarily show a source of loss in the mixer 
other than mismatch. With a mixer designed for use with a tunable TR 
cavity, the reflection coefficient that can be tolerated depends upon the 
phase, because of the transmission loss of the TR cavity, as shown in 
Chap. 3; therefore, a test in which only the reflected power is measured 
is not so informative as the one d^cribed, which measures both the 
reflection loss and the dissipative loss. 

8*2. Local-oscillator Coupling. — In most unbalanced mixers, the LO 
coupling circuit has some effect on the transmission of received signals 
into the crystal. It is important to know whether sufficient local- 
oscillator power can be coupled into the crystal without a loss in received 
signal strength at the crystal because of interaction of the two circuits. 
Such a test can be made with the apparatus just described, by measure- 
ment of crystal current only. 

The test for local-oscillator coupling, too, must be made with each 
of the selected representative crystals. One of these crystals is put into 
the crystal mount of the mixer, and, with the TR cavity tuned for 
maximum crystal current at a level of 0.6 to 1.0 ma, the crystal current 
is observed as a function of the LO coupling adjustment. This observa- 
tion is made with the local oscillator inoperative. Then the signal- 
generator power is attenuated to the extent that the crystal current 
produced by this signal is vanishingly small, and the local oscillator is 
turned on. The local oscillator must be set at the proper frequency, 
relative to the signal generator frequency, to produce the desired inter- 
mediate frequency, because when a resonant TR cavity is used, the 
coupling depends on frequency. The crystal current produced by the 
local oscillator is observed as a function of the coupling adjustment. 
Two curves can be plotted from these two sets of observations as a 
function of the same parameter. If an effect of the LO coupling adjust- 
ment on the signal power delivered to the crystal is observed in the first 
test, the second test must show that sufficient local-oscillator drive is 
obtained when the local oscillator is not coupled too tightly to the 
signal circuit. The test must be repeated for each of the representative 
borderline crystals and, if the mixer is to be used in a wide band of fre- 
quencies the test must be made at several frequencies in the band. 
The local-oscillator tube used for the test should be one that gives, in the 


mixer circuit, the smallest local-oscillator drive to be expected from 
production tubes of this type. 

A plot of data taken in a test of this kind on a 3,33-cm mixer with an 
iris-coupled local oscillator is shown in Fig. 8-2. The abscissa is the 
number of turns outward, of the capacitive screw in the coupling iris 
from the position in which it completely crosses the waveguide. For 
each of four borderline crystals there are two curves, one representing 
the crystal current from the local oscillator, and the other representing the 

Number of screw turns outward from position of deepest Insertion 
Kuj. S-L>. Dut.n from IonI. of LO with inixor and fo\ir bordcrlino <u'yHtalH. 

(irystal current from the signal g(«ierator, entering the mixer through 
the TR, (^avil.y. Tlu^ hcw.w us(w 1 was long enough to allow the coupling 
iris to be tuiuMl through n'sonanee, where the maximum local-oscillator 
power is (joiiph^l to th(\ (crystal. A very large diminution in signal power 
occurs in the iuuglil)orhoo<l of resonance of the iris, and therefore that 
region must Ix^ avoidcxl. '^Fhc parts of the curves to the left of the 
rcsoniunu^ n^gion c()rresj)onfl to a screw longer than sufficient to produce 
resonance, and those to the right to a length shorter than the resonant 
length. A crystal curnuit of 1 ma can be produced from any one of the 



[Sac. 8-3 

crystals, for either screw length, with a signal loss of no more than 0.6 db; 
hence, the coupling iris could be operated on either side of resonance. 
In practice the screw is cut off to a length sufficient to produce about 
1 ma of current, at maximum insertion, to avoid the use of a local- 
osciUator tube delivering insufficient power to drive the crystal without 
loss in signal power. 

With a 10-cm mixer, using a capacitive probe for local-osciUator 
coupling and without provision, by such means as a resistor disk, for a 
matched load for the local-oscillator cable, serious absorption or reflection 
of signal power by the local-oscillator circuit can occur. A test of the 
same kind as that just described may be used to detect this loss. If, 
with the local oscillator inoperative, power from a signal generator enters 
the mixer and produces a crystal current about equal to that which would 
be produced by local-oscillator power, it is found that the crystal current 
falls off when the probe is screwed in for close coupling. The magnitude 
of this effect depends upon the admittance presented to the coupling 
probe by the local-oscUlator circuit. If the length of line between the 
probe and the loop in the local oscillator is varied, a length can be found 
at each signal frequency, for which the effect on the Ri gna.1 circuit is 
very large even with a small probe insertion. This length corresponds to 
resonance in the local-oscUlator cable. Because the local oscillator is 
operated at a different frequency from the signal, the resonance may not 
correspondingly enhance the efficiency of the local-oscillator coupling. 
Thus a serious loss in received signal strength can occur. If a resistor 
disk is so placed relative to the probe that the local-osciUator line is 
matched to a wave traveling toward the mixer, this resonance is prevented 
because the admittance at the probe cannot be made smaller than that 
of the disk. Such a disk thus serves a double purpose, since its original 
purpose was to prevent LO frequency discontinuities. Even with a 
reastor disk, the 10-cm mixer may still be subject to interaction between 
the signal circuit and the LO coupling circuit, and any design should 
be checked by a test of this kind. 

8-3. Over-all Noise-figure Measurements. — One technique for mak- 
ing over-all noise-figure measurements of receivers requires a very well- 
shidded c-w rignal generator with a calibrated output power, a stable 
i-f amplifier of known equivalent noise bandwidth, and a reliable output 
power meter for the receiver. 

Suitable signal generators with calibrated output attenuators and 
power-measurement apparatus for making an absolute calibration of the 
available output power are described in Chap. 4, Vol. 11 of this series. 
The i-f amplifier should be desired for the output admittance of the 
mixer to be used, and its effective noise figure with this generator admit- 
tance must be known. The output meter need not be calibrated in 

Sbc. 8-3| 



terms of absolute power, but the law of response should be known, to 
allow precise measurement of power ratios. For this purpose a thermo- 
couple and microammeter, or a crystal and microammeter, may be used 
as a second detector. A crystal used for this purpose should be tested 
to determine the relation between the rectified current and available i-f 
power. If the current meter has a full-scale sensitivity of a few micro- 
amperes or less and a resistance less than 100 ohms, most crystals will give 
a rectified current directly proportional to the square of the impressed 
voltage and thus proportional to the available i-f power. To avoid the 
necessity of an output indication of known response, or to allow calibra- 
tion of the output meter, a calibrated i-f attenuator may be used in the 
receiver. Instead of increasing the incident r-f power to change the 

— Ai)i> 2 irul.ii.s for iiioiiHiiroi turrit, of fcho ofToc.Uvo ov»ir-jill iioIho liKiire of ii rocoivor. 

output nioter r<^i(ling by a given factor, a known attenuation may be 
put into th .(5 ainpli fun’ iuid the input power ine.rcased to make the meter 
read th<^ same value as l)<‘,l'ore. 

Figuns 8-^^ is a bloc.k diagram showing the way in which this apparatus 
is us(«l. With the local oscillator at the correcdi frcicpienciy and at the 
(^ornw^t pow(u* hn'cl in i;h(^ mixer, and with the sign al-g(ui orator attenuator 
set t.o giv(^ no output power, the i-f aniplilicw gain is S(^t to make noise 
from th(^ ainplilicn* giv(^ a reading less than lialf scale on the outpulr-powcr 
met(u*. d'luui the sigiuil-geruu-ator ])ower is incr(‘.as(^d until the output- 
meter reading is doul)h‘<d, (‘.are Ixung taken tluit tlu^ local oscillator and 
TR (‘.avity tumxl i-o giv(^ maxinuiin nxuMVcu* reS])onse. The elTecdive 

over-all noise ligun* of th(i nMuuver is then tlui ratio of the availabh^ 
signal-g(uun*ator powc*r at this last setting ol* tluj attenuator to 
whore W is th(^ e<iuival<uit noise bandwidth of the i-f amplifier. 



[Sec. 8-3 

For this measurement to constitute a measurement of the merit of a 
mixer, sev-eral other things must be known. In practice the TR cavity 
will be coimected to a duplexer, which affords effectively a matched 
waveguide generator for the received signal power. It is, therefore, 
important that the combination of signal generator and calibrated 
attenuator does represent a generator matched to the waveguide. Since 
a cutoff attenuator is usually used as the variable attenuator of the 
signal generator, an additional matched dissipative pad should be used 
in the output line of the cutoff attenuator. The i-f admittance of the 
crystals used in the tested mixer must be known to allow the i-f-amplifier 
noise figure to be known. A noise figure larger than expected could result 
from an i-f output admittance for the mixer corresponding to a large noise 
figure for the i-f amplifier. This could not be considered a fault of the 
mixer, for an amplifier with a different input circuit would correct the 

The TR cavity has been included in the diagram to illustrate a point. 
The over-all noise figure for a receiver using a mixer and TR cavity 
must be measured with the TR cavity in place, since this component 
influences not only the local-oscillator coupling but also the conversion 
loss, effective noise temperature, and i-f output admittance of the mixer. 
In addition, the transmission loss of the TR cavity is affected by the r-f 
admittance of the crystal, and consequently the effect of the TR cavity 
cannot be taken into account by the assumption of some average trans- 
mission loss for a cavity between a matched generator and a load. 

If all of these precautions are taken, the test still does not constitute 
a test of the mixer unless the noise figures to be expected from the crystals 
used are known. These noise figures may be evaluated by independent 
measurements of the crystal conversion loss and noise temperature, 
or relative values may be obtained by measurement of the noise figures for 
the same crystals in a mixer known to operate properly with these 
crystals. For this purpose, a mixer that does not require a TR cavity 
and that has a tunable crystal moxmt is useful. Such a mixer may be 
substituted for the mixer to be tested, and tuned to give minimum noise, 
figure for each crystal. The ratio of the noise figure obtained for this 
mixer, to that obtained for the one being tested, does represent a measure 
of the operation of the mixer on test, provided that the i-f amplifier 
noise figure is known to be the same for the i-f output admittances 
associated with each mixer. If it is not the same, one of the sets of 
measurements must be corrected to compensate for the difference. 

Because of the effect of the reflection of the image frequency and the 
filtering of local-osciQator noise by the TR cavity, the noise figures of 
the receiver with these two mixers may not differ by an amount to be 
accounted for by TR-cavity loss. The noise figure of a mixer-and- 

Sec. 8-3] 



amplifier combmation, including the TR cavity, is often as small as that 
of a mixer without a TR cavity. When this is so, the filtering of local- 
oscillator noise and the reflection of the image frequency by the TR cavity 
more than make up for the transmission loss of the TR cavity. It is 
apparent that an over-all noise-figure measurement is not the best way 
to determine the r-f tuning of a mixer, although it does represent a 
measurement of the quantity which is of most direct importance. A 
better set of quantities to measure would be the conversion loss and 
effective noise temperature of the mixer. 

The same apparatus, with the addition of an i-f noise diode and an 
adjustable capacitance at the input terminals of the i-f amplifier, can 
be used to measure the effective noise temperature and the i-f admittance 
of the crystal. From these values, in combmation with the effective 
over-all noise figure and the effective i-f-amplifier noise figure, associated 
with the measured i-f admittance, the conversion loss of the crystal can be 
calculated by substitution into the standard formula for the over-all 
noise figure as a function of these quantities. The noise diode may be 
added in such a way that the crystal appears as the load admittance at 
the plate of the diode, as shown in the circuit of Fig. 2-35. In addition, a 
small variable condenser across the output terminals of the mixer allows 
the susceptance part of the i-f admittance of the crystal to be tuned out. 

The noise diode may be used as follows. Several resistors, having 
conductances covering the range of conductance expected for the i-f 
terminals of a mixer (800 to 8000 /imhos, for instance), are put, in turn, 
into the crystal holder of the mixer. The effective noise figure of the i-f 
amplifier aasociated with each of these conductances can be found by 
measuring the plate current of the noise diode required to double the 
output noise power from the receiver alone. For each resistor the vari- 
able condenser is sot to minimize this current. The effective i-f noise 
figure is then 

where I is the diode plate current and G the conductance of the resistor 
unit. It is very important that sufficient plate voltage be used on the 
diode to obtain saturation plate-current values, and that the plate 
current be regulated by the filament temperature. This ensures that 
there is no space-charge smoothing and that the noise is pure shot-effect 

When the valuers of the i-f noise figure for all values of i-f conductance 
are known, the effective noise temperature of the crystal can be found 
by a comparison of th<i output noise power of the receiver when the 
crystal is in pla(?e, with that when a resistor having the same i-f (‘.on- 


ductance is in the circuit. A measurement of the i-f conductance of the 
crystal is required, and for this, too, the noise diode can be used. The 
i-f-amplifier gain may be set to give a particular output noise power with a 
resistor representing the i-f conductance of an average crystal in the 
mixer in place of the crystal. With this gain setting, the diode current 
required to produce a given deflection of the output meter for each of the 
various resistors may be measured. The values of diode current obtained 
in this way may be plotted as a function of i-f conductance. If the 
crystal is put into the mixer and the diode current that is required 
to give the same increase in output noise power at the same gain is 
measured, the i-f conductance of the crystal may be read from the plot. 
In each of these operations the susceptance of the output terminals of 
the mixer is resonated out by proper setting of the variable capacitance. 

The labor of these measurements can be lessened by the use of the 
equivalent five-eighth-wavelength-line input circuit used in the crystal 
noise-temperature test sets and described in Sec. 2T8. This method 
has the advantage that the noise output power is independent of the i-f 
conductance of resistors put into the mixer, and the i-f noise figure is 
reasonably constant for the range of conductances of interest. The 
addition of an adjustable condenser would allow compensation for the 
susceptance part of the i-f admittance of a crystal mixer. Unfortunately, 
however, this condenser may not be adjusted by simply maximizing 
the receiver response because the equivalent eighth-wavelength line 
transforms its effect into that of a variable conductance at the first 
amplifier grid. If mixers in which the susceptance part of the i-f admit- 
tance varies are to be tested, it may be safer to use the simple input 
circuit and to take into account the effect of the i-f conductance on the 
output noise and on the noise figure. 

Measurements that involve the beat frequency between two c-w 
oscillators, as in the above example, are often rendered difficult by the 
drifting of the relative frequency of the oscillators. This is particularly 
troublesome at the higher frequencies and with a narrow i-f amplifier 
pass band. Continual adjustment of the local-osciUator frequency must 
be made to ensure that the beat frequency is at the peak of the i-f ampli- 
fier response. Sometimes the signal generators may have frequency- 
modulation components, due to ripple in. the power supplies for instance, 
sufficient to cause the beat frequency to spread over a band of frequencies 
mder than the pass band of the i-f amplifier. In such a case, the measure- 
ments of over-all noise figure and of conversion loss would be in error 
because the r-f power measurements would include the power contained 
in the whole spectrum of the oscillator. 

To reduce these difficulties it is helpful to add to the test apparatus 
an AFC circuit arranged to maintain the correct difference frequency 

Sec. 8 - 4 ] 



between the signal generator and the i-f amplifier. For this purpose a 
standard f-m communications receiver (Hallicrafters — S-27) has been 
used. A small amount of the i-f signal in one of the later stages of the 
i-f amplifier is applied to the communications receiver, which is tuned 
to the intermediate frequency. The d-c component of the f-m-discrimi- 
nator voltage may then be used as an AFC voltage, added in series to the 
reflector voltage of the local oscillator. The only changes that need 
be made in the circuit of the communications receiver are the removal 
of the discriminator circuit from ground potential, so that the reflector 
supply voltage is not short-circuited, and the addition of fairly large 
condensers (0.01 jif) from the reflector lead to ground to prevent oscilla- 
tion of the AFC circuit. A reversing switch that inveris the sense of the 
discriminator voltage at the reflector lead allows the local oscillator to be 
operated either above or bdow the signal frequency. 

This AFC circuit will maintain the correct difference frequency 
between the signal and local oscillator even when the signal strength is 
sufficient to increase the output power of a 1-Mc/sec-wide i-f amplifier 
by only about 10 per cent. At the level of signals usually used for noise- 
figure measurements, the control is very good. The pass band of the i-f 
amplifier may be observed on the output meter of the communications 
receiver by tuning the receiver through it, since the intermediate-fre- 
quency voltage developed is always almost exactly that read on the dial of 
the communications rec^civer, provided the AFC circuit is locked. That it 
is locked can 1)0 confirmed by variation of the reflector supply voltage. 
As this voltage is varied there will be an opposing variation in the output 
voltage of the discrimiiuitor and practically no change in the beat 
frequency or in the output voltage of the i-f amplifier of the noise-figure 
test apparatus. 

84. Radio -frequency Noise Generators. — In many respects, it is 
more C(uivenient to use r-f noise generators for the measurement of 
over-all noise figui’cs than to use c-w signal generators. An r-f noise 
generator that has a uniform noise spectrum over a freciuency band that is 
broad compared with the receiver pass band allows the elTec.tive over-all 
noise figure to be measured, independently of the shape or width of the 
receiver pass band. R-f noise generators are disc.ussed in some detail 
in Chap. •!, Vol. 1 1 of this series. Only a (lualitjit.ive <loscription of the 
tyi)es which luive Ixuui us(xl an<l the methods of application to noise- 
figure measurcMiKMits will be given here. 

A reflex-klystron osc^illator (uin be used as an r-f noise generator if it is 
supplied with the usual hcuiter and accelerator voltages, but with a 
refle(‘.t<)r voltages that does not produce oscillation. The noise spectrum 
in the output line is determined by the resonant cavity of the tube, and 
therefore the tube must be one which would ordinarily be used as an 



[Sbc. 84 

oscillator at the receiver frequency. To make the tube appear as a 
matched generator, a matched dissipative attenuator pad is used between 
the tube and the mixer of the receiver. In the 10-em band, for instance, a 
type 417 reflex IQ3rstron with a flexible output cable having about 10 db 
of loss has been used. At 3.2 cm, a 2K25 oscillator, coupled directly to a 
waveguide but with a resistance-strip attenuator between the tube and 
the output end of the waveguide has been used. 

The available noise power from these generators can be defined in 
terms of the equivalent noise temperature of the matched termination 
formed by the attenuator. If this temperature is T times room temper- 
ature, the effective over-all noise figure of a receiver is simply the value 
of (r — 1) that produces twice as great a noise output power from the 
receiver as is produced when the noise generator is shut off. With ordi- 
nary oscillators, and with receiver bandwidths not exceeding a few mega- 
cycles per second, the equivalent noise temperature of the generator can be 
regarded as constant throughout the pass band of the receiver. There 
may be a contribution of noise converted from the image frequency of 
the receiver, but an intermediate frequency of 30 Mc/sec in a receiver for 
9000 Mc/sec is sufl&ciently high to make the noise temperature of the 
generator nearly unity at the image frequency, because of the selectivity 
of the oscillator cavity. Thus, a generator of this kind can be used to 
make measurements of the over-all receiver noise figure, if the equivalent 
noise temperature of the generator can be measured. 

For the purpose of calibrating a noise generator, an apparatus for 
measuring crystal noise temperature may be used. A standard mixer 
with a local oscillator and a crystal of known conversion loss are required. 
With the noise generator connected to the mixer and the generator tuned 
to one of the two sensitive frequencies of the test set, the noise tem- 
perature of the crystal mixer is measured with the noise generator on 
and off. The difference between the noise temperatures of the mixer 
measured with the generator turned on and off is directly the required 
value of (r — 1) of the r-f noise generator divided by the conversion 
loss of the mixer. Values of T up to several hundred, including the 
effect of the buffering attenuator pad, can be obtained from reflex 
oscillators if sufficient accelerator voltage is used. The effective noise 
temperature may be varied by changing the attenuation, or the acceler- 
ator or heater voltages of the tube. 

A noise generator of another type is a crystal-rectifier unit mounted in 
a standard waveguide or coaxial-line crystal holder. Considerable r-f 
noise power is generated by such a crystal if a direct current is forced 
through it in the backward (high-resistance) direction. A current of 5 to 
10 ma, which may require a voltage as large as 6 volts, results in a noise 
generator having an effective temperature 30 to 100 times room tern- 

Sec. 8-4] 



perature. Currents lower than 6 ma do not reduce the noise temperature 
greatly, and give somewhat more stable operation. It is well to allow the 
current to flow for several hours before calibration is attempted, because 
it is observed that the device becomes stable after such a period of opera- 
tion. A current meter, used with the noise-generating crystal at all 
times, allows detection of a change in its d-c characteristic which might 
make necessary recalibration of the unit. 

The calibration procedure for the crystal noise generator is similar 
to that for the reflex oscillator. It is important in this case, however, 
that local-oscillator power from the receiver does not reach the noise 
crystal because such local-oscillator power would certainly affect the 
effective noise temperature of the device. All noise components that, 

j~ Crystal noise generatoH 

' j 

• Attenuator i 




Noise-temperature test set 


) o igi I — — 




z I ^ 



l-f amplifier 


j*— Attenuator 

of test set 



Local oscillator 

Kid. 8*4. — Appurnlus for calibration of cryHtal iioiao Ronorators. 


when mixed witli the local-oscillator frequency, would give components in 
the ixM^eiver pass band would contribute to the noise power available in 
the vicinity of tlu^ hx'.al-oseillator frequency. A circuit such as that 
shown in Fig. 8-1, tlKxx^foro, may be used with the crystal-noise-tem- 
poratiirc t(tst sc^t. All of the pieces except the magic T and the noise 
generator atx^ ]:)a.r-ts of tlie tc^st sot and the part labeled ''I-f Amplifier" 
is meant to in(ilud<i the fivo-oighth-wavelength-cquivalent line, the 
preamplifier, and tlu^ c.ommunications receiver of the test set. The local 
oscillator, filter (‘-avity, and ])iilTcring attenuators of the test set are 
dis(a)nn(‘.(^t(xl from th(^ mixer and attached to aim (4) of the magic T. 
A matc.hed termination is ])la(‘.ed on aim (1), and the ciystal of known 
conversion loss in ilu^ mixer is selected to bo matclied to the waveguide 
at the local-oscilhitor frequency. Thus no local-oscallator power is 
coupled into the noise (uystal. An attenuator is shown as a ])art of the 
noise gcinorator. This attemuator serves to make the generator appear 



[Sec. 8-5 

matched to the line, both when it is turned on and when it is turned off. 
An alternative to this procedure is to select the crystal or to tune the 
crystal mount so that the crystal is matched to the waveguide for small 
signals when the current is flowing. A larger noise power can be obtained 
in this way, but an attenuator must be inserted when the current is 
broken because the crystal is then no longer matched to the waveguide. 
In the 1.25-cm band, a dummy load that makes the crystal mount 
matched to the waveguide has been inserted in place of the crystal. 

The noise crystal develops a noise spectrum that is unifoim over a 
relatively wide frequency band. When the noise ciystal is used for 
measuring receiver noise figures and for calibration, there is an equal 
contribution to the converted i-f noise power from the r-f noise in the two 
sidebands of the local oscillator. The desired value of (T — 1) of the 
generator connected to the crystal mixer of the test set would, therefore, 
be just half the change in mixer noise temperature times the conversion 
loss of the mixer. The value of (T — 1) of the noise generator con- 
nected to the magic T is the whole product of the change in i-f noise 
temperature and conversion loss, however, because one-half the available 
noise power is lost in the load on arm (1) of the T. 

The noise crystal must also be protected from local-osciUator power 
when it is used to measure receiver noise figures. The local oscillator 
and the noise crystal, therefore, should be coupled to a nonresonant 
mixer circuit with a magic T or a similar circuit, as in the calibration 
apparatus. For this reason, an ordinary unbalanced mixer and local 
oscillator cannot be tested with the noise crystal unless a resonant 
cavity, such as a TR cavity, prevents the leakage of a large amount of 
local-oscillator power into the noise crystal. If such a cavity is used, 
filtering of the image-frequency sideband is also obtained, and the 
calculation of the noise figure of the receiver from measurements vrith the 
noise crystal must take into account only a single sideband. 

Because of the difiSculty of removing local-oscillator power from the 
signal circuit of most mixers, the reflex oscillator is a more dependable 
noise generator than the noise crystal. It has the disadvantage, however, 
that it must be tuned to the receiver frequency. On the other hand, its 
calibration may be expected to hold under much less restricted conditions 
and over a longer time than can that of the noise crystal. If the output 
line of an oscillator can be made nonreflecting, the equivalent noise 
temperature is practically constant over the range of frequencies to 
which the tube can be tuned. For example, a single calibration can be 
used for a 417 Klystron, with a matched-cable attenuator, for the wave- 
length band from 9 to 11 cm. 

8-6. Apparatus for Measurement of the Effect of Image Reflection. — 
As an example of apparatus of the kind that is useful for experiments 

Sec. 8*5] 



with converters and mixers, an apparatus developed by E. R. Beringer, 
M. C. Waltz, and C. P. Gadsden for experiments with welded-contact 
germanium crystals will be described. It was desired to measure the 
conversion loss and noise temperature of the mixer under many conditions 
of tuning at both the signal- and image-frequency terminals of the mixer. 
The i-f output admittance of the crystal was known to vary over a very 
wide region including negative values of the conductance, and the i-f 
input circuit was designed to allow measurement of the mixer parameters 
for the whole range of expected i-f admittances. 

A circuit diagram showing the essentials of the i-f input circuit used 
is given in Fig. 8-5. There is no transformation of the crystal output 
admittance, since small conductance values were expected. The induct- 
ance L resonates at the intermediate frequency with the combined 

Rrst i-f 

K-f). -l-f itiput c-irciuil. uwkI for iiiotuiuriiif; iipparutuH for woldocl-cont.uct ftornuinium 


(^iipac.itaiic.o of thc^ mixer, tlie tube, and tho variable condenser when the 
(condenser is scd'. at about the middle of its range. The adjustment of the 
variable comhuiscu- allows compensation for the susceptance component 
of the crystal output admittance. A switch allows a resistor to be 
shunt(‘,d a.(U‘<)ss the crystal output terminals if desired. If the output 
(‘.onductaiK^e beciomes m^gativo and lias an absolute value exceeding that 
of the positive conductanc.e of the input circuit and tube, oscillation at 
tlu^ intei’incdiatc friuiuency occurs. The added conductance of the resis- 
tor allows the total conductance to bo kept positive. 

Tho r-f ])art of the cir<;uit is shown symbolically in Fig. 8-6. The 
local oscullator and noise generator arc connected independently to the 
mixer through the first magi(5 A filter cavity is used to remove noise 
sidebands from the hx^al-oscillator signal, and attenuator pads are 
provided to make ca(di of the generators appear matched to the wave- 
guide. In tho arm attached to the mixer there is a second magic T 


with a resonant cavity in one arm and a plunger in another. The 
plunger is adjusted so that all signals at frequencies other than those in 
the region of the cavity resonance are transmitted through to the mixer 
crystal. At the resonant frequency of the cavity, the input admittance 
of the cavity is a very small conductance and, therefore, waves of this 
frequency are reflected from the T. If the cavity is tuned to the image 
frequency of the mixer, any image-frequency wave developed by the 
mixer is reflected back to it from the magic T. The phase of the reflected 
wave is determined by the adjustment of the variable length of line 
between the T and the mixer crystal. A sliding-screw tuner in the arm 
between the two magic T’s allows tuning of the signal-frequency admit- 
tance of the mixer. In this way, independent control of the signal and 
image frequencies is obtained. 

Fig. 8*6. Kr-f circuit for measuring the effect of the reflection of the image frequency on 

the receiver noise figure. 

This apparatus is used in the following way. With various dummy 
resistors substituted for the mixer crystal a curve of the i-f-amplifier 
noise figure, as a function of the i-f conductance of the mixer, can be made 
from data taken with the i-f noise diode. Also, by use of the i-f noise 
diode and the resistors, a corresponding curve can be plotted of the i-f 
amphfier output noise power. The change in output power of the receiver 
with a given gain setting is measured as a function of the conductance 
of the output terminals of the mixer when the diode current is increased 
from zero to a particular vfflue. From these data the i-f conductance 
of the crystal, for any condition of the r-f tuning, can be found. There- 
fore, the i-f noise fipire is known. The r-f noise source may then be 
turned on to determine, from the change of the output noise power from 
the receiver, the effective over-all noise figure of the receiver. Since the 
available r-f noise power is known from the calibration of the r-f noise 
generator, if the available i-f noise power at the crystal due to this r-f 
noise power were known, the conversion loss of the crystal would be 

Seo. 8-6] 



found. The available converted i-f noise power can be found by com- 
parison with the available noise power from the i-f noise diode, since the 
crystal conductance is known. Thei-f noise diode may be set at a current 
that produces the same change in the output noise power from the recover 
as does the r-f noise generator. The conversion loss of the mixer is 

7 - - 1) 

^ ~ 20 / ’ 

where I is the noise-diode current, T the effective noise temperature of 
the r-f signal generator, and G the i-f output conductance of the mixer. 
From the conversion loss, the effective i-f-amplifier noise figure and the 
over-all noise figure, the noise temperature of the mixer can be found from 
the usual formula 

= L(Fu -|- i — 1), 

where t is the desired noise temperature. 

Thus, the apparatus can be used to find the two quantities, L and t, 
which are the mejusiires of the merit of the mixer. The apparatus has 
been used in a study of the dependence of L and t, for welded-contact 
germanium crystals, upon the various tuning conditions of a mixer, 
in the hope that some condition would be found which gives an unusually 
small over-all noise figure. No such tuning conditions were found, 
although, as discussed in Chap. 2, the i-f output admittance could be 
varied by the r-f tuning elements over a very wide region, including a 
region of negative conductance. If a similar apparatus were to be used 
for measurements with ordinary crystals, the shunting resistor in the 
i-f input circuit would not be needed, since negative conductances do 
not occur with most crystals. 

Apparatus of this kind would bo useful for the measurement of L and t 
for ordinary ciystals, as a function of the phase of the image reflection. 
Some work of this kind has been done, and the indication is that some 
improvement in the over-all noise figure of a receiver is to be gained by 
proper plmsing of the imago-fro(i|uoncy reflection. The data are insuffi- 
cient to allow a definite statement to be made about the magnitude of this 
effect which (tould bo realized in practice, or about the best phase of the 
image-frc(iucncy refleiition. It does appear that the improvement 
resulting from tlm decrease in conversion loss accompanying image 
reflection in the best pluise is not offset by an increjisc in the crystal noise 

8-6. An Apparatus for Measurement of the Admittance Loss of a 
Mixer. — In Bee. 2-11, it was shown that a quantity termed the admittance 
loss of the mixer can be found by measurement of the dependence of the 
signal-frecpiency admittance of the mixer on the i-f load admittance 
presented to it. Since for most sili(‘.on crystals the admittance loss is 



[Sac. 8-6 

equal to the minimuxu conversion loss obtainable from the mixer with any 
value of signal-generator admittance, the simplicity of this measurement 
makes it a good tool for experimentation with mixer circuits. 

An apparatus that has been used for measurements of this kinrl is 
shown symbolically in Fig. 8-7. A magic T is used as an adnoittance 
bridge, in which the admittance of the mixer is compared Avith that of a 
well-matched load on the opposite arm. It is actually the small-signal 
admittance that is measured, in the presence of the proper local-oscillator 
power supplied from the operating local oscillator of the mixer. The 
mixer shown under test is one with an iris-coupled local oscillator and 
requiring a TR cavity for proper operation of the coupling circuit. 

Fio. 8-7. — Bridge for measurement of admittance loss of a inixor. 

The TR cavity is included in the measurement and the measured admit- 
tance loss includes the loss of the TR cavity. A small signal (less than 
1 ti-w) is applied to arm (4) of the magic T through a matched attenuator 
pad. On arm (3) is a mixer for detecting the unbalance signal of the 
bridge. A matched attenuator pad is also used, to stabilize the input 
admittance of the mixer and to reduce the amount of local-oscillator 
power leaking from this mixer to the test mixer. The mixer used for the 
detection of the unbalance signal is of the same type as that shown in the 
test position, in the diagram. The TR cavity also decreases the leakage 
of local-oscillator signals between the two mixers. 

Two sliding-screw tuners are used in the circuit. One between 
the attenuator and the magic T, on arm (3), provides sufficient tuning 
to make the test arm, arm (2) of the magic T, nonreflecting to a wave 

Sec. 8-6] 



sent back from the mixer under test, at the signal frequency. The other 
tuner, in the test-mixer arm of the magic T, is used in the test procedure. 
An r-f switch, formed of a plate sliding betw'een a pair of choke connectors, 
is also placed in this arm of the bridge. The plate has a rectangular hole 
of the dimensions of the inside of the waveguide, and can be adjusted 
to make the waveguide unobstructed or can be moved so that, instead of 
the aperture, there is a short-circuiting plate a6ross the waveguide. 
This short circuit provides a reflection coefficient of unit magnitude for 
calibration of the unbalance detector. 

An i-f amplifier and an output power meter are connected to the mixer 
for detection of the unbalance signal. An f-m communications receiver, 
tuned to the center of the pass band of the i-f amplifier, provides auto- 
matic frequency control of the local oscillator of the unbalance detector. 
Connected to the i-f output terminals of the mixer under test is a shielding 
box containing a shunt-resonant circuit that has an adjustable capaci- 
tance and resonates at the beat frequency between the signal and the local 
oscillator of this mixer, when the i-f capacitance of the mixer itself is 
included. The capacitjince has sufficient tuning range (at 30 Mc/sec, 
about plus or minus 7 /xAtfd) to compensate for any susceptance component 
in the crystal output admittance. The coil of the resonant circuit is 
designed to have a small shunt conductance. Number 12 gauge solid 
copper wire, wound on about a 1-inch diameter is used, and the turns 
are spacnad about one wire diameter apart. The three-position switch 
allows the resonant circuit to Umwc the output terminals of the mixer essen- 
tially opon-cir(uiited, to i)r<)vido a load near match for an average crystal 
(with a 4()()-ohm rc^sistor) or to short-circuit the output tenninals of the 
mixer. The d-c5 circ.iiit of the "mixer is unaffected by the switch, and 
crystal (uirrcnt <‘.an 1)0 read at all times. 

The proc.edure used with this test apparatus is the following. First, 
the unbalanc.o-signal mixer and the tuner in arm (3) of the bridge are 
adjusted. To do this, the test mixer is removed and a choke-type 
shoi-t-circ.uiting i)lunger is slid into the waveguide of this arm of the 
bridge, with th(^ tuner of this arm retracted from the waveguide. This 
gives a large unbalaiK-.o signal, and allows alignment of the unbalance- 
signal mixei’, (cavity, and local oscillator as well as the AFC circuit. The 
tuner in arm (3) is then adjusted until the unbalance signal, read on the 
output m(4i(^r, is not alTec.ted by sliding the plunger in and out of arm (2). 
This m(^ans that the output meter roads the magnitude of the reflected 
power in this arm, independently of the phase of the reflection coeffi- 
cient — a situatioji that results when arm (2) appears matched to the 
reflected wave. 

With the plunger removed and the mixer to be tested replaced, and 
with the local os(;illator of this mixer and the TR cavity tuned to the 



[Sec. 8-6 

proper frequencies, the test may now be made. These two tuning adjust- 
ments are not easy to make with the circuit shown, however, because 
there is no indication of their proper adjustment. To remedy this, 
the addition of a second f-m communications receiver would be a great 
help. A small resistance (about 1 ohm) placed in series between the 
shimt-resonant circuit and the first bypass condenser of the crystal- 
current circuit would have little effect on the operation of the test circuit, 
even if the resistor were not shorted out in the short-circuiting position 
of the switch. The crystal is an i-f generator of several hundred ohms 
internal impedance. Consequently, one ohm represents as severe a 
reflection for the crystal as does the shunt impedance of the circuit in the 
open-circuit position. A signal large enough to excite the communica- 
tions receiver could be taken off across this 1-ohm resistor and the receiver 
used as an AFC circuit for the local oscillator of the mixer under test. 
The amplitude of the signal into this receiver would be a measure of 
the TR-cavity tuning. With the TR cavity tuned to maximize the 
signal to the receiver with the switch of the i-f circuit on the load-resistor 
position, nearly optimum results should be obtained. 

With these adjustments made, the r-f switch in arm (2) of the bridge 
circuit is set to the short-circuiting position, and the gain of the i-f 
amplifier of the unbalance-detecting circuit set to make the output meter 
read full scale. The fraction of a full-scale deflection obtained with other 
terminations on the test arm of the bridge is then equal to the square of the 
absolute magmtude of the reflection coefficient, if there is no contribution 
to the output-meter reading from receiver noise. The r-f switch is then 
opened and the r-f tuner in the test arm of the bridge is adjusted to 
balance the bridge with the i-f switch set to short-circuit the i-f terminals. 
When this switch is changed to the open-circuit position, the signal 
admittance of the mixer changes, and the bridge becomes unbalanced. 
If the variable capacitance of the i-f resonant circuit is adjusted to make 
the unbalance signal a maximum, the relation between the admittance 
loss Ly of the mixer and the voltage standing-wave ratio r is 


Vr + 1 
Vr — 1 

as shown in Sec. 2* 11. Since the bridge reads the square of the absolute 
magmtude of the reflection coefficient, the relation between the meter 
reading and the admittance loss of the mixer is 

L = (1 ~ + 1 — y/v 

^ (1 - - 1 + 

where p is the fraction of full-scale deflection of the meter. A cuiwe for 

Sec. 8-6] 



this expresmon, for Lr expressed in decibels for the range from 0 to 10 db, 
is given in Fig. 8-8. 

For silicon crystals it is found that the reciprocity condition holds. 
The admittance loss in this measuremait, therefore, represents the actual 
conversion loss that would result with the mixer under test if the signal 
generator were adjusted to have the internal admittance ^ving minimum 
conversion loss. In practice, there will be some additional loss because the 

» tl,., smorator, i. makW to toe 

th(^ mixer mny bo somewhat mismatched. An approxima e 
the resulting rollcHdlon loss cun be obtained with the apparatus, '^i^h the 
t mu- in the test arm of the bridge retracted from the waveguide and ;^hh 
fchrswitch in the i-f circuit in the position that preset. 
resistive load. Sima, the resistor wUl not m general, 
conductiuicc for the mixer, the r-f mismatch is not 
but is close to that value for any reasonably large ry faction 

output-meter reading, with the switch in this position, gives the fraction 


of the incident power reflected, if the amplifier gain is set to make a 
complete reflection give a full-scale deflection. 

Measurements have been made, with the bridge, of the conversion 
loss of many 3-cm mixers, and the results have agreed well with measure- 
ments made by other methods. As discussed in Sec. 2-11, the variation 
of conversion loss with the distance from the TR cavity to the crystal 
has been observed with this apparatus. Those measurements were 
complicated by the fact that the TR-cavity loss was included in the 
measurement. To prevent variation of this loss with the phase of the 
image-frequency reflection, the crystal mount had to be retuned for each 
line-length setting. Better data would probably have been obtained 
with a mixer circuit, such as that described in Sec. 8-5, in which the 
resonant cavity reflects only the image frequency. 

8-7. Tests of the AFC Mixer. — ^To obtain satisfactory operation of a 
separate AFC mixer, the input signal level must be properly set, and care 
must be taken to ensure that spurious signals, such as TR leakage power, 
and signals at harmonic frequencies are not large enough to mask the 
desired i-f signal. The usual procedure in setting the power level is to 
design the AFC attenuator for about 30 db less attenuation than the 
total amoxmt needed, and then to adjust the diameter of the coupling 
hole between the AFC attenuator and the main line of the radar set to 
give the desired level of 1 or 2 mw of peak power at the mixer crystal. 

If it is known that no spurious signals are present, the power level 
can be checked by measurement of the average rectified current with a 
low resistance microammeter. Most crystals develop about 1 ma per 
milliwatt of dissipated r-f power if the resistance of the meter circuit is 
less than 100 ohms. With the local oscillator shut off, a microammeter of 
less than 100 ohms resistance may be connected to the output terminals 
of the crystal. With the local transmitter operating, the milliammeter 
reads the average rectified current. This is simply the rectified pulse 
current times the fraction of the time during which the transmitter is 
turned on. With a pulsed transmitter producing 1-jusec rectangular 
pulses and a recurrence rate of 1000 cps, an average rectified current of 1 
to 2 /xa indicates 1 to 2 ma pulse current. 

Some precautions are necessaiy to make sure that the microammeter 
reads the correct current. Stray radiation picked up in the micro- 
ammeter or in its leads can give rise to a rectified current, because the 
crystal is in the microammeter circuit. Shielding of both the meter and 
the leads is usually necessary to prevent this. That no such pickup is 
present can be shown by blocking off the r-f signal from the mixer, where- 
upon the microammeter reading should go to zero. A microammeter 
has a rather large reactance to the frequencies involved in a current pulse 

Sac. 8*7] 



of l“/4sec duration. This causes the current pulse to be stretched out 
and, therefore, to persist after the r-f pulse has ceased. Because the 
crystal response is not linear, the average current is reduced, since the 
current must flow through the crystal as well as through the meter. 
A bypass condenser should, therefore, be used across the meter to give 
the pulse a low-impedance path. It is only under this condition that 
the simple relationship between the average current and the r-f pulse 
power holds. 

It is sometimes informative to observe the video-frequency pulse of 
rectified current in the AFC crystal on an oscilloscope. An r-f envelope 
viewer, with the AFC crystal used as a detector, makes this possible. 
The impedance connected to the output terminal of the ciystal should not 
be high, however, since a bias voltage would then be developed which 
would change the r-f impedance of the mixer ciystal and, therefore, 
alter the amount of power delivered to it. An instrument of this kind, 
calibrated as a current meter, can be used to set the r-f power level, for 
the pulse current can be obseiwed directly. 

A more informative observation of the operation of the AFC mixer 
can be made with the help of auxiliaiy apparatus. With a pulsed r-f 
signal generator having the desired available AFC power, and a spectrum 
analyzer, the r-f power level can be set and the presence of any objection- 
able spurious signals can be detected. These pieces of apparatus are 
used in the following way. The crystal to be used in the AFC mixer is 
first placed in a simple mixer that has no input attenuator. This mixer is 
substituted for the regular mixer of the spectrum analyzer. Power from 
local oscillator of the spectrum analyzer is introduced into this mixer 
at the proper level, or, if a local oscillator is included as an integral part 
of the mixer, this local oscillator is connected to the sweeping reflector 
voltage of the spectrum analyzer. If the pulsed signal generator is 
connected to the input tennmals of the mixer, the spec.trum is shown on 
the indicator of the spectrum aiialyz(M‘. Thc^ gain of the analyzer is 
then set to show a giv(m amplitude, in the (tenter of the spectrum, with 
the desired level of puls(^s sent into the mixer. 

The AFC mixer is then substituted for this mixer in the spcctmm 
analyzer. The i-f spec.trum coming from the AFC mixer is shown on 
the indicM‘it()r, and if th(^ transmitter sample has the desired amplitude, 
the amplitude of the sixudirum will be the same as Ix^fore, with the same 
amount of local-osc.illai.or drive. Blocking off the AFC attenuator 
path with a metal plate should cause the spectrum to disappear if the 
leakage of signal from the radar mixer through the local-oscillator circuit 
is sufficiently small. 

Spurious signals leaking into the AF(" mixer with enough amplitude 



[Sec. 8-7 

to interfere with the operation of the AFC circuit are made obvious 
in a test of this kind. The presence of large pulses of harmonic power, 
for instance, can be detected from the appearance of the indicator 
of the analyzer. The presence of the intermediate-frequency components 
of the rectified pulse resulting from such harmonic-frequency pulses is 
evidenced by a continuous spectrum that covers the analyzer screen and 
is unaffected by the tuning of the local oscillator. The amplitude of 
these components has sometimes been found to be so great as to mask 
completely the desired beat-frequency spectrum. A signal incident on a 
crystal mounted in a waveguide far beyond cutoff for the fundamental 
frequency, connected to the output terminals of the AFC attenuator 
and to the input terminals of the i-f amplifier of the spectrum analyzer, 
produced the same pattern on the indicator. It was a test of this kind 
that showed the need for a dissipative attenuator in addition to the 
cutoff attenuator for the AFC signal. The addition of the strip of carbon- 
coated Bakelite inside the AFC attenuator completely removed the spur- 
ious signal in a 10-cm system, and the desired spectrum of the AFC signal 
was then shown clearly on the indicator. Excessive leakage of spike 
energy from the TR cavity, through the local-oscillator channel into 
the AFC mixer, can be detected in the same way. 



Absolute frequency, 294 
Admittance, I-f {see I-f admittance) 
Admittance, i-f output, 90, 1 78-185 
Admittance bridge, 80, 367-372 
Admittance loss, of mixer, apparatus for 
measurement of, 367-372 
Admittance measurements, 362 
Admittance scatter, 134-136, 168 
AFC, 6, 190-202, 290-351, 360 
absolute-frequency hunting systems, 

beacon, 227-231, 234, 244, 287, 341 
reflector modulation s<5heinc for, 

for thermally timed tubes, 347-351 
d-c amplifier typo, 313 
diode-transit roil , 326-33 1 
double-balanced mixer, 283-287 
double-mixer, 103-202, 300 
drift-in hunting system, 314-331 
gas-discharge-tube, 315, 345 
gas-dis<;harge-tul)c design tliwry, 317— 

Nibbe-Duraiul, 333, 337 
nonhunting systeniH, 312-314 
separate-channel, 300 
separate-in ixer, 1 1 )3-202 
thermal hunting systcMim, 331-341 
wide-range tunabh^ .systems, 331-341 
Whitford, 332, 333, 337, 330 
AFC attenuator, 106-100, 372 
AFC diff(^renco-frequeney systcuus, 205- 

AFC feedback loop, 205 
AFC mix(^r, tests of, 372-374 
AFC systems, elassineation of, 204 
Agitation, thermal, 10 
Amplifiers, 201 
d-c, 300, 312, 327 
i-f, 24 

r-f, 2, 23, 43 

Amplifier design, 1 

Amplitude control, 317 

Antenna, temperature of, 12 

Anti-TR switch, 10 

Aperture coupling, 160 

Attenuator, cutoff, 196, 374 

Automatic frequency control {see AFC) 


Back resistance of crystal, 54, 113, 297 
Back resistance meter, 100, 113 
Bandwidth, 2, 26, 302 
effective noise, 14, 22, 27 
optimum, 5 

Bandwidth requirements, 5, 302 
Barrier capacitance, 53, 92 
Beacon, 223, 231, 287, 295 
Bea<!on AFC {see AFC, beacon) 

Beacon mixers, 190 
Beacon stations, 23 
Beacon tuner, 226, 234 
Bell Telephone Laboratories, 43, 83-86, 
115, 300,307-308, 312, 314 
Beringer, K. R., 83, 366 
Bias, d-<‘., 88 

effect of, on mixer crystal, 249-256 
Bifis voltage, 96, 249, 251 
Boloinoters, 19 
Bridge, 368 
Buncher, 37 

Burnout, 96- UK), 118, 172-174 
Buniout tost for crystal, 111-113 

Capacitance, l)arrier, 53, 92 
of contac.t of crystal, 53, 92 
i-f, 120 
Cat(jh<!r, 37 

Cavity, prec.ision ri^iTcnci^, 342 
reaction, 218 
referem^e, 228 




Cavity, transmission, 216, 220 
use of, to reduce local-oscillator noise, 

Cavity circuits, 34 
Characteristic, d-c, 50, 90 
Channel coupling, equivalent network 
for, 166-160 

Chokes, harmonic, 174-178 
Clutter, ground, 300 
Coincidence detection, 344 
Coincidence tube, 342, 346 
pentode, 347 
Cole, P. A., 30 

Conductance, i-f, 111, 249, 360 
negative, 90, 92 
Conductors, 48 
Control, frequency, 25 
Control circuit, hard-tube, 326 
Control voltage, 296 
Controlled reflector, 324 
Conversion, frequency, 26 
Conversion efficiency, 58 
Conversion gain, 90 
Conversion loss, 100, 249, 359, 365 
dependence on image-frequency ter- 
mination, 75-83 

Conversion-loss measurement, 101—105 
Converters, 3, 26-28, 44, 119 
crystal, 66-66 

linear-network representation of, 69- 

three - terminal-pair - network repre- 
sentation of, 61-66 
frequency, 24, 56 
regenerative, 90, 93 
superregenerative, 93 
tube, 28 

Couplers, directional, 146-150, 201 
Coupling circuit, i-f, 271 
Cross attenuation, 194, 195, 284 
Crossbar mount, 171, 172 
Crossover, 307 

Crossover frequency, 296, 302, 304, 310, 
314, 328 

Crystal burnout, 96-100, 118, 172-174 
test for, 111-113 
Crystal checker, 113 
Crystal control, 294 
Crystal current, 95, 256 
Crystal detector, 19 
Crystal mixer (see Mixer, crystal) 

Crystal mounts, 101, 122-126, 171-172, 

for balanced mixer, 279-283 
broadband, 281 
inverted, 280 
tunable, 131-134 
for 1N26 crystals, 171 
for 3-cm bands, 124-128 
for 10-cm bands, 124r-128 
Crystal rectifier, 47-118 
Crystals, borderline, 134, 353 
germanium, welded-contact, 87—93, 
104, 365, 367 

noise temperature of, 58, 93-96, 100, 

representative, 134, 354 
specifications of, 100, 114-118 
table, 117 
testing of, 100-114 
video, 56 
Cutoff, 301 


D-c return, 126 
Detection, 20 
Detector, 3 
crystal, 19 
first, 3 
gain of, 20 

low-level, 17-19, 47, 54, 111, 115, 124, 

regenerative, 45 
square-law, 19-21 
quality of, 20 
video, 115 

Deterioration, 99, 114 
Dicke, E. H., 12n., 63, 74 , 77, 87 
Difference frequency, 294 
Dimensions, 114 
Diode mixer, 32-34 
Diode transitron, 345 
Diodes, temperature-limited, 109, 365 
Directional couplers, 146-150, 201, 301 
Discriminators, 296, 302-308 
efficiency of, 305 
Foster-Seeley, 304 
gain of, 305 

good video balance needed by, 300 
hum in, 311 
microwave, 342 
theory of, 308-312 



Discriminators, voltage gain of, 306 
with triode detectors, 307 
Weiss, 305 

Down-pull rate, 318, 322, 326 
Drift-in, 314, 318 
Drift-in systems, 331 
Drifts, 25 
Driving power, 34 
Dupk^xer, 6, 96, 199 
Duplexing, G 


Ecclos-Jordan trigger circuit, 333 
Effee.tive noise bandwidtli, 14, 22, 27 
Eku*.trode, keep-alive, 8, 99, 174, 176 
Electronic-tuning factors, 291, 292 
EkK^trostatic. discharge, 100 
Enabling circtiit, 300 
Enabling fc^ature, 314 
Energy l<*vel, 48 
Envelopes vi<w<^r, 97, 373 
Ecpiivalent circuit («cc component for 
which c<|uival(uvt (jircuit is given) 
Error voltage^ 295 


Feedback, invcrs<', 321 
Feedba(4i loop, 290 
Figure of in<*rit, for r(M*.(‘iverH, 1(M7 
crystjil-vidco, 51, 50 
Filter, r(\sonanl., to riMluce local-oscillator 
nois(\ 243 245 
Filter cavity, 235 
Filt(^ring, 24 (i, 358 
Flat, 97, 300 
Flat power, 173 
Following rate, 317, 318 
Forward r(*Histanc.(% 297 
FohUt, I). E., 304n. 

FoHt.C!r-S(^eley diHcriininaU)r, 304 
FrecpKMicy (control, 25, 39 
of local oscillators, 290 351 
Fre(pM*nc.y-control ehMd,rode, 312, 314 
Fre(pi(*ncy-c.ontrol priinuphs 317 
Fretpumey convm'sion, 20 
Frecpnaicy discontinuity's, 208 
caused })y high-Q loa<l (circuits, 209- 

prevented l)y padding, 219- 223 
Fn^iiKmcy drift, sourccw of, 290-292 

Frequency principle, 346 
Frequency spectrum, 6 
Frequency stability, 6 


Gadsden, C. P., 83, 365 
Gain, 11, 12, 68, 325 
of detector, 20 

effective gain of the system, variation 
in, 346 

Gas-discharge tube, 300 
General Electric Co., 43, 46, 87, 90 
Generator, slow-sweep, 314, 316, 326 
Germanium crystal (see Crystal, ger- 

Ground clutter, 300 

Hard-tube control circuit, 326 
Harmonic, 197, 300, 335 
second, 83-87 
Harmonic chokes, 174-178 
Harmonic generator, 3-4 
“Harmonic hash,” 298 
Harmonic response, 298 
Harmonic shutters, 174-178 
Harmonics, 61, 82, 286, 301, 372, 374 
Heater voltage, 294 
Hold-in range, 295 
Hum, 349 
Hum pickup, 306 
Hunting, 296, 331 
“Hybrid coil,” 267 


I-f admittance, 71-76, 79, 106, 253, 277, 

I-f amplifier (see Amplifier, i-f) 

I-f capacitance, 129 

I-f conductance. 111, 249, 360 

I-f coupling circuit, 271 

I-f impedance, 256 

I-f output admittance, 90, 173-185 

I-f output lead, 128-131 

I-f resistance, 115 

I-f spectrum, 302 

Image, 43 

Image frequency, 27, 60, 256, 276, 368, 
362, 364, 366 



Image-frequency termination and con- 
version loss, 75-83 
Image reflection, 367 
Image response, 26 
Image termination, 62 
Impedance, cold, 9 
i-f, 266 

Impedance loss, 66, 68, 80, 89 
Impurity centers, 49 
Incremental method, 103 ^ 

Input admittance, 66-71, 122 
Insulators, 48 
Interference, 276 

Intermediate-frequency amplifier {Bee 
Amplifier, i-f) 

Iris, coupling, adjustable, 164 
with adj\istable choke screw, 165 


Jamming, 193, 300, 331 
JAN-IA specifications, 324, 341 
Johnson, J. B., 11 
Johnson noise, 11, 55 


Keep-alive electrode, 99, 174, 175 
Klystron, 36 

reflex, 37-43, 206, 236, 361 
Kuper, J. B, H., 237n. 


“Lazy man” reversing switch, 333 
Leakage, 198, 199 

particularly troublesome in AFC, 299 
line, coaxial-to-wavegiiide transitions, 

Lighthouse tube, 18, 29, 33, 35, 46 
triode, 290 
littelfuse, 18 
Llewellyn, F. B., lln. 

LO {see Local oscillator) 

Load, matched, 200, 206 
Load circuits, containing transmission 
cavity, 215-218 
high-Q, 209-215 
with reaction cavity, 218 
Local-oscillator circuit, 172 
Local-oscillator coupling, 172, 354-356 
capacitive probe, 140-144 

Local-oscillator coupling, channel, 150- 

for coaxial-line mixers, 142-144 
iris for, 160-166 
in waveguide mixers, 144-146 
Local-oscillator coupling mechanisms, 

Local-oscillator drive, 58, 262 
Local-oscillator frequency, ripple in, 318 
Local-osciUator noise {see Noise, local- 

Local-oscillator power, 57, 115, 275 
Local-oscillator tubes, table of, 40 
Local oscillators, 3, 35-37 
channel, 232 

frequency control of, 290-351 
Locking, 246, 292, 302 
Loop, 168 
Loss, 58, 115, 353 

conversion (see Conversion loss) 
impedance, 66, 68, 80, 89 
transmission, 169 
Lumped-constant circuits, 25 
Lumped-constant circuit elements, 27 


Magic T, 7, 259-262, 363-365 
equivalent network of, 264 
matching of, 262-264 
voltages and currents in, 264r-269 
Magnetron, 290 
Manual tuning aid, 342 
Matching, 261 

Measurement (see quantity to be meas- 

Mechanical shock, 96, 100 

Merit, figure of (see Figure of merit) 

Microphonics, 349 

Microwave receivers (see Receivers, 

Miller, J. M., 328 
Mixer circuit, basic, 120-122 
Mixer tubes, 28 
Mixers, 3, 119 

AFC, double-balanced, 283-287 
balanced, 257-289, 301 

crystal mounts for, 279-283 
Magic T, 269-279 
simple, 257-259 
broadband two-channel, 231 
coaxial-line, with loop coupling, 180 
complete, drawings of, 180-189 



Mixers, crystal, 34, 56 
circuits for, H9-189 
double, 194 
double-balanced, 286 
four-crystal, 283, 301 
high-loss, 122 
iris-coupled, 183 

measurement techniques for, 352-374 
multiple-function, 190-234 
examples of, 223-234 
resonant, 122 
for 10-cm band, 188 
single, 299 
triode, 28-32 
two-channel, 199-201 
waveguide, 188 

local-oscillator coupling in, 144-146 
for 10-cm band, 171-172 
Modulation, velocity, 36 
Modulation method, 101 


Nibbe-Durand AFC, 333, 337 
Noise, Johnson, 11 
local-oscillator, 236-256 
effect of, 235-237 

effect on over-all noise figure, 239- 

generation of, 235-237 
magnitude of, 237—239 
reduction by resonant filters, 243- 

reduction by use of a cavity, 246-249 
by Til cavity, 241-243 
suppression of, 257 
random, 10 

Noise diode, 109, 264, 359, 367 
temperature-limited, 101 
Noise figure, 10-17, 29 
in cascade, 16 
of combination, 14 
effective, 13 
measurement of, 15 
over-all, 15, 249 

effect of local-oscillator noise on, 

effective, 16, 17, 43, 58, 100, 235, 
250, 263 

measurements of, 356-361 
Noise generators, 236 
crystal, 363 

radio-frequency, 361—364 

Noise spectrum, 236 
Noise suppression, 247, 270, 273, 276 
Noise temperature, 16, 235, 359 
of crystal, 58, 93-96, 100, 115 
measurement, 105-111 
Nonhunting, 295 
North, H. Q., 46, 87 
Nyquist, H., lln. 

Nyquist theorem, 296 


Oilcan tube, 18 
'‘On-off’' principle, 294, 331 
Oscillation, 90 
Oscillators, beating, 3 
phase-shift, 344n. 
reflex, 292 

Output admittance, i-f, 90, 178-185 
Output lead, i-f, 128-131 
Overload, 206, 207 
Overshoot, 335 


Padding, 219-223 
Peak-to-peak separation, 304, 310 
Phase-shift oscillator, 34471. 

Polyiron, 198, 199, 285, 301 
Power, local-oscillator, 57 
Precision reference cavity, 342 
Preselection, 6, 8, 27, 43, 123 
Preselector, 2, 23 
Pre-TR switch, 175 

Probe, capacitive, as local-oscillator 
coupling, 140-144 
Production tewts, 352-354 
Pull-in range, 295 
Pulling, 290, 317 
P\illing figure, 203, 206, 213, 291 
Pulse radar, 4 
Pulses, 4 

stretching of, 306, 312 
Pxishing, 291 
Pushing figure, 291 


Quality, 100 


Radar, puls<s 4 

Radio Corporation of America, 43 



Radio-frequency amplifier (see Amplifier, 

r-f ) 

Radomes, 291 
Range-set control, 316 
Raytheon Manufacturing Co., 43 
Reactance tube, 292 
Receivers, 1, 2 

crystal-video, figures of merit of, 64-56 
figure of merit of, 10-17 
microwave, classification of types of, 

noise figure of (see Noise figure) * 
superheterodyne, 3, 24-26, 236 
superregenerative, 46 
Receiver unit, complete, 1 
Reciprocity, 64, 66, 74, 87, 371 
Reciprocity theorem, 63n. 

Rectification, physical description of, 48- 

Rectification efficiency, 207 
Rectifier crystal, 47-118 
Reflex klystron, 37-43 
Reflex principle, 36 
Rcflexing, 314 
Regenerative detector, 45 
Representations (see component repre- 

Resistance, back, of crystal, 54, 113, 297 
Resistance, i-f, 116 
spreading, of crystal, 51, 91 
Resistance card, 197, 231, 301 
Resistor disk, 141, 149, 206, 356 
Resonant stub, 176 
Rieke diagram, 203, 211 
R-f amplifier, 2, 23, 43 
R-f envelope viewer, 97, 373 
Rr-f switch, 369 
Ripple, peak-to-peak, 321 
Roberts, S., 77 
Rochester, N., 319 
Roder, Hans, 304 
Rotary joint, 291 
RT switch (anti-TR), 10 
Runaway, 324 


Scaling, 119 
Schwinger, J., 156, 201 
Search stopper, 314, 317, 326 
“Second chance*' feature, 338 
Seeley, S. W., 304n. 

Self-protection of mix6r crystal, 172-^174 

Selove, W., 308?il 

Semiconductors, 48 

Sensitivity, 10, 21 

Separation, peak-to-peak, 304, 310 

Sharpless, W. M., 83n. 

Shock excitation, 298 
Shutdown, 176 
Shutters, harmonic, 174^178 
Sideband, wrong, 294, 314, 331, 332 
Signal, minimum detectable, 10, 21-24 
Signal-input drchit, 166-171 
Sink, 204, 206, 208 
Slow-sweep generator, 314, 316, 326 
Spectrum, i-f, 302 
Spectrum analyzer, 347, 373 
Sperry Gyroscope Co., 43 
Spike, 8, 97, 98, 300 
Spike-blanking circuit, 300, 314 
Spike energy, 99, 111, 174, 373 
Spreading resistance, 92 
of crystal, 61, 91 
Stabilization, frequency, 292 
inverse-feedback, 325 
Stability, 290 
frequency, 212 
Static, 10 

Static discharge, 115 
Strandberg, M. W. P., 308n., 347, 349w. 
Superheterodyne receiver, 3, 24-26, 235 
Superregenerative receiver, 45 
Susceptance, 360, 369 
Switch, r-f, 369 
RT (anti-TR), 10 

TR, 9, 70, 78, 96, 97, 114, 172, 353 
Sylvania Electric Products Co., 118, 

Symmetry control, 304 

T-junction, 155 
jS-plane, 260 
fT-plane, 260 

Temperature-limited diodes, 109 
Terman, F. E., 294, 312 
Test mount, 206 
Tetrodes, 44 
Thermal agitation, 10 
Thermal strut, 292 
Thermal time constant, 293 
Thermistor, 18’ 



Th6veniii^s theorem, 320 
Time constant, 331 
Tolerances, 114 

Torrey, H. C., 76, 77, 91, 92, 111 
TR-aided tuning, 170, 173, 280 
TR cavity, 28, 72, 139, 157, 162, 166, 174, 
179, 224, 266, 276, 358, 364 
equivalent circuit for, 167 
output loop of, 168 

reduction of local-oscillator noise by, 

TR leakage, 192, 201 
TR leakage power, 173, 372 
TR switch, 9, 70, 78, 96, 07, 114, 172, 353 
Transit-time effects, 17, 34 
Transition, capacitance amplification in, 

'IVansmission loss, 169 
Transmitter sample, 206-299, 30 1 
coupling of, 196-190 
Travis, C'harles, 304 
Travis circuit, 304 
IViggor circuit, Eccles-Jordan, 333 
Trigger shaper, 349 
^IViode, 35, 293 
Tube mount, 146 
Tuning, 70, 123, 293 
ele(d,ronic, 38 
fixed, 123, 134-136 

Tuning, TR-aided, 173 
Tuning range, 2 
Timing screws, 132 


University of Pennsylvania, 95 
Up-pull rate, 319, 322, 325 


Velocity modulation, 36 
Velocity-modulation tube, 290 
** Video hash,’^ 298 
Video pulse, 297 
Video unbalance, 307 


Waltz, M. ()., 83, 237n., 366 
Wavegui(le-to-coaxial line transitions 

Weiss discriminator, 305 
theory of, 308-312 

Weldcd-contact crystal (see Crystal, ger- 
manium wclded-contact) 

Western Electric (^o., 43, 118 
Whitford AFC system, 332, 333, 337, 339 
Williams, F. C., lln. 

Wolljiston wire, 18-19