Skip to main content

Full text of "The circumferential propagation process for the magnetization of tape wound cores"

See other formats




Institutional Archive of the Naval Postgraduate School 


Calhoun: The NPS Institutional Archive 
DSpace Repository 


Theses and Dissertations 1. Thesis and Dissertation Collection, all items 


1963 


The circumferential propagation process for 
the magnetization of tape wound cores 


Davis, George W. 


Monterey, California: U.S. Naval Postgraduate School 
http://ndl.handle.net/10945/11776 


This publication is a work of the U.S. Government as defined in Title 17, United 
States Code, Section 101. Copyright protection is not available for this work in the 
United States. 


Downloaded from NPS Archive: Calhoun 


Calhoun is the Naval Postgraduate School's public access digital repository for 
| (8 D U DLEY research materials and institutional publications created by the NPS community. 
«ist sia Calhoun is named for Professor of Mathematics Guy K. Calhoun, NPS's first 


NY KNOX appointed — and published -- scholarly author. 

ia) LIBRARY Dudley Knox Library / Naval Postgraduate School 

411 Dyer Road / 1 University Circle 
Monterey, California USA 93943 





http://www.nps.edu/library 


NPS ARCHIVE 


1963 
DAVIS, G. 





THE CIRCUMFERENTIAL PROPAGATION PROCESS 
FOR THE MAGNETIZATION OF 
TAPE WOUND CORES 


GEORGE W. DAVIS 




















78 


THE CIRCUMFERENTIAL PROPAGATION 
PROCESS 
FOR THE MAGNETIZATION OF TAPE 


WOUND CORES 


kK KE SK 


George W. Davis 





THE CIRCUMFERENTIAL PROPAGATION 
PROCESS 
FOR THE MAGNETIZATION OF TAPE 


WOUND CORES 


By 
George W. Davis 
U4 


Lieutenant, United States Navy 


Submitted in partial fulfillment of 
the requirements for the degree of 


MASTER OF SCIENCE 


IN 
ELECTRICAL ENGINEERING 


United States Naval Postgraduate School 
Monterey, California 


HP lo) 7) 





tater? — — DUDLEY KNOX LIBRARY 
U. 9. Naw yiimeiiii Scloo” =WAVAL POSTGRADUATE SCHOO! 
fornia MONTEREY CA 93943-5109; 


Rn . Leer | 
sae 4 ‘ # 


THE CIRCUMFERENTIAL PROPAGATION 
PROCESS 
FOR THE MAGNETIZATION OF TAPE 
WOUND CORES 
By 


George W. Davis 


This work is accepted as fulfilling 
the thesis requirements for the degree of 
MASTER OF SCIENCE 
IN 
ELECTRICAL ENGINEERING 
from the 


United States Naval Postgraduate School 








ABSTRACT 

A theory is developed describing the process by which a signal 
induced at one point on a ferromagnetic toroidal core propagates to 
other locations about the core. Both qualitative and quantitative 
arguments are presented to support this description. Am experiment 
is discussed which tests the proposed theory. A complete analysis of 
the results of this experiment is made and includes a quantitative 
comparison of the measured results with those predicted by the theory. 
In as much as this comparison shows excellent agreement between the 
experimental results and theoretical predictions, the proposed theory 
appears to explain quite adequately the circumferential propagation 
process in magnetic cores. 

The author wishes to express his appreciation for the assistance 
and encouragement given by Professor Charles H. Rothauge, and Mr. 
Raymond B. Yarbrough of the U. S. Naval Postgraduate School and of 


Mr. Bernard M. Loth of the Lawrence Radiation Laboratory. 


Li 





Section 


TABLE OF CONTENTS 
Title 
Introduction 
A Theory on the Circumferential Propagation Process 


Experimental Verification of the Circumferential 
Propagation Process 


Analysis of Experimental Results 
Conclusions 
Appendix I 
Appendix IT 


Bibliography 


iii 


Page 


17 


22 
34 
36 
47 


49 





Figure 


2-1 


ee 
Nee 
2-4 
2-5 
2-6 
1S 


3-1 


3-2 


4-1 


4-3 


4-4 


4-5 


LIST OF ILLUSTRATIONS 
Title 


Radiation Pattern for a Single Current Carrying 
Conductor 


Radiation Pattern within a Thin Ring Magnetic Core 
Derivation of Core Trigonometry 

Theoretical Propagation Curve for Impulse Signal 
Normalized Magnetic Field Attenuation Curve 
Representation of a Ramp MMF Function 


Theoretical Propagation Curve for Ramp MMF Signal 


Equipment Arrangement for Measuring the 
Circumferential Propagation Velocity 


Oscilloscope Presentation of Signal Pulse 


Comparison of Experimental and Theoretical 
Propagation Curve for a 225 A-T Pulse 


Ramp Function Idealization of MMF Pulse 


Comparison of Experimental and Theoretical 
Propagation Curve for a 117 A-T Pulse 


Comparison of Experimental and Theoretical 
Propagation Curves for Pulses of Various Rise Times 


Normalized Predicted and Experimental Attenuation 
Curves 


LV 


Page 


11 
12 
14 


18 


20 


24 


25 


27 
29 


33 





iM 
_ > Se () eee aS 


= —_———— —————— 
4 a 
@ _ “=o « oS — 


— 9 9 eee eta 


=-—= @& © © a> & 























Fon] 










a ee ol oe 
_ as oD -= (ee 


> «* == eS a a [ea la 


: — 





1. Introduction 

There is a relatively large volume of information in today’s 
literature explaining the processes believed to occur in the normal 
magnetization or "switching" in tape wound ferro-magnetic cores. Since 
most of the interest has been eeneeen around the magnetization in small 
cores with uniformly distributed windings, little information is avail- 
able on the process this author chooses to call "the circumferential 
propagation process"; that is, the process by which a signal induced at 
one point on a magnetic core migrates to other points about the core 
circumference. Such a process is not normally of consequence when the 
core has a uniform distribution of windings since the signal is in- 
duced at all points about the core circumference. When large diameter 
cores are to be used in very fast pulse circuits, such a process becomes 
quite important. To illustrate this point, assume that a core of diameter 
25 cm is excited at one point by a single turn primary. If the signal 
traveled on or in the core at the speed of light, it would arrive at a 
secondary winding placed diametrically opposite the primary after a 2.5 
ns delay. One would guess that the actual velocity of signal propagation, 
that is the circumferential propagation velocity, would be somewhat less 
than the speed of light. If the velocity were an order of magnitude less, 
a delay of 25 ns would result. A 25 ns delay is somewhat longer than 
rise times encountered in modern high power pulse circuits. Even though 
these delays are significant in such circuits, this author could find no 
published reference explaining or even theorizing on the process by 


which a signal might propagate from the region of an exciting winding to 










ee 
a _—— ££, - — _ 
= ——_— ©  =-_ mee toma foe om hom 
- 2 1 Ce cD a ” 

© @& =a ==) ee «(eT oben 


-— —_—— « Ga ae = 
























— 
















o—— ———— —e her @ 
a — ee cee | im oe 
ly i le i li il, Ais ayy ee om 
————— _ —e sete elses VY GG cee im 
—_ = Sa Pe ee | 


= 








= <_ —————— a ©» — Faas 
ee @ fe - —  —_—_——-—-— — a | 36 





a Se ae =a SS - 7 ww! a hit a — 











-_ - « ‘ oe hee 6 OD @ ake eo 
_— -_ =? ee Cee a el 
—_- — = — a aN ast * 

ia ° —— TT i deny 





- _- °° —- ey = ee + ea 


other locations about a magnetic core, It appears that further improve- 
ment in high power pulse circuits might well depend on an understanding 
of this process. Therefore, it is the intent of this thesis to develop 

a theory, based on presently accepted ferro-magnetic concepts (such as 
those presented in reference 1) to explain the process of circumferential 


propagation in ferro-magnetic torroidal cores. 








2. A Theory on the Circumferential Propagation Process 


2.1 Development of the Theory 

Under the action of an applied field, flux reversal in magnetic tape 
begins with the formation of domains of reversed magnetization, In the 
normal polycrystaline magnetic tape, these domains form at crystal imper- 
fection such as voids, inclusions, etc. on or near the tape surface; 
then grow inward into the tape. The formation of these domains, the so 
called nucleation process, requires a certain minimum applied field and 
hence energy. Once this nucleus of reversed magnetization is formed, it 
expands by domain wall motion at a rate dependent on the magnitude of the 
applied field. As these domain walls grow, colliding and consolidating 
with those from neighboring nucleation sites, the region of reversed flux 
continues to enlarge. This process will continue until either all of the 
flux in the tape has been reversed or the applied field is reduced below 
some minimum coercive force. (1) 

While the above constitutes only a very brief description of the 
magnetization process, two concepts essential to the development of the 
subject theory are introduced, First, the nucleation process will take 
place whenever a suitably oriented applied field at a nucleation site ex- 
ceeds some minimum magnitude. Second, provided the applied field is 
maintained above some other minimum value*, the domain wall will grow into 
the tape from the nucleation sites. Hence, there exist only two modes by 
which a signal induced at one point on the circumference of a magnetic 
toroid can propagate to some other point on the core. Once applied, the 


signal must either travel internally by means of domain wall motion or 


*The applied field necessary to move a domain wall is less than chat 
required to form the wall. See reference (1). 


3 







-——— —— « 
ee al ta 
oe —— Ki — = am 
he eee tee 
°_ —_. — 
—_——.— 
aw eh aie a 
~—<—-- «~~ © | 
a= — ¢ =r“. .<26 
cS 6 a ame Qe 66 
a 

—_ et eee Magee ie 
mm ee 
- —— —_ es ae 
— - ——_— =- — SS — ome 9 (a om 








= 
s ’ és 
r 






















‘> Se Sey Cee Gee fee 
-— —_ a a a Gee 
= _ ——_ Coe — —_ a ee 

— SS | RO oh 

_— 2 eee ee Fi 
—- | — — ee " 2 ee “Ce me a «eg « 


_-_ = pes eEEe eS ea 


_ > =—_ aes eee 





over the surface in the form of an E-M wave originating flux reversals 
at surface nucleation sites wherever they occur in the path of travel of 
the wave. 

Domain wall motion constitutes a linear transfer of energy in the 
direction of this wall movement. Since this energy is supplied by the 
magnetic forcing field, the direction of transfer must be that of the 
Poynting vector associated with this field. Therefore domain wall motion 
is in a direction perpendicular to the applied magnetic field. This 
domain wall motion is always accompanied by eddy currents which circulate 
in accordance with Lenz's law in such a manner as to oppose the applied 
field. These currents increase with increase in wall velocity, thus creat- 
ing a requirement for higher applied fields to maintain the initial wall 
motion, A signal, then, could not be propagated in the circumferential 
direction by this mode if the applied field were always parallel to the 
core lamenations. Certainly the leading edge of the signal wave has a 
component of its Poynting vector in the direction of the lamenations (or 
else no energy would ever transfer in this direction) and hence it is 
possible for domain growth to occur in such a direction. However, this 
growth is severely damped by the eddy current effect and its rate of 
propagation is many orders of magnitude less than that of the E-M signal 
wave over the surface of the tape. 

Finally, the propagation velocity of a domain wall is directly related 
to the applied field. Hence, if the induced signal were propagated in 
this manner, the propagation velocity would be dependent upon the magni- 
tude of this field. (2) That this is not the case will be shown experi- 
mentally. 


From the above, it must be concluded that the signal applied to a 


4 




















=> = =p © & 
= , to - Zi min yt 


et © cee = © ee See oe oe 6 


— i | 

















— 7 - ee 
—— =a oe 8 - en 
- ; Si ——_ 
—— a | + 
a 7 ee wel eel ae 
~ 9) ca — in, — i ill le 
— car . 
: “= —_= |e ee | 
. a i 
| oh) eae, - 
- — a a 
—- P <i je 
_ ——_— > oa 


core is propagated from the point of application to the various points 
about the core by an electromagnetic wave. The signal radiates from 

the exciting winding and becomes evident in the core whenever it reaches 
a nucleation site with a suitably oriented component of its magnetic 
vector greater than the nucleation force required by the site. This is 
the manner in which the signal must make its circumferential progress. 
Since the E-M propagation velocity is independent cf its amplitude, the 
signal applied to a toroidal core will likewise be independent of signal 
magnitude. Those factors which affect the time of transmission of the 
E-M wave from the exciting winding to outlying points on the core will 
also affect the time of signal transmission to the various points about 
the core, These effects have been investigated experimentally and the 


results are included in chapter 4, 


2.2 The Propagation Process(for an Ideal Impulse Signal) 
To illustrate the above theory graphically, consider the radiation 


from a single current carrying conductor as shown in figure 2-1. 





Fig. 2-l(a) Cylindrical Radiation Pattern for Impulse of Current 
in a single Conductor (b) Decay in Magnetic Field 
Intensity as a Function of Distance of Wave Travel. 


5 





















| 


7 


— ee 15° =a ow 
@ @& _ 5 = ames 


SS eG 5... eS —— 


——_— <=? 
a, _— 2 








— nl = ae) Q———-» 









— —| «— >= a 
7 


-—— -_ a -_— — oe 
——— ££, oe | = —- « 
- — EE  e 
= — 
 —=> <«/! = = 7 
ae = = « 


* =——- << —_— = Gea 


If a unit impulse of current is applied to the wire, a cylindrical pulse 
of magnetic field propagates radially outward at the speed of light. (3) 
The magnitude of this pulse field decreases in amplitude as the inverse of 
its radial distance of travel, as predicted by Ampere's law. This magni- 
tude decay is illustrated in Figure 2-l(b). This attenuation can be 
thought of in terms of a thinning out of the energy radiated in any one 
segment of the cylindrical field. Once this energy has been committed to 
a particular direction of travel it remains so directed as long as it is 
in the same medium.* Hence the energy density becomes less at the more 
remote points in space. 

These ideas can now be applied in the analysis of magnetization in 
a large diameter magnetic ring as shown schematically in Figure 2-2 below. 
When an impulse of current flows in the exciting winding, a radiation 


pattern similar to that described above results. The characteristic of 





Fig. 2-2 Schematic Representation of the Magnetic Field Radiation 
Pattern Within a Thin Ring Magnetic Core. The Pattern is 
Produced by an Assumed Impulse of Current Through the Single 
Turn Exciting Winding. 


*The direction of energy transfer will be altered when the E-M wave strikes 
the core, 















i Ss a 
———-—— a <= 
><a ' 
es & 4 RP. 

eo = — eee 
—  —_—_-_—-- «eee 
¢C——————— St 6 ees 
«<8 «+s. —_— «& 


ee Ss === eas © e® « 
— — = re ee ie | eae 
> — = © (| == i Oe - 








this process that is of most interest in this discussion is the time 
required for the applied signal to reach points A, B, C, etc. about the 
core. The relationship between these time increments and the are distance 
of the points A, B, C, etc. from the exciting winding will yield the ap- 
parent circumferential propagation velocity. This apparent velocity can 
be examined in the light of the proposed theory as follows. By trigono- 
metric manipulations as shown in Figure 2-3, we can obtain the arc lengths 
OA, OB, OC, etc. as functions of time elapsed between application of 


the impulse and the arrival of the impulse signal at any point on the core. 


diameter of core 


NR Guwcud de st) d 


it 


Sin ae = = (2-2) cA. = half angle subtended by an arc 
with respect to the toroid center 
or a = Ca ch Cc = velocity of light 


By solving the above equations graphically with an assumed core diameter 
of 40 cm, the plot of arc length against elapsed time shown in Figure 2-4 
was obtained. The slope at any particular point on this graph represents 
the apparent circumferential propagation velocity for the corresponding 
location on the core. Obviously this slope, that is velocity, is not 
constant even though the energy associated with the signal travels over 
the chord lengths at a constant rate. In fact, this apparent point 
velocity must approach infinity as r approaches the diameter of the core. 


This can be shown by substituting sin! ch for o0 in (2-1). Then: 


Are = d sim. of 


differentiating arc length with respect to time to obtain apparent propaga- 


tion velocity: 











Pe £- 38 DERIVATION OF Coes 
“TRIGONoOmM ETRY 





tt Pi ee 
ECHECHECEECE EEE Srsias 




































4 
ab - sseties 
be a oan on 
crise ae 
- | P-L tt 
N - HH ze 4-4-4 
a 
- \a om Ebel Fe 
srersesenaracce EEE EEE 
= i CES PEE Sea 
7 PEEP mbelot=folal Sune EL ssa a 
EERE i ee Se --L = 
pooh SUESHRAEAEEECEEESCE set ail = 
ea aise th PEEPS EE : 
enn Seer sale Ae Ee ise tk SSSReEeeuEE 
= acsdastesfanteatactecttctprttets GH aE . 
‘Sianeaaeeee CEE PEE eh FEECN Soper ec ceSETUSSBEreGeeesrace ~ 
EPEC eousaossoesssessseres PEELE EEE SuSaererevensenszei 
eee SEER ECE PEEEEEEEEEE HEE EEE PREECE Har] 
rh fd eee ae 
= =a . aa ar ha ae we 
CHECEE HEE ieee eee Gere 
“FERRE PEE an Soabeascatostentastestastons oO 
Settee ZEEE PEEEEE EEE EEESEEENE EE PEE 
PEERS PE cle ere EN elu coer | 
ie a PHT Hj HH HS Fae et SE REE I 
He EIE: Senne eras 
S robiare elon BEER saa le lt -E HE 
Sapxn aie Sere a Sal oP a S 
|e eae Neue 
A a CS : at EI ole icl atcha | 
PERE | res a PEE | 
= : Sia r — 
Saree tee Sreeetests: 
FEELERS EEE BE No 1s | 
O0eN =e ae pit) ELT Lt i et | 
see aHESHEES TEE eH 
fbb EE HEE HH pet J HEE 
TT HERE EEEEEEEEEEEEEEEE HE vane 
PEER SEE EEE PEEP Eee cone ae 
ias! mele ia a uF Feat oma fe tpt | ele et em ladle | 
rai i FEEEEEEEEEEEEEE EEE PEEP im ot ty 
srsrarie essai toed iecaetonadfasastize Fo 
BEC ERE CE REE EEE FEA 8 | 
fe a NEES 
CCE eBee ea ele EERE EcrEEEE - : 
SEERA BEEN 
Sasuneusnaana\ 


+ ee 
Sunasesea elalalahahe = fe 

=r Sint eran AR } 

hl ll HL EEE 


| ce t Fe = 
ee 
~ De cee aaa 

mimpt tt EL 


9 








C 


dire = Tre d = Apparent Velocity 
ol 
App. Vel. = ——— => DUES CEy—— 
ia 
Cc 


Se (2-3) 
V1— Gy 
A 
This expression goes to infinity as r approaches d. 

The amplitude of the signal (or the energy) arriving at the points 
A, B, C, etc, around the core varies inversely as the chord length of 
travel. Using the trigonometric relations introduced earlier, Figure 
2-5 was constructed to illustrate this decrease of signal amplitude with 
increasing arc length. 

In the above discussion, second order effects or signal noise 
resulting from reflections of the H field from the tape surfaces have 
been neglected, This is justifiable in the first approximation since 
they cannot effect the arrival time of the radiation at remote points 
about the core. Also, the magnitude of these reflections should be 
small since the reflecting surface is a lossy magnetic material. None- 


theless, they may be apparent as oscillation in the signal. 


2.3 Propagation Process for Signals with Finite Rise Times 

In the above discussion a.unit impulse of sufficient amplitude to 
cause nucleation at the furthest point on the core was assumed, In 
reality, the signal cannot show the abrupt discontinuity of the unit 
impulse but must be accompanied by some finite rise time. This alters 
the results of the above in a small but important way. As was pointed 


out earlier, the signal amplitude (or energy level) must exceed 2 


10 







a ee OU O Sa 
——— ae freee 6! 
— SS ao 
— — —— Cie 
7 “ar graib« 
-_ ee — 
— A 
~~ © (ant ee D 
; "<9 == ae 
i SP ee Ss ey a 
. —_—— = oa | 
- —— tot 1 ia, 
_ —_— = a ee a 













al 


















| BRIG EEE EEEE EEE EEE EEE EEE EEE PETE PERE 
EU eerste gece ge GUE ESE 


seansesenane ale pt Siiep ap eatirti 
PERE eee ecmaay | He =| 


ene +b Er SE Minidde hicms 5 


Tees dnecorhes | 


ge tele 

etl tines BREE 

ae ee a Saar, WRNIE sits tae | a ial 
SRE Se Vela alia eae le Ts 









ee EEE 

















eg Meade 
: Spee 
: : FECES 


PERE EEEEEEE CECE EEEEEEEEEEEE EEE EEE 





! NE a [J ER! a * 
{ + i Se ee b- : Pa ame 
' 


i 
Mee 


‘ae 
Bene Ree oa 


SeSnEEe BRRMRBEMBE! 
PEPE BEREEEEE EEE EEE EEE EEEEEEEE EE 
Be Rn eR RR oo ee —- = ime ae 


a 









: 
F 


te [Seale a 


- 





Pee ENED TRANVAE pees Tine Wino neste 


a > aaa BEciceie ot feseateeeeteeeceees beeen 
1) 


| <raoom 


© 





certain minimum level before nucleation can take place. Hence, when 

the finite rise time of a realistic pulse is encountered, a certain 
delay will result while this pulse increases from zero to the minimum 
nucleation requirement for each point on the core. This delay is ampli- 
fied by the decrease in pulse magnitude with increase in radial travel. 
To illustrate these two points, consider Figure 2-6. A ramp of current* 
is assumed to be applied to the exciting winding to produce the magnetic 


intensity pulse shown in the figure. This pulse can be expressed as a 


; 
to 


tx 


Fig. 2-6 The Ramp of Magnetic Field Intensity Resulting from 
a Ramp Current Function Showing H Critical and Hx as 
a Function of Time. 


function of time in the following manner: 


H = a = — (2-4) Where K is the slope of the applied 


ramp of current in the units of amp- 


turn per second, 


*As was the case with an impulse, a true ramp of current cannot be 
realized. However, the ramp is closer to reality than the impulse 
and serves well to illustrate the pertinent points. 


12 








If H crit is defined as the minimum magnetic intensity level which must 
exist at some point X on the core in order to produce nucleation, then 
the magnitude of this critical field at the exciting winding must have 
been, (from Equation 2-4) 
H crit = i: Where r_ is the chord distance from 
2nr x 
the exciting winding to point X on 


the core. 


Solving fort: 

k= a aaa (2-5) 
Thus, the time Ee must expire after the application of the ramp current 
function before a field of sufficient initial magnitude to cause nuclea- 
tion at some point X on the core is radiated from the exciting winding. 
An additional time, defined as At, must elapse while this H field 
travels the distance r to the nucleation sites at point X on the core, 
Again referring to the trigonometric relations of Figure 2-3, a relation- 


ship can be developed between core arc length and the total elapsed time 


from application of the ramp to nucleation at points on the core. 


arc =qd and smde oe — 


vy =Kty and Tretar= tz + At 
By assuming a value of K' and using r as the independent parameter, a 
graph of arc length as a function of total elapsed time can be construct- 
ed. The slope of this plot will represent the apparent circumferential 
propagation velocity for the ratio of signal slope to coercive force, K'.* 
For the sake of concreteness, a value of K' = 3.33 = is assumed, For 
artitrary value of Es and Z\t, and hence T total, arc length can be 
calculated. A plot of values so obtained is shown in Figure 2-7. 


*The derivation of numerical values for K' will be discussed in Chapter IV. 


1b 








= Oe ee 6 im 
7 i ee | 
v ‘—_ =—iee «= 











a tn li Ti << 
oo © = ee ee eee 9 ee 


. —_° =e 
Se See 













































































EEE 
cae 
rE a saaunneg SEEREEEEE 
fa FF 
 _ 
ee ae 
SEE aes re FcrECECEE CECE SEE EEE EEE 
SSS peeanngaa 
a a serezaaze 
ESE ee rEEE i 
soeeteastets oe ESHER Heer 
oe | 
| [ 
| 
HEHE | 
aa HE ee eerie 
esalisensuezeee BILESeEEEEE a ee 
a init ESE 2 EEE aa ESSEC 
srentorstiis sseerezects EEECENCEPEEEEE SEES 
a SEE sai tt PEEEEEEEEEEEEE cereeeT ele 
es = age eaeareiit 
Ht PerHES ieee SHEESH Nee SHULL CoH at 
if chee ane 
 . 
aii ieaii Ssrent — 
# e ear He a 
f SHE scsavate PEEEEE CEE EE Seopa EHEC 
eee oe ae 
tE jute eerie a Sees seer 
THEE fe Siberonets SESEESEEEE Eaeagentei 
crt Se ESN Eas 
- Le SEH CHEE SS ie 
EEEEEEEN 7 sC 
EEE PECRBEE See gee PEEP sanaue 
eat eee strate EERE REEEEE FEENCEEH 
- PELE EEE : srstosestoriss Seat ch 
see Ee a HaTaEEAS 
Slate ieaiaie tale coe ale ieee iii PCC es t-\ 
Hiicedaiesstastic made ere ce EEE 
Euuaeae emia 


14 





The relatively long delay in the arrival of the signal at points about 
the core is obvious from this graph. Comparison with Figure 2-4 shows 
the total time required for an impulse signal to reach the point on the 
core diametrically opposite the exciting winding is only 1.3 ns while in 
the case of the ramp pulse just considered, the time required was over 
13 ns. This large difference in time is clearly the result of the slope 
on the ramp pulse. 

At this point, it is appropriate to bring together the various ideas 
presented and to sketch a single picture of the circumferential propaga- 
tion process. The proposed theory suggests that all signal transmissions 
from the exciting winding to other points on the core takes place by means 
of an E-M wave propagating across the inner core diameter at the velocity 
of light. However, the intensity of this wave attenuates at a rate 
inversely proportional to the distance of travel from the source. If 
consideration is restricted to signal pulses having finite rise times,* 
then it can be shown that this attenuation becomes a major determinant of 
the apparent propagation velocity. Recall that domains of reversed magnet- 
ization are formed by the nucleation process providing that the magnetic 
field intensity at the nucleation site exceeds some minimum or threshold 
magnitude, Therefore, the signal level at the exciting winding must exceed 
this minimum nucleation field by the appropriate attenuation factor if it 
is to cause flux reversal at some remote point on the core. Since the 
signals being considered have a finite rise time, a delay will result 
while the signal reaches this “remote nucleation level" (that is, an 
intensity level which includes both the minimum nucleation field and the 


attenuation factor). This delay will increase with the distance from the 


*Any physically realizable MMF pulse will have a finite rise time. 


15 












= | 
_— mea — 
—e eS —<_ 
——_ < | = € <a 
a me 
AP @ 6 rea) a 















—- —s- = ae oe 6 


aaa -. —_a——-< 


(Bs oma - Oo a> 
ad => —_> 
—_-— —————— SS a CF ere 


= 
a nee ea ai it = =a 


> *& ==> Ga 6 aa) 
—-— - —_ ° ce, — aaa i oh a 
-_ a GZlcmaian 
’ -_ = - — 


- ad ——_— ae <a” 


exciting winding and will thus give an apparent retardation to the 
propagation velocity. This is readily seen by comparing Figure 2-7 with 
Figure 2-4, Figure 2-4 illustrates the time required for a pulse with 
zero rise time to reach various points about the core. Figure 2-7 il- 
lustrates the time required for pulse with a certain finite rise time 
to deliver the minimum nucleating field to the various points about the 
core. In the former illustration, a time of 1.3 ns is required for the 
signal to reach a point diametrically opposite the exciting winding while 
in the latter case, 13 ns are required. The difference, 11.7 ns, is 
identically the time required for the ramp excitation to reach the "remote 
nucleation level.'' As far as the core is concerned, it took 11.7 ns 
longer for the ramp pulse to reach the remote point in question than it 
did for the pulse with a zero rise time. Therefore the apparent signal 
velocity of the ramp pulse is less than that of the impulse. 

A general verification of the proposed theory by experiment will be 
considered next. An analysis of these experimental results (Chapter IV) 
will further illustrate the effect of finite rise time on apparent 


propagation velocity. 


16 














= —~s> 


- 
| + = FOE oer 
oP «= i 


=———- —— 6 ts hs 


Oo cee ee ee ee 
6 ee © @§ 1) a et 
Am me me ee mmm en) mn, : 
> *. =a wid bee Fm 
am — a ae 
= =) —P> © @ SH ie 
a ™->—  —EE———_ == «& 
er —& —- lh OE etme 
—— ee ee rey 
Le 


= ( -° ee Gp -¢ 
> —- ~~  ——_~€,~—~.. ail *_ mai a 

_ <7 | cs seas 
| 


oe 






3. Experimental Verification of the Circumferential Propagation Process 


3.1 Purpose 

This experiment was designed to measure the circumferential propa- 
gation velocity defined in Chapter I and to observe the effect of varia- 
tions in pulse amplitude and rise time on this velocity. A comparison 
of these measurements with those predicted by Chapter II will be made in 


Chapter IV. 
3.2 Procedure 


The general procedure used to measure the signal velocity was to 
induce a fast rising step of current in an exciting winding located at 
one point on a magnetic core and then measure the time required for 


this signal to become apparent at other points about the core. 


3.3 Equipment Setup 


To carry out this procedure, a thin ring of 1 mil Ni-Fe tape with 
a ring cross section of one-half square centimeter and a mean magnetic 
path of 127 cm was wound with a three turn primary and six (6) single 
turn secondaries (or pickups) spaced about the core as shown in Figure 
3-1. A reference winding, designated G, was placed inside the primary. 
A 2 megawatt pulser capable of delivering a 20 KV square pulse with a L5 
ns rise time was used to deliver the signal to the primary. A non induc- 


tive resistance R was placed in series with the pulser to give it 4 current 


17 








Shunt for 
Measuring Pulse Current 


20KV 





Isolation 


V 
Choke 6 

NOh— | — 
———__—_—_—.— 

Variable 


Bias Current 


Fig. 3-1 Equipment Arrangement for Measuring the Circumferential 
Propagation Velocity 


18 








drive capability. The magnitude of the applied current was changed both 
by varying the applied voltage and by changing R while holding the 


applied voltage at 20 KV. 


3.4 Velocity Measurement Techniques 

Various methods for measuring the signal velocity were considered. 

The two methods used were selected because of their simplicity, reliability 
and reasonable accuracy. 

The first method was a photo technique - consisting simply of present- 
ing the output signals from the six pick up windings on a tektronix's 
517 oscilloscope using a common time base for the horizontal sweep. When 
displayed on a multiply exposed photograph, the time difference between 
signals could be measured and compared with the known relative positions 
of the pick ups to obtain the velocity. 

A second method using a tektonix's 576 oscilloscope with dual beam, 
sampling, plug in units presented an even more attractive method of 
obtaining the necessary data. Here, the signal from the reference winding* 
was presented on the "A'' trace with the pickup signals being presented one 
at a time on the "B" trace, The two signals were simultaneously presented 
on the scope face as shown in Figure 3-2, The time difference between 
corresponding points on the reference trace and the pickup trace was record- 
ed for each pickup. The points chosen were typically the time from 507% 
of the peak voltage on the "A" trace to 50% of the peak voltage on the 


"B" trace. A Tektronix's RS 1 digital readout unit was used to automatically 


*It was found necessary to use the signal from the reference winding as the 
common time base for all time measurements. This eliminates the problems 
of accounting for time delays which might result from differences in the 
"A" and "B" channel probe leads. Also, since pulse comparison is the 
method used to determine the time delay, it is necessary that the pulses 
be of similar shape. 


19 








AL ShEace. or 
Reference 
Signal 





is Sage gl 


"B' Trace or Pickup Signal 


Lt = Time delay between 50% 
Level of "A" to 50% level of 
yoy 


Fig. 3-2 Oscilloscope Presentation of Signal Pulses 
read the time difference between the selected points. A plot of the re- 
lative positions of the pickups against the time differences so measured 


readily yields velocity. 


3.5 Variation of Pulse Rise Time 

In order to observe the effect variations in pulse rise time have on 
the apparent propagation velocity, the circuit of Figure 3-1 was altered 
to produce pulses with rise times of 45 ns, 55 ns, and 75 ns. To ace 
complish this, small valved (that is, 1 to 5 ohm) wire wound resistors 
were placed in series with the non inductive resistor, R, of the original 
circuit. This technique satisfactorily produced the desired variations 


without significantly altering the final pulse amplitude. 


3.6 Attenuation Measurement 

An effort was made to determine the attenuation of the signal at 
the various points on the core. These measurements consisted of record- 
ing the peak magnitude of the first voltage spike appearing on the pickup 
signal. Under most circumstances, the spike was quite evident and little 


room for doubt remained as to what relative point was being measured, 


3.7 Summary of Experimental Results 


The above procedures were carried out by successively pulsing the 


20 








core with MMF steps of 225, 168, 117, and 50 ampere turns. The rise time 
was maintained constant at 30 ns. Time delays between the “A' trace 
reference signal and the "B" trace pickup signal were recorded for the 

20%, 50%, and 80% levels of the peak voltages. The position of the 

pickups on the core were plotted as functions of these time delays. Graphs 
1 through 7 of. Appendix I show these plots. The rise time for the 225 a-t 
pulse was altered successively to rise times of 45 ns, 55 ns, and 75 ns. 
Graph #8 is a plot of the apparent propagation velocity for these various 
rise times, Finally, pulse amplitudes at the various pickups were measur- 
ed for each of the MMF pulses listed above. These are plotted in Graph #9. 


Graph #10 is a normalization of the data from Graph #9. 


% 


21 





4. Analysis of Experimental Results 

In an analysis of the results of the experiment described in Chapter 
III, the proposed theory will be examined in two respects. First, the 
results will be used to support the theoretical argument that the circum- 
ferential propagation of a signal by means of domain wall motion is not 
reasonable. Second, the results will be shown to be explainable in termsof 
signal transmission by means of the E-M wave as discussed in Chapter If. 

It was pointed out earlier that any signal propagated by domain wall 
motion would travel at a velocity several orders of magnitude below that 
of light (2). Examination of the experimental data presented graphically 


in Appendix I shows the lowest value of apparent propagation velocity to 


be 0.294 x ng eal This is only one order of magnitude below the 
velocity of light, 3.0 x 10m mat Furthermore, the slope of these 


plots continuously increases as the distance of signal travel grows and 
eventually approaches infinity at the furthest point from the exciting 
winding. Since domain wall motion constitutes a transfer of energy, its 
velocity cannot exceed that of light, let alone approach infinity. Final- 
ly, there is no appreciable change in the apparent circumferential velocity 
with variations in the applied field which is in contradiction to the known 
behavior of domain wall motion. (3) In view of these experimental facts, 
it is evident that the apparent circumferential propagation velocity 
cannot be explained by domain wall motion. 

To show how well the proposed theory predicts the actual experiment- 
al results, a comparison of the theoretical propagation curve of Figure 
2-7 is presented in Figure 4-1 with one of the plots of experimental data. 


There is excellent agreement between these two curves. Not only do the 


22 









SD Nagy ge 
-_ | — » awe 
m_D & @Qniy==>®,. 
- 





— cima, 

> eee <=] 
_ = ie os 
ail - — tet Reames all 
= & ca—H_—— a er aa oie 
- = ee eel ee _sere 
em 6 ee eee 

—_—_——— - cea ag 
> a 6 oe 7 

—_=— eee @ 

a ©) <= ee 





experimental points fall close alongside the predicted curve, but also 
the plot of the experimental data shovs the increase in slope with in- 
crease in arc distance of signal travel as predicted by the proposed 
theory. To strengthen these arguments a detailed analysis of the experi- 
mental results will now be made in the light of the concepts presented in 
Chapter ITI. 

Figure 4-1 shows a predicted curve constructed from measurable geo- 
metric parameters and a somewhat mythical parameter K'. There can be no 
debating of the core geometry as it is real and measurable, However, an 
inspection of the definition of K', 

tiie NennlS 

R= page 
reveals room for considerable disagreement. H critical is the minimum 
coercive force necessary to cause nucleation. The value of He from the 
static hysteresis loop for Ni-Fe is approximately .1 oersted or about 
.085 = . However, since a constant current bias was used to reset the 
core, the reset H field must be overcome before any "Suitably oriented" 
magnetic field can affect the core. Furthermore, the bias current for each 
of the different levels of excitation was altered so as to just insure 
complete reset of the core between pulses. For example, for the 225 a-t 
steps a bias field of approximately 25 a-t was used while for the 117 a-t 
step, the bias field was reduced to 10 a-t. Therefore, the H critical 
appearing in the definition of K' must be computed @s that amount of the 
applied ramp of magnetic field necessary to overcome the bias field plus 
the nucleation value of the magnetic field. Thus, for a 25 a-t bias, the 


magnetic field intensity at the tape surface would be 


Aeeatc ~ Y core circumference’ 125 cm ~ em 


23 









> *- ———nZm—~z£,l-; 
—l™..= gg 
—GQ™”™—p=>> @© %® ——EEE\a» G 


=—_ & —-— — 9 


= _— —— See See) ae 












= \ = 
“ot — — a tae 


: = —_ 


=~ «. = > ha } Pe 1» a 







- jy? > 

-_ : a Ls 
a! 

— ie <r oe + oe 


— 


- 


<= = nn td 
a 


























=> => => 
_ ane . = —_£ a 


: —= . = —> ees 
>. =? on i 

























7 at Oe 
- : = : .s 2 es 
° Te - 


“ _ - at dom — 
. ° <=? ©. «mee 
_ >. —> = — = <i 

— < la lie 


S< amt 
















<5 a 
HEE EFEEGeeEEEeCCeee seve ge EEE EEEEEEESPEE 
Scaractabtasteastantesteantastasteastortv-ttazt‘ctestectestesrtastaap 
EEE erecta feer-oaetfareesooceenee aa Eeeoro 
BEELER EERE ECEECEEEECEEE EERE EEE AEE ee Ce epee 
Heeeeeeeet eee CooSSSe Gsnbescend a Soteapostertastars 

So EDEontousantaad spestestestestastan satratarecteoe-teatosterents 
BREESE pee PEEPS” 
Sosoussdastangantateetentantastevestaivartareetcifesice stenterector 
Sstasastantanteve: Wetansstantarsetastoar‘fentevsetantece fostevace 
EEEEEEEeEeneeenea emcee tere es eare eee eeoceeee 
EEEEEEEEEEEEEEEEEEEEEEEEBREE EEE EEE EEE EERE EEE EEE EEE EEE EEEEEEEE AS 
soedosdontasantantasestens<tantastert etastetarsazestastersstonsstan 
Regge eee Oe Cee eeeee eee SEER PREP eee 
PEEEEEEEEE EEE EEEEEEEEE ECE EEPRSEEEEEE EEE EEE EEE 
Seaaredeaantanta estantantastetsctastarestantestesectantessstontarl 
oe doa anton tantaatan antes ostasten' ceestestastastastartastessea: ie 
Sooataa tan tontassosteseesen ton astont ss Ceseetestantantestatertactas Re 
EEEEEEEEE EEE EEE EEE EE ENS EEE EEE EEE EP PE Ht 
{nnn Sener {EEE =my HOEEER QuRE TUE EEEEEREENT SEN GHEE EEEETEEECCECEE=S= == ai 
sd dosoe’ ge-da env saves vested vadsetaerataes (greeter savaeveeranzez= (a 
FR eq eS Per aN toes) L 
oe He rey Socoees Tete fate le se ete ie Cape eb eet ee -- = 
jpeg <b A 
Bad (Spans ee > peel ues BEC ou nntes Games COS ouoes Cnspeeuusmsneanes BIE 
EEEHICE ERE Ba) eeSeeeree 12 
Sia OC CSSGR SE eOCRMERRSCSGSRCCC ce ose oeeeeseeee a 7 
fF Ceeecceiait CHEESE EE EEE FEELERS 
eee eee sre at eee eee 

SECU ereeeataeene areata cree EEE EB 

HEE EEEEEEEEEEE EEE EEE EEEEE EERE CEE EEE EEC EEE EEA 
aera ee eee eee 
EREEEEE CECE CHEECH EES EerE EcEEEECEEEECECEHE ‘C 
EEE SSE SHEeSEastaceeceteaeentacts SOSSEEGECERSaTeeeeeESSeeeeen IN 
Sree eee Sa : 5] | 
seeenentestcrraipitace ate aticee ates srry eects 
FERRER Bee cece caecateca erate EEE Pee eer 








vq 


Then the apparent H critical (hereafter designated H’) would be H 
reset plus the ‘086 =— value obtained from the static hysteresis loop; 
or 

H' = .285 25 

cm 
Next consider the factor K which corresponds to the slope of an 

applied ramp of magnetomotive force. From photo #4 and #5 showing 
respectively the 20 KV driving voltage wave form and the resulting cur- 
rent pulse, it is clear that a ramp function describes these pulse faces 
quite well. This is particularly true between the 10% to 90% of final 
value points which defines the rise time quoted in oie thesis, Figure 


4-2 presents the ramp idealization of the current pulse shown in photo 


#2 for the 225 a-t pulse. 


— 
4 


90% Level (202.5 a-t) 
225 a-t 


10% Level (22.5 a-t) 


ee 





30 ns 
Rise Time 
NI 202.5 - 22.5 180 ,, a-t 
> ee 30 i) ee 


Fig. 4-2 Ramp Function Idealization of MMF Pulse Rise for 
Calculation of slope constant, K. 


25 





As seen from the calculations accompanying the figure, K is dependent 
on the amplitude of the applied field. Hence, as we reduce the amplitude 
of this MMF pulse, the value of K will likewise be reduced. However, 
during the conduct of this experiment, H reset was reduced proportionate- 
ly with the MMF magnitude in such a way as to just reset the core be- 
tween pulses. This tends to affect the variation in K with the result 
that K' varies only slightly over the entire range of MMP pulses. Since 
K' fixes the apparent propagation rate, a corresponding small variation 
should be evident among the experimentally derived propagation curves. 
Such is indeed the case as can be observed from the graphs #1, #2, and 
#3 of Appendix I. To further illustrate these ideas, the valve of K’ for 


the 225 a-t pulse of MMF is found to be 





a=€ 
wes _ 6.0 ns _ cm_ 
KR’ = On H'  2n(.285 at ) | Bee ns 


cm 


This is the value used in constructing the theoretical propagation 


curve shown in Figures 2-7 and 4-1. Now, if the 117 a-t pulse is analyzed 





in the same manner, a value of K' = 3.1 is obtained. That is 
94 a-t 
K 30 3.53 ae 
) Bisa t _ < 
H reset = 125 = .08 hence H* = .165 
K cm 
ae — ns 
Thus, halving the MMF only reduces K' to a value 3.1 = ~ The curve for 


this value of K' is shown in Figure 4-3 along with the experimental data 
obtained for the 117 a-t pulse. Within experimental accuracy, the resuits 


are again quite good. However, it should be pointed out that above analysis 


26 


_> =? i ie apg 


—— —_ —«—1 
—— 

=_> 

- _— = «as 
> 3) aE 





cI eS 


— [— — ae 





a TE 








cc — 







SU DRREEREETETEEESEEES saeatentetartstarzs 
BEEEEEEEEEE CEE ECCS CEE 
— - coer EEEEEEEEEEEE PEE EN. seer PT tee LL ee 
ane FEE soeostonsatestartantares coon coe - = 


ae 


|_| 
eet eet 
re 

i 


= 


aoa |||} + 
BEEEEEEEEEEEEECEEE EEE PEPPER 












suas 
eee 
PEE 


Peper 


im 

FEEEESCEEEEEEE EEE EPP 

~ 2G 6m lid 
aie eee : im ee 
Tas | 7 wae ao ied 
Pic | ee a a me 
abe SPeeeELEEEE EE 
Ab Cy a inal Peer ee 
a ava ae ale cl 

i : Ea 
7gew Passio ae 
retcuee EPEC 

——— tks 


EGGS eoeom 


I 
EEE (SE UNe) 
SRE CRESS) Te IEEE 


Jorn FIAPSED Tie (ns) 


} 
ae ea 
as (eee 





PCH 
PEEECHEEHEHE i 
Baffle icesestnstceee 
SERIE 
Se tea oteeecttotse ace 
ECE il FAEEESEECEEEEEE PEP 





a FRE 
ips 1g) Eca(canfestossntae 
ann 








jf, a _ = 


has compared the predicted results with the experimental measurements 
taken for points on the pulse corresponding to 50% of the peak voltage. 
Comparison of Graphs #1 and #3 with Graph #2 (or an inspection of Graphs 
#4, #5, #6, and #7) reveals a moderate difference in the propagation 
curves plotted for 20% and 80% points as compared with the 50% curve. 
Certainly some of this difference results from experimental inaccuracies. 
However, a close examination of the current pulse shown in Photo #2 will 
shown that the pulse face is not a true ramp. The ramp approximation is 
at its best for the 50% points and less valid at the 20% and 80% levels. 

In order to induce a significant change in K', the rise time of 
the applied MMF was varied as discussed in Chapter III. Since the final 
pulse magnitude remained unchanged for all of the various pulse rise times 
tested in this part of the experiment, the reset current remained un- 
changed. Hence H' remained constant and K' varied with changes in the 
pulse face slopes. Figure 4-4 is a comparison of the predicted curves 
with the actual experimental data for pulse rise times of 45 ns, 55 ns, 
and 75 ns and a pulse magnitude of 225 a-t. There is fair correlation 
between the predicted and measured propagation curves. Again, the data 
presented was for the 50% level and hence corresponds to that portion of 
the current pulse rise best suiting the assumption of a pure ramp func- 
tion. 

Before examining the third and final part of the experimental re- 
sults, (that is apparent attenuation) the method used to convert the re- 
lative time recorded for the experimental data to the absolute time of 
the predicted propagation curve must be discussed, Recall that the delay 


time measured in the experiment was the relative time delay of the pickup 


28 
























crge OUT be | ofc _ esl ne 
CECE EEE EESEECEEEEEEE EECA Pence eee C 
Sega ECE ae aueiea (ae ai imi a cer a8 
Eeeeeeeeceeeeeettt aazsccccccocceeeeeeceeeeeeee RURRttE ia 
PESEEEEEEEEEEEEEEEEE EEE EEE EEEEEEEEEE EEE EEE EEE EEE EEE EEE 
EESEad coed oceeocds Ee casteatessteosstocttoctecttes teecstecetecatesati oe of 
-cHECE SuUaN Ua9eSoban( 7 ee eeeeeee COGESESEES CHEESE SGEH CSET EEEEES PEE EEE 
EEEEEEEPECERLEEEEEEEEEEEEEE EEE EEEEEEEEE EEE EEE ECE EEE Eber aac 
PEEP REE Bbc Pear EERE SEEEE CE EE EEE EE EEE HCE eer ttt PEE EEE 
ES esasasosbnpasesosd gatededanazevacsctatatetaveretanszs=zcd0tatato™cdtueAcseatae 
suasedafadenezeveved cuauavavey avevezevessvaveveratar’7ofatal Ues-at tees @;zuseanenae 
baad oeeeas decatenad focttoctresttenttent asttaeez FH ce speeEEECEERETEe 
EEE EEE EEE EE pee Eee OAR Cece 
Seeeeaud Haceeeee eataaaaseeeeee tg ttt aassoe coset ped td dassseeet PERM Mia aceeees 
SEcede eas bdas Feasvattifeaeatzoezotcoccutttee-adttansity “dcsateeeaatatassaia seeceseeceeenceet ci 
Ebegaeaad faceeeeeeeeeqaséageesceee ty taaes emcee cere tareaeeasereerea eesti 
BBureeuae LCL CEscHsEseesecdl Fuassazasge7APsrseeel aya cuaseaessaraasseeavis'2 vac ia1/oq bs Pauesmeees 
ia a aus suafateieeezeteza HHECESHHLY ocaua EE ent aaa CeRC AAS he oe He 


et | A a ee) ‘N 

Ex OW BSRUSEE OF roe) | ee ae, | ee a ae ee ae ReEES iin 32 4 La a 
PEER NeaE 1S ioseueeee apelin | AE ny bleh sz 2 | ete! -& 
pis ft 


an 








BCE lay so oee eC ey, 
Ege eee eae ee aac ie ) | arf Sas 
aime ee I fe eS ce isi 9. poesia gai Gay Ein aon 
mine (ae | mete Ce | ele ee ec eee ale Pe Oo hoe gar eis Sey, eee 
a seSme sea ise ee ey ae ae Cima ie te! ie ere ll ey et | ae 
[oo S67 da jac ie | ie et ts O12, Sas SOA NOS, a 2 Ren f 
Tee ee aes SC JEESRneRe oe Cae ae 1/4 ae ee Bee ‘a ies SCrrr sr 
crea ooo Pa A ', 68 €eD Mes ope a, ac 7a = TIT] 9 S 
ee tae eg Bi > ee ee ic, a Ooo a 1 wy; Taal ee 
BL tate cod. SC 2D OO ane oe aoe cee ee \= cin 
Beanie ee er ee Pie eae tae wet ee a ale is coo her ae 
"Se Cll A 120 2 CReR eee 18) se eee ees ee Fila 2 o | 
meee Play JE JOS GSS eee ORE Sema cime asta Se, el ae , a a ; . 
USS C6, SC oe 20 8 BSC 0mh aM Pt ioe | ich) i | mi i is) 
[SLOG Se) Eee Cio hos aoe coo >. 
Ae ee SC Eee me Bie EEC EE ACEE EEE Oa ep 
Ll a BEBE EEE EEE EE EEE CEE EE ere Sore 9g 
Se ET yee ea ia az 9M: i PARE SRE IOC ee 
RECRE Tok Sam mee aaesae ee a toa) (oa me iad 
aa. 128 Re fam 7 ae SeGE C1 
HR ff 12? (ee ae ae ce i ee. Se 
cece eee ae : nee 
Pano sla 200CSRe rae aoe CoUar IaRase 1a ee Sane 
SC e eee eee ee nema Rigi mn 
1g ua 2 es a a t lean (a ae peat 1 7 H read & f 1 

















signal with respect to some fixed reference signal. Therefore the plot 
of these delay times presents only the relative times of signal propaga- 
tion. For example, to find the absolute time for the signal to travel 
from the 8.5 cm pickup to the 25.4 cm pickup will be the difference be- 
tween the time delays of both pickup signals from the reference. To 
put the experimental data on the same time base as the predicted curves, 
it is necessary to shift the experimental time base linearly. This 
amounts to superimposing the experimental plot onto the predicted curve, 
neglecting the measured time base. Obviously there is a certain amount 
of curve fitting involved which may tend to make the experimental re- 
sults coincide better than is really the case. However, the relative 
position of the plotted points of experimental data are fixed both by 
the position of the particular pickup on the core and by the time re- 
lation between the various points. Hence the only degree of freedom per- 
mitted in matching the predicted curve with the experimental one is a 
linear adjustment of the time base, 

In a final test of the theory, a single winding was placed through 
the center of the core and excited with a 225 a-t pulse of MMF with a 
rise time of 30 ns. Since the exciting winding was equidistant from all 
points on the core, the magnetic field reached all points on the core at 
the same instant. This rather obvious experiment yielded the expected 
results. 

Although the magnitude of the voltages appearing as the pickup 
signals is far too large to be the result of the MMF wave alone, a test 
was run to insure that these signals were actually the result of flux 


reversal within the magnetic material. The magnetic core was replaced 


30 


=> ==: 
_ 

er gs 
2a 2 = 
> _—r =a] @ 


rere — 
- ee es 7 


eye} 
-_——_t —- ae 

——— eT 

== > Cees (1 eed 
a 

—_ OES [SEE as | 
a LHe <i, a, alia, 

_— = | == <1 ie 

—_——_—— = | 

me — =<) Ge =e & eal §aQ) 

= Se eee ee 


_ 








a Sih 
eee 
~_ 














-— EE ap Ge rf © 
J a a ee 


— lly eae He 







= x= ii» 
= ° mm  —~ ir ar mamas 

= —- - 7 - om 
‘_—t *® Gee 


by a thin ring of stainless steel.* The exciting winding was then 

pulsed with 225 a-t MMF pulses with 30 ns rise time. The amplitude of 

the resulting pickup signals was less than 2% of the corresponding 

values obtained for the magnetic core. The signal to noise ratio was 

too high to permit collecting accurate data with the stainless steel 
configuration; however, the measurements taken yielded an average ap- 
parent velocity of approximately Al Se ane Within the accuracy possible 
with these small signals, this result conforms to that predicted in 

Figure 2-4, 

One final element of the proposed theory remains to be discussed 
and that is the apparent attenuation of the induced signal with arc 
lergth of signal travel. In Chapter II, Figure 2-5 was constructed 
assuming the pulse amplitude decreased as the inverse of che chord 
length of travel. The magnitudes of the voltage spikes appearing on 
the pickup signals were measured and are plotted on Graph #9 of Appendix 
I. These curves were normalized with respect to a position on the core 
10 cm from the exciting windings** and Graph #10 of Appendix I shows the 
resulting plot of these normalized curves. Assuming the voltage at a 
pickup is directly proportional to the MMF reaching that pickup (3) the 
normalized plot of Figure 2-5 and Graph #10 of Appendix I can be compared. 
Figure 4-5 shows the superposition of these two plots with the 10 cm 


ordinate intercept used as the common comparing point. It is evident that 


*Stainless steel was used instead of copper since it is both non magnetic 
and has a conductivity approximately equal to that of 50% Ni-Fe. 


*xkNormalization is necessary since a comparison is being made between a 
MMF and a resulting voltage. 


SL 


 ——= > & 
Ss «=f 


[]=_ >_>  . 
————S—— ———— 1 aD 


=| eae © 2, ac! 


—— eg GD 
Sg ST Se 


eo —_—s 
= 
°° te = 





ll - e - -— ——>> eo =e 


—" Fad pe 


oo — 
— 


the attenuation measured is somewhat greater than the predicted attenua- 
tion. This is certainly to be expected since initial nucleation of 
domains must consume a certain energy from the exciting pulse. This 
energy is permanently missing as a result of the ohmic losses resulting 
from microscopic eddy currents and anistotropic energy consumed in 


nucleation. (1) 


32 





Peete EERE HEE HE EEE 
JBaa8 a = 





: or fl ES) 
i: SS 
soe costea tetoes SEER EERE EEE 


=— =F SA "pe Pa 
Lari ie i (a a vaige INCI A ON TT 
EEE SCORCH IRCAIT HE Dre re ih ATOR 


eee Bbsrececceeceeccste anges 


Jane “ % 3 HEH ‘ ATT 

Ree SE EES SEEnTEEEEES CePEETESCELT Goat cial auctaestesnees 
Het EBERLE PERSE BUST ptt tt Coe 
mje | Ht SECC AIM IStooa oes PA RAVES 
If fo TPP ak ot dt et et eS Petrie Saeenneee 
EAE EOE EEE EE EEE EEE EE EEE EERE EEE EE CERES 

@ ™ aa ExRa PRES =m mek 


al i) Sg 
1 to tl 
|_| 
Sen 
ae 
ial 
| 
nee 
ZC ERE 
PIE= 
AAA | 
(wl 
t | 
Lisle 
El 
hal 
im 
; | 
a 
im 
r | 
F 
dl 
x 
a 
| 
es 
on 
an 
el 
lm) 
a 
ie 
al 
| 
| 
| 
| 
| 
| 
|_| 
| 
|_| 
: | 
Tt 
| 
| 
|_| 
g 
é 
“ 
| 
| 
|_| 
a 
a 
a 
: | 
£ 
# 
| 


_ 
il 





o) SSC ed a 
Pomeroy 


0 ee a a a ts 0 ss ae] 9 an 

Gee itech SHE LE Hoe Ej I et 
TE BRO RERBEBCA BER BIR BEE tol BaD 
S08 See fa 9 Ae LES a 0 em a FS jt Ge fr: Ft te Sete poe 
TS EER ERE Tle le, Elan! Me lal a, [a4 een aeem 





wl 

oon een OY tL a Pel ode ale |. 1 | Pee eee eee 
IEREE rm a, GRRE RC Reee eGR Coe RoCEeee Cees ro 
IB EBRARRARTERS BDRM VO DERE Ee EDEL TOC Tae 
SreriAlAyt tit} ar | a'a EER SaRECERRCASBS BERRE TARE Le 
JEN 2 CURE eee BeBe E SU aR RERERRRE ARNE 
 __ | JERR RES ERE ARERR Fa ee Se BREE REREAERSTERVLAS_ FY 
 TEEUREE Jee see + a ERR RRREO 
| JERR SEREE a ERRwWaeiael BERERERERRL Ase 
my et EAB J ics eal lil BEMESESRERBERERMA a 
ert | ea +H WLS EBRae t.2aRoe 
«| Ue) A ee ST tal de al ee ee 
JES FREER 73 ER x = LETC LS 
TE CP éiseceee SSR Ree BEEF RSE EEE EEE EEE EEE EEE EE S23 
i158 die Geese AL asl Rcaleee 
|S 4C AB BR ~SRRnkP wee FRPP ee 
| J oe ee eee BRE RRR RRR. THe KU BSG * PEPPERS 
Sen SSS 0S00 ee BERBER ERPRE BORER RRP. 86 ee ed on 
TERRACE AR PRR HESeSSse SSSSSS SSSR oP Seif shs, MORASS Srl es Ses SSeS 
UE (RES BRR EHH SR SRE Se 3K See SR LEE eae 
 ) JSR RR GEOR OEe CO eee eel a eel | lat 
mei Py ttt ins BRM RRR REL 
| JADE SS eee SRR LE REARS la eee ie 

ime) Tt eet A ea a | | ae) ee 


{Seas ele SRR RRSREAERR OREM ANBRA ONES LeeLee 

Jee EE BR Rees PISS EEE 
nammeamme| | TT ie Tt ee th OAL Pee eee LS eee ee eae 

JI SEDER S aaa eee ees Lay SO RSGR GSN Goce OeRee eee eecogeacca 
JJEC SERS ee aa CCCCRICS COS CCC sai 
Semper | | | dete Tt Sae0 bE eee eee eee Tes eee Eeas 
meee ge PEt AAS IN A te A eet bol cel ay Tt Tt TE 
ere | ttt | HaSaB BG = SR eS WEI OREO 
ISS Son Saas ae BERD = "SC ens ESM eee 
00? Vie eRe Ht abd ee BRAaaSAALASRE 


i al | Larios elspa | oe 

ieiieeeeiiiiiaes SSS ESERFSESEEGNEE 2EUSACSEPAERY ALORS A027) 
aus (| a aa f | 4 

Bi FECES hE did eo CM Rowe BCH 





33 








5. Conclusions 

Certainly, no theory is adequately tested by a single experiment 
conducted by a single experimentor. Such is indeed the case with the 
theory developed in this thesis. While the implications resulting from 
the experimental data are strong and support the theoretical arguments, 
the theory must be tested under different conditions by different experi- 
mentors, using different measuring equipment and techniques before it 
can become accepted. What, then, can be concluded from the work present- 
ed in this thesis? 

First, it is fairly evident that any circumferential propagation 
process taking place in a ferromagnetic torroid will be the result of 
a magnetic wave radiating across the inner diameter air space. Clearly, 
the velocity of such a signal transfer is far greater than cam be ex- 
pected from domain wall motion within the core tapes. Further, since 
magnetic lines of flux must always close on themselves and link the 
current in the exciting winding, it becomes impossible to establish an 
H field about the entire core without the magnetic field first sweeping 
across the inner diameter air space. The proposed theory complies with 
both of these concepts and in addition, it is certainly a possible method 
of signal transfer. When the results of the simple experiment of Chapter 
II are considered, the theory becomes more convincing. Obviously energy 
cannot be transferred about the core circumference with a velocity great- 
er than the speed of light. Yet, there is the undeniable evidence in 
Graphs 1 through 8 of Appendix I which shows this velocity to approach 
infinity. This seeming paradox is readily explained by the proposed 


theory and is, indeed, one of its fundamental characteristics. Further, 


34 


= 22, © 
Gait. 122 





ae 22h 
— _ 
— — =< em 
a - 
== 
—_ ee Es 
- . - - ” 2p § = = 


a «461i _ 


the reasonable predictability of apparent circumferential propagation 
velocity using simple trigonometric methods offers strong support to 

the argument. In view of these facts, it is concluded that the circum- 
ferential propagation process takes place by means of an E-M energy 
transfer directly from the source of MMF to the nucleation sites about 

the core, Subsequent energy is aiso transferred by this radiation process 
with the final result being a growth of the domains of reversed magnetiza- 


tion and radial domain wall motion. 


35 





ON  ————— 


APPENDIX I 


PLOTS OF EXPERIMENTAL 


DATA 


36 


















Srarentatatezezoreracesfataas 










Sraeoaostostocteastontenns 





















i ee wae 
| TEESE Coe 
F ro ec a, 

} 





ECP 









— TT TTT Tas 
ScELHEEE CHE an +t x 


sretaie PEELE EERE PEC att ae rEescossssa i 


ae PERE EEE EEE EEE EEE EEE ae ge yet 





























Pate at tt me ¥ 



































| ST ea. font p tf EPCS” 1209 PEEEEE EEE oe 
| CO Souauanae poe et BRP ARRAS aS ea 


| 2anpggueeeueeauacs FECEC REECE EERE EEE EE EEE EEE EEEEEE EE 
-SESEESSSSESESEESEE ASU neea ceeatostoe Sees 


















Pe TIN 



































































SESE eeer eee eee EEE 
He 


Sodessssusantastentesstent HE ae serie 







— 



































































































SES ay | ESHER EE 
HEHE Hee EEE SSHERETCS tf Hitt ann eet cH 
mH . pdt} | -!t-)-|-}-f--}-- PERE 2) 
cc PEER 

E + =H LL, ar - PERE EEE oer fad as 

pee SS SHEE ee EEE FESR 






















sah ih 


“Re hE by ee Suna 
HES MME ila app} fa 
= 


. sl ie bd na Be Hi ae 
EEEEEE = ' IEE 



















































-- Peo PEEP = -|- ERPSEESZOMSaee ae ee) 
EEE Bab EE EBLE Eee coossatasttteoossze BaNg seeneeeee teers 
BCE ee g feveedentetentetenterastarae See: & 

zm CEE Bizeoe mee spp - 

di atl at oocem a 

eee saseeenne 

































la Ee Pie sat aint Lc it aie aie Peet ee no Aa ba 


Ro? SSO IIAEAALL EK PCT Y LE le COR EVELNY Cave SRE 












EEE iit 


Hit ag 



























ECEEHEEEHE LEEPER EE uae ee g 
oeuune Oe sSRee See : EE Seeeeeee sur STE 
























suas PEBELE eaeeara vaca 


FO Ss aeeeere Loh lalla ae to to eee ote 
37 




















Eee aie Pooh 7 
SEEEE EEE Er 
ae pees seus 


a 




































EEE ESSE Ee 

ees Braue 

Bie: Eee Ee ete aie ECEEEEEEEEEEEEEEH * 
3 = Lao peseereccairs pM a ceed 





E PEERS gener eae 





Pereleceeel 


el ae ——- 3 AS HY 
SP SERSE Reese eee Hott 


i SCPC Se Soe 









SUMS) 1 COR 
EBERLE EERE EEE SERS 
Boer SS be | ls nin ei SSP eBes ese wee 
Reece Pe ee ea ee eee Lt. 
_Saamnn | SRS J00ee0 55 00ese0000000000000000555555050s jel chee lee) ll gle 
mi | tl ee CS lelalaiaime 5 iio A ee tra a i a 











aa 
16,0 







BEGUEA fd beaten cer bozos socued pet ae7 eg Rea cGSEScoceaceer des 
FEEEEEEEEEPEEESE ESSERE EEEEEEEEEEEE EEE ESSER 
eee Seco poo et Tt NE glee ET HO ee eee ees 

aeeeees i ie Ls -) +4 PEE SRR eee ’ 

he | meee Soe al | ate et = = ae ely 

eee eee A JERR SERRE We oe me oie Pe a AT a 
Ez LT pf SaR RSS SERRE See chee * ie, 
mt lee Me ft ye ee EaR RE PRP ee eae ee on 








codes dunteatantasteatentectesttartassoctostastantareeteerententectsctt| 


CUGREERARRIRReRees ae PEE ELEPEL Eres 

. _. | SP SEER Eolinesssuseserecees Bz" ZERERY ARERR AS A AAA 2 
 __ "DE Se Se PR ee oe ed 
PEEEE ETERS ee ee LN | Poe ptf tt a4 | 
ae — cE Rae es Jee coe ci mee Ht jt a Ps me 










ae SSS SEESSE ame angtiai ate ate ain a (a EZ Be COE eee 

PE iin do pHa ttt pt He NEE SRR MN BRie Ape. « 

| -aa TS 3SElL 6558 72800 eee Sikaew eas Pale 

Aa). | e Bera elas soil cll PCE PRR ere eee oe ei + 

Aan a LEER 4 ER RE BRREE RN ee Par ce ee Lele 

7" oe Lk irre tte tte Eee BRE FCO SH 9 
ims Se NE eS Se eee 














2 lO SHUI ESUanNUEEE lal r ar ae a  So eae a 
E one = cera EEE 
Oe ae 
Emel pees) y S SEE I ca Ps Se hate Nbabelie be tt ie a 
Eat Pues CESEETaaeenaneannnsesunt@ CHMtEEaE= 
See sssavaeazend say avazenanerararans: qari 
a =e SSSseSSRRe8 PERCE —H4N8 S 
at posed eaamea + “Core SEE CEE aes PSHE 
ee ecrEEEE CHa tee snovesererects 
Het Se Ee, HEH @ 


ae ia Seu SEEEEEEaK: lds neste © 


roe ‘a 
fae a oe oe ee act 








ae Flee puna 











a ee 


| 


Poo EEC PEER REEL te el Nah eth ope) | 
| 














pe eee oe Beaenee Re 
Fro ald coe bel DP FN PO 0 Pe PERE a i I oO ~ oer ~ 
SaasRAgd assceeeeEEEEEASEEEEEEEEE ETE eeae Cree eee EEE 
Hr te Ht ais eal | csMicth ahs all 
JSeEERES Sea eenseEneb {-Seeeeuee uae enn U uae euuuueaneeueceneunne Qesepenees 
Base Lai) PM FASE EEE = SaaS oe ee wei IR 
Suda ansad ovantadandadantevastedtctetastatareatocectarcctetarestersze= Be 
SEE Ear eee Eee eee 
$ou85dozanesdazestasantasactatorsstsesatstantetansnteforeatatorssevar 
_ J |. “SL SSD es ee eS ae ee ee ee +t 
EEE PEELE eC HSER EEE 
ee i 
|) oS a Pa PF FF a 8 pf PL ee EERE eee ~ 
Beta Dnner net Een OPeeEeeUOOEBEESHEEET EEE 1 
EEE eee eee EEE eee eee 
oats Lela EEL lae Sere laieiale ey tet tel 
PEEPS EE EEECEEEEEEEEEEEEEEE EEE EEE EERE ECEEEEE EERE 
2 SRO 2 b Ty 9 
BH gee an ieeeceee aH ESSE 
StH eS PEEP oT PREP PERE a 
ap Suee eeeeenceeeil SEER ERE ees a a 
Bs-terars seegatsiiasstettasee SeSeadatecssssteocetzaasvtiitacah 
Pelee ris at Se eegeereeCSS0"0 SEE ae Fee eeeennes : 
peor eeuissteSete SocoooosstniSeeeEEeceeceTannRTEEEEEECe 
| oNeEE : suacce 2 a bor fo et it ti caus ce elale latte 
at | J SEO oe PERE EEE Ht Bake Ms 
fittest reel Sinem , 
— ~~ PERE ot BEECHES ; 
dag Ee 3 
: 


Ech 


ee meet ie 


Hane Hr 












el kh ad ie AR, a tS 
mh ee ee H+ sta —++-H+4-4 _ a aa---4 PAH 
Le _— a ——- 
| a 





i . 











Seo SBrneHabeseenceracercen 







i BERRY ORR ERe CHa EE BERRA RE 
es 





































I 





| SEBESSESED SAO 
Lace en ae Soe Se ee 
CECE EERE EERE EEE EEE EEE EEE 


39 





SoH SER IRREGREGEEEEeotesdos ects au Cc satectesttontectents 














a a a a 
OSS 
eee CCC Cece CCC ae aie tate cel) iece sitet alata halal 
1 a 
| 20 
(2 0 ee ee 
(0 SES Se Se 

a fk a 
C020 0 a 
BEEEEEEEEECEEEEEEE EERE EE ECC CE CCOC CET Ce RECN CREE ECE Peer ere 
BCC CECE CCC CREE EEE eee reese SCP 
2 
Le aS a 
BECERRA EEE er ERS CRS 
BECEEEEE EERE EEE CE ECC CCC EE ERE TEE Crea Oe Ce PoCCe eee ert 9 
BSCE CECE a a PCE EEE ELE SS 
BEEECECEECCCCEPe eer aN of a Coo 
EEE EERE CCEEEEEEEEEEEE CECE ECE EEE EEE EEE 
BECCOE CCC CRE CEC CP err ree CER Her EEE EEE 
Bee OOS Oe COCO CCC ECCS Cees CCE Eee oe 
SDE a eee 
12 eee 
BEER EECCA CECE REET CCC ECC CE CECE EE eee Eee e reer errr rere 9 
BECECEC EEC CCC CCRC COC ECC E ETE CE EEE Cee eee eed S 
- [SDE MO 2 eRe 
— | SS | 
SS a eee 
(00000052 e OS 
BEECEECEEC ECC E CACC CACORE CEE ECE ECE CCE eee eee eee 
BECCEE ERECT EEE TEC COTE RE CECE CCE CEE 
55500 0 eo ee see ee 
SSS C SES Se Se eee eee 
E0200 0 Reso 
- FESS S00 oe 2 | 
SUES 
Semis CCC CCC COCCCE CLEC NCCE CCE GCC Lee ate 
SS a a 4 
fa a a a 
mmm COCO COCCOCCOCCCCC COCO lee 
Bm CCC CCOCLCCCOLCLOLO CCC CC ee Ce ie 
SS a a 
© A a 0 
SACS a Ne Re 
EEE EE ECE EEE CEE CeCe CCC CE CCOCePSECeCCeECCe eee eee eee 9 
SS ee . 
Meee CCC COCO CCC ee 8 
SCC | 
SECRETE EEE EEE EEE CECE ECE COC ECR COE CECE 
Beemer COC CCC COL COC CeCe CEC 
See a a 0 
| OSE O SoS eee 
Smee CC CO CCC CCL CCC tI 
OOS SSC Soe a oe A | 
(000 00S Se 
> ESC OER oe esses 
°c SSS eo OeD I ee a ee SCS 
{oC COS ROO ee a 
SEO CSL ee ee ee 
CLOSE 
56 5 CORD Re ee ee | 
S008 BOGS0eD Sea eR RRS 
BESO RREETHELCCCCCRRBEEE CEC EEECCCOCE EEE EEE EPEC 
5 Se SS AN 
Se ad Pe | 
SS SSCL S00 Oo Reso 
PCE CE EEE eee 8s 
FECOECCRCC COSCO TREE EEE ECE 
AE Geom eS eee ce 
Sao Se 
Sy Sees rR) OS a a a a 
| SUES! oe SEER eee 
OCS SE oe el ee ee oo 
Se se 
paneer SC COC old enh 
HEH SEE EER TEE ECE CCE COCO Eee & 
ECCUEERC ERS COCECOE RE OEE C EEC CEC CC CECE eed se 
See Se CCC COSCO CC 
Bee CECE LLL CLEC LCC eee 
ml | aes | J) es eee Se ee eee eRe EERE EEE EH 
| SCO oe 
BEELER E CECE 
eee SCE et 
BEC E EECCA OEE 
BEE EEEEEEE EEE EEE EOE EEE EEE ECC rece 
Pt EEC EEE EEE EOE oy] © 
oo SSSny GOR SRSA SS ERAS 
SOSSSSGN (eee BOOS Dek 
EEE EE ESE EE CEC ECR CCE CCE E REECE CER COO CECT ORCAS ECE 
(EGGS SCG o Ree EOE Se cso 
ad seseeredaesedcesedauetnevstabccscessucessncecsseessreessaerots== 
SeERBBREEEE UE, Ay uuuUZ_Lca@SeccaccdlUucaaaduwade: nusa7/ cunaeseses 
i | am 
He Soe a Bie. Poe cialaal 
BREE E EEE CREE REE EEE EEE FH SREBSSESROMME co 


& 
© 


ee ee 


oft hy “ett_epere =~ oe 


— om << 


eT 2 eae Pw rer 





i | 1 1 


ft imonent 
| 7 iP ' 


( i 
as 


























eu eres seeriaee 
Beseeseeeile Sauaae it PERE a) 
Pe EEE EE EEE PECmonoag HEHEHE PEER EEE EEE 
Eee srscecseoverestts == PEE ae Ssssteetocatita aan 
ae SESSEEE CaN BEEEEEE Se 
sree pe Bee Se rereereesastasi 
ee eeeereeeeeee iF --e-oPoSHe tp SEE 
peceeceeana ee 
i a SSE 
a 
Se ee seer aie 
SLU 
Se SrssaSucESuneeeteeeeee EERE EEE Saeestenestorter estore 
SHeDDEUEE Sreeseieectaats eee 
aes eee 
ee 
sazaaavaasveersees PCE ooh seasestoseetantesars Beate 
aEeeEEESE Se 
saison aieatastantitare PEERS CPE Soares restontontstactosae 
ee | 
seis ia erent eer , 
PECL EEE Peco seerestestasestae Sere testastesestars 
EGRERREEESE . 
Fe i a...) 
EES aa Seen eee cooeee eeeeeaes 
ane fF : nee re Ses (sens veeneseers [OSES 
eine SEEN eee ta 
PELE ice STS eae EEEEE Ssdecsecdocgocrestontasilt 
(3m ca EEE EPR EH Ht cise ppt ee eos Hip oe 
cee rcHELERSEEEEEEE sus UES BREEEEEESGE HERE ECHR HSN EEE 
tel SS 
EEE HU SRARa Lua gee adea SPEHHH 
Hitiia Eee Pere HEE =a 
SUCRE PES ican es PEC EcEEEE EEE CEE 
EEE : FEE a Sc esatecsec rast sueeEESESRaaaas 
Eeleeeeeeert ta iiatsee ee oe 
——~ ae 1 Sl ale cea BAP ae r : Beeec HEH 
Eetetiiet ERO aR Seratens 
42 sasesesssseeseewersssssa ae 











een ty tery Pp er a ELT Pe LEE LL ee EL Cee ae ee ea eee 

6 | (Se esses ReEERRES PARR EERSTE SRR AL eweaeE 

it eee es eee te te fete ee ee ie ith a te 

| IS SaaS Ree eee eRe eee EEA 

He pei ET ZEReR ez mo fef tt BER eeeeae ee sh 
SERRE EEE EEE EEE eer PERE eee a SEE E EEE EEE 
apa ae ible. hse | BERR | aac — aif 
SU UUUUEU GaSe SUEd CERES ened BEE RE EES EEEEEC oat BReEe Nees eee EE goSUE 
BEE EEE EERE ECE EEE EEE CoC 
PEREEEEEEE REECE CEE ECCI EERE CCE CECE CR 
mir tt i ty ae ae EE EH HEHE eee Pa YY | | ft td tf 
mie yt tt tl sat} eee eps tea Mt deface ee <cho-f Watahel | eal cts fondant ool ee ea S27 EER SISRERET AAs 
i ee eee eee ee ee ta EeaRRee 

a ee ee as een ea ef (Pe eee | cle lee lia (sel ae _ . OA e pit tit tt} 
SE UUDHUU US UUSE DSSS Eeeetencen Suseeeeneneeeee, Gna \am ine Gn) SeGoEEoaa IN 
See rad rer eeEeEnESEecll sans snnnnnceueseenecoeseceh Coustas sau yeserenhs 
mies | tt te se Saas SNe RRERREeeUSes: Sees ae | Re {ee 

| JSS EREE Sas hse eee eee Ree Saar Se eect eo (og oa a 

JT RR ae ee ee See ee a ee ae REeSEricSs RERERSESe 
eee ttt tt tee ase Sees mt Ge So — —— 
Bee eee hee EEE tt pe re 4 
| 6K TRE RES ERMA a ae ee 8 
SE aE nti nee val Eee oe aloes tear wn --fepe Hp I -— 
BREE EE EE EEE EE EH HSE REE EE EE EEE EE EEE EE EEEEEEEE EEE EEE SS 
BEEEEEEEECEEEECCP PES CECE EEE ECE EEE ECE EEE EEE spr 
Bien ECC C ee Cree eee ste EERE ARES BREREREMBaTT EA 
= St ee ba |] | BRE ERRER STs Beha = 

BEER EE CECE EEE EEE EERE EEE EEE EEE EEE 
SO S2 Soo Se ee LN 
| (SS RRR PEELE Pear ee Pt Le tea mee 
| TR asses Rn aSeRRRE TANNA lt Le ae aie ee ie) 
| | Raa TELLER SN ETL LL Lo ae eae See 

6) UL OE a se PELLET TLIVELELEELEIN ELL LE ee See eee 

|) SES Ree eee ey Po SE LE ea a te Oa BP 
TES eee eee eee eaeee rE LTT tty LL Ey ea Pea a 
eee EE EA La se tf tt} | | 
ems tT tt ET EL LLL ELLEN EERE RRERE SATs Q 
emit | iT | TT Pp eE TT ET TT LET TTL LEI Tak LE Ea a ea eee eee ee 

meee tt il i ELI tT ee mis et || SS TS aa ee BE 

| | (ities eee eT N a e e REREEE pe 

| J Pe ae rE LT TELL LE ET ELT IN ea eae a 1, ™ 
| TERR Pe a aaa a ee | 

eet | | ltl | ELE LET ELL ELLE LLL ET EE LL ee BRE SRR PERERA | | 

| (Jl Ta ea eRe BRR Sa wReAPe Aw ia] 
ORES ae aes a te BORER RBS See eS eae oe 

| SE ESR ERHSuCS ears BRERA RRR LAUREATE ALI sO. 
‘3 meee tl ee ee BERE eR REaRBERRTSERRSL aS OS A 
| os Sonesta ee LEE LT Laat ea eas ee 

a miei |} i ERS HERA ABEL MURRELL cy , BRR REREEAe Tee 
Tae me tole | ee ERED EMAsREREeAaEe STUNT LL UL TLof od 
mel. mT “Bene iy -) EPR a EL Le Ye al ee zB i. 
PERCE CR COE ARC EE EEE EEE 

|_| -| : + HHH HA ~ BEE BREE EEE EEE EHH 

| | & ao ft ty tt pat ot | eae ae a ee eee ie RRSRABNES nee is 
S| | im «SEDs BRR RER RRR CLR e ese 
| { | a ne Pe EEL TE LEE LE Lae IN 

EEE Sr REECE EEE EEE EEE 
BECO ERECE CREE EEE ECE EEE ECE Oe 
aa Chat Sasene Oe) PERE EEE CEE EEE EEE 

i i & fil | ERE REE RRRERR SRE VE EESREBERRERNS SS. 

Je NT] NSIS eee ee eee eeaieleinia eo aa a 

met eal “ae See oe | eee TE ee ae REERERERNEEEREVe Ss 

met | ee) fae es Pe ea |e ae PILL TN seein aie 

ee “ERROR er EER RARER Seas esaee EARNER as 

g he lee tel ier is RARER RRR RAED EAR EASAsSoes |_| 

| met t.|. eRe Aw Eee SAREE RMES A eeReAS ZR RRR oC & Q 

mil aes |} lee ail |_| eT ee a ae ee Eke ERe& 

et | BRE RSanaes g Pepe tebe Pf Ue et Ye ea | SESS lo een 

a eee dae cee alle ebay petiole pelea es ea ee eae a 

| me |) oe ale eet LA ey ee | {| Laas meee 1 ale ol Seis 

et oe | | ze SS eee Ieee Sse a RES 
BEEEEEEE CEE EEE CEE EEE EEEEEE REE EEE 

EERE EEE EERE EEE EEE EEE EEE EEE EEE EEE EE CECE EE EERE EEE EE 

EH eta 4 ptt tt eres ok ote cae FEE EEE EE HE o> 
Sees ep el tt ae RARE SRERREBEST TASES as REFEREE RRS aeEe re 

PECEECAR CECE RSE CECE CEES EEE Ee 

Hoel ceo Bees Jammie oH ECEEER REECE EEE ESE EES FEE 

EERE EEE CCC ECE Co eee 

Boe ota NAT i S15 aE Porc AC 

_— ppt [SRS@e0" Oeeeee {ptt nif Ht tt | ze al 

EEEEEEEEEEE EEE EE EEE EEE EEE EERE EE EEE EERE EEE EEE Eee 























FEE 

: +H 

a 

: | : EE 

ee 

. a 
_ 

a - a a 

os ee 
= 

ae = BEE 2 : 

a = 
= — a 

= 
2 scr 
at aa : : | 

ae = 7 : | 

7 Ht rte a 

/ a = cH a 

: : Be — 7 3 

HE = : 

i i ae a rf Bue He ee : 

: ae . i 
; . a ce ae 
| - = _ 

He : cS “ a a 
He io _ a 
_ a. ce ef — a : 
ae 7 . cS | | | | 
i a He Se He a He 
: a - cc th 4 He = a 
a a - _ = ae af 
LL Lo a = + 
: ce 
is = 7 
a8 
. Se Ff = 
a 
i : 
_ 
_ — 
= a Ne = =e Q 
ce a ote i 
\g a es a 
ves 7 
_ ene a Fl ee Ft 
= ct ae st te Q 
cite . 
re a 
ae 
an = 
ae | 
a | , 
\- _ S 
tf a 
Ett = a 
| a = 9 
“ 
ae 
| a =i = 
= i 
a es 
¢ 
_ wu 
- 
7 
ee 
a 




























































Seseegseedeseeessseedoceses 
i eee Hu Sua 
Soest crea 
E ooh LY e ces Bo 1 
eee = oe rae ee E 
na HEH HS ES NEE 
aoe ee ae Ssfaatecttess suetasassts 
Lif Seite Lol Tl 
i: SEEEEE iSrsees Mindi ae) Bi ile PERE prccerase. 
cS Sa eee ieee ist 
EE EEE EEE FURSE OEP 
“HH BEEECEEEEE EL HE ll esl OE, es ER: Lad wad ima zt te; BE Ak af 
8 ea aaa area 
ABSEE Weesdasen favestantstestensetsnsazestasteeessezsetensere= 
Sch (eseeeee F 
SeeEeEEEEEEEEEEEEeee eH Ceo eee 
SEE SbSEosscsabessssebseorasrsceseessersetsccecssacszs 
£ EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE eeeeeCeSeCoSooooos 
sodaseatante teatantovestastasestantentoteatectartetastarsstoctersctae 
peace Se epee eee oe ees re eee eee eels eenes COME EEEEEE 
Soe Seaton stand cntesteses teertested festasestestentastantastastars 
Bb: ome uuet eanes bee SEmeUE ECESESEARECHIT essen eeanenns ete eeeces 
SuHeE ood coon eats testestentectestestectestostestestestertstentostan 
Depts sea GPaUEM (EoM ert ots peeeeenes cones nce perenes pee ceneeeneeneeenaes 
EE eae eee Eee ag eee 
sss she pene pentam (suet ban Sam UU OFS REN 100 GRAS RETEECECEEEE ese mecones 
ecreceactertart NSE ESESEEDEeSdectectastastastatestestontostsseaton 
Bez bosunasupanceace nceseCea GEIS EREACCETEGEES EGR eseeresersscat ene 
Seer a ese BEEDEOSESEE A CEEREEEN Fes eenueesseeens seat secs seneeeeeeeesees 
“EREEEEEE = Et aeIN Eee EE EEE 
pusstsiguvesrentasstasannc Sadia tesasectaetazaas Birssevssesee 
nani ir an VES Si cen ie sae M1 t 7 
i es Hy aan PCE EEE Ne — = BeS=SS6 les SSaS00eS0 000000580 
sGaHCaisa oaestestantandandan cctententastetecses teatantart oszefantae 
ace aaa aerate ae eee 
aan i BI alae 
PEPE EHH eet se Ueeeaeaaneias SeGEEEErevecepecce 


fa ca a Pctale Soe FP rss aia 
EEEEEEEEE aoe PEERS Feeeeeeeelec ens Erett antiifise 
iy 30 


a4 eC DiSTAVCE FLOM EY¥GITATION Cem) 





APPENDIX IT 


PHOTOGRAPHS 


OF 


PULSE SHAPES 





Puoto * | 
2ZOK N) DewinG 


oO eet 


Vonage Pulse 


J 4 
f ie \ a 
4 Si eet 
reer «> aa Serre 2 = 


ers te 


N 
+ 

; 

at 





48 





BIBLIOGRAPHY 


Magnetization in Tape-Wound Cores, R. C. Barker, AIEE Transactions 
Pt I, Communication and Electronics, Vol. 80 pp 482-503. 


Solid State Magnetic and Dielectric Devices, (book), H. W. Fate 
John Wiley and Sons, Inc., New York, 1959. 


Fields and Waves in Modern Radio, (book) Simon Remo and Jy 4A. 
Whinnery, John Wiley and Sons, Inc., New York, Second Edition, 1953. 


Theory of Domain Creation and Coercive Force in Polycrystalline 
Ferromagnetics, J. B. Goodenough. Physical Review, Vol. 95, no 
Aug. 1954, Pp. 917-32. 


Superposed Magnetization in Materials with Rectangular Hystevesis 
Loops, C. B. Wakeman. Doctoral Dissertation, Yale University, New 
Haven, Conn., May 1955; also Technical Report 56-195 Wright Air 
Development Center, Dayton, Ohio, Pt. II, also available, No. FB 
131209, Department of Commerce, Washington, DB. C. 

Flux Reversal in Magnetic Amplifier Cores, F. J. Friedlander, AEE 
Transactions, Pt. I (Communication and Electronics), Vol. 75, 

July 1956, pp. 268-78. 


Propagation of Large Barkhausen Discontinuities, K. J. Sixtus, L. 
Touks. Physical Review, New York, N. Y¥., Vol. 43, 1933, pp. 931-40. 


Introduction to Solid State Physics, (book), Charles Kittel, John 
Wiley and Sons, Inc., New York, Second Edition, 1956. 


49