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\ /

n /

NAVORD REPORT \ /

3759 \y

£/gLF-COMPENSATED MULTILAYER DISTRIBUTED CONSTANT DELAY LINES

7 OCTOBER 1954

t-P S 7i m-

V. S. NAVAL ORDNANCE LABORATORY WHITE OAK, MARYLAND

r

NAVORD Report 3?59

SELF COMPENSATED MULTILAYER DISTRIBUTED C0T1STAHT DELAY LIKES

Prepared ayi

William So Carley

ABSTRACTt The inductance of a line is known to decrease with frequency,. The stray capacitance between turns is actually in parallel with the inductance of a turn. This forms a parallel circuit which can help offset the variation of inductance with frequency,. In the multilayer case the stray capacitance is increased many times. From these principles, design equations are developed for the multilayer line.

In the impedance range of 2.500 to 10s000 ohms these lines have delays ranging from 0.05 to 0,5 microsecond per axial incho These lines have characteristic impedances which are at least three times greater than conventional lines and delay times per unit length of about 10 times that of delay line cable.,

Experimental results in the form of photographs of the pulse response of several of these lines to pulse durations of 1.0 microsecond are given* RG-65 U delay line cable is used for comparisons

Experimental results shov; that the rise time of multilayer lines can be shorter than commevoi&l delay line cable if the delay is in the vicinity of h microseconds,

The investigation was mac?e as cart of Foundations! Research Task Numbers FR-^-52, FR-1;-^, and Ffl~29~5*K

1

U. S, NAVAL 0RDMNCE LABORATORY MI ITS QAKS MARYLAND

4te 11

i

H^OBP Hrporfc 3759 7 October 195^

The results of an investigation of high impedance delay lines are plven in this report. References are made in the text to thy following publications:

References

lo Wtao S» Carley and Edward F„ Seymour "High Characteristic Impedance Distributed Constant Delay Lines for Fractional Microsecond Pulses", Proca N.E.C., vol 8, pp 787-789§ 1953

2 c Wm. 3, Carley and Edward F* Seymour "High Impedance Arti=- ficial Delay Lines", Electronics, vol 2b, pp 188-19^5 Apr 1953

3o Vtoo S„ Carley "Distributed Constant Delay Lines with Characteristic Impedances Higher Than 5000 Ohms", Convention Record of the I.R.E. Part 59 PX> 71-805 1953

'4c, WE* S, Carley "Self-Compensated Kultilayer Distributed Constant Delay Lines", Proc N.E.C, vol 9, pp 150-1602 1951*

5o Wm» S<» Carley "Multilayer Distr3.buted Constant Delay Lines", Tele-Tech & Electronic Industries, May 195^» P T5*

60 Blewitt, Langmuir, Nelson and Rubel "Delay Lines", General Electric Rpt* May 31, 19H*3» Similar to T. P» Blewett and Jo H. Rubel "Video Delay Lines", Froc I.R.E., vol 35 pp 1580~15S>+* 19^7

7. G. N. Watson "Theory of Bessel Functions", Cambridge University Press, Cambridge, England; 192*

8, Stanford Goldman "Frequency' Analysis Jfodulation and Noise"* McGraw-Hill Bock Co., New York, New York, p 120? 19^8

9o B» A„ Erickson and H. Somraar "The Compensation of Delay Distortion in Video Delay Lines", Proc* I.R.E. s vol 38, pp 1036-iOifCs 1950

10o Ernst Weber "Electromagnetic Fields, Theory and Application" vol 1, John Wiley and Sons, New York. New York, p 150s 1953 David Ka Cheng 5 "A Note on the Reproduction of Pulses" 9 Proca I.R.E., vol 3*0, p 963; 1952

JOHN T. HAYWARD Captain, USN Cotisnander

9

Ha J. PLUKLEY By direction

HI

p

r<

NAVORD Report 3759

CONrJEKTS

Page Introduction • • * • i Theory 2 Line Construction . . • . . . 16 Measurements » • • • • i7 Experimental Results » • • • 18 Conclusions • •••••••••••••••••»•• 20

•;

iii

r -i NAVORD Report 3759

TV t- YT.-irnr> « niTMTO

Pag< Figure lo Cross Section of Line Figure 2„ Schematic Diagram of a Section of Line Figure 3« Plot of Number of Layers of Multilayer Bank

VS K -*/ 7TT>- Figure V., Plot of /£ vs ' >> for Various Values of q figure 5\> Plot cf % Variation in T vs q Figure 6, Plot of $ Variation in T vs ftf%) max Figure 7* Plot of fTTPA) max vs q ' ' Figure 6% Effects of Amplitude Distortion with 3D Phase-

Distortion Response to a Unit Impulse Figure 9<» Phase Shift vs Frequency Figure 10„ Effects cf a Sinusoidal Phase Distortion -with

;"o Amplitude Distortion on ths Response to a Unit Impulse

Figure 11„ Wound Delay Line, Slotted Gore- Slotting Equipment- and Wire Feeding Device

Figure 12o Photograph of the End Portion of a Bank Wound Line

B'igure 13 „ Block Diagram of Measuring Equipment Figure 140 Video Amplifier Circuit Diagram Figure 15* Block Diagram of Equipment for Cpen and Short

Circuit Data Figure l6c Pulse Response of Several Bank Wound Lines and

a Short Length of RG-65'/U Delay Line Cable Figure l7o Comparison of Pu2.se ResDonse of a Bank Wound

Line with RG-65/U Delay Line Cable and Gc E0 5111891 Delay Line Cable

Figure 18o Comparison of Several 3 Layer Bank Wound Lines for Various Types cf Insulation on AoW„G0 hi Wire

Figure 19o Pulse Response of a Line Wound with A.W.G. h? Wire

Figure 20,. Pulse Response of a 10^000 Ohm Line Figure 21o Pulse Response of a Line to Various Pulse

Durations , TfP/ Figure 22o A Plot of T/To vs 'A for a Typical Line

(Line C) Figure 23 o Comparison of Pulse Response of a Long Bank

Wound Line with RG-65/U Delay Line Cable Figure 2ha Plot of Rise Time vs Time Delay for Self-

Compensated Lines -sirf RG«-65/U Delay Cable

Table I Table II

IV

NA70BD Report 3759

SELF' COMPENSATED MULTILAYER DISTRIBUTED CONSTANT DELAY LINES

INTRODUCTION

1. Increasing application is being cade of distributed constant delay lines as circuit elements in present day electronic equip- ment* The characteristic impedance of these lines has been limited to values between *+00 and 3,000 ohms and delay times up to 1/2 microsecond per foot. The author recently reported pre- liminary investigations on multilayer bank wound delay lines with impedances from 5,000 to £0^000 ohms and delay times up to 1/2 microsecond per inch1*2*^****?. 2he object of this report is to consolidate the theoretical work in the design of multilayer lines with experimental results in the impedance range of 2.500 to 10,000 ohms.

2. Figure 1 is a view of the line, with a section taken along the axis of the solenoid. The line is assumed to be infinite in length and of a multilayer bank wound construction with capacitance to ground. In general the line was wound over the ground as shown in Figure 1 but several lines were wound with the ground over the line. 2 is taken along the axial direction of the winding. It is assumed that a mutual inductance exists between two elementary lengths of the wire which is dependent solely on the distance between them* A stray capacitance also exists between each turn and several of its neighbors. The overall diaceter of the wire with its insulation is b and that of the uninsulated wire is a. The number of layers in the bank winding is p. It is assumed that the wire in traveling from a top layer to a bottom layer, does not take up any space. It Is further assumed that the diameter D is a small part of a wave length at the highest frequency of interest*

3* The schematic diagram of the line in terms of lumped para- meters is shown in Figure 2, The section of the uniform line dZ in length is characterized by a shunt conductance dG * GdZ. a shunt capacitance dC » C0dZ. and a series resistance dK = mZ„ The structure is further complicated by the stray capacitance between turns and by the fact that the total phase shift is so large that the inductance of the infinitesimal section under study is influenced by the phase cf the current flowing in many other turns o It is assumed that the phase difference between the currents in the other turns is dependent on the distance between them aid the turn under consider a tion»

k-0 It will be assumed that the characteristics of the line can be deduced from the characteristics of any one elementary section taking Into account the effects of other sections on the ele- n«ntary section.

1

NAVOBD Report 3759

5. As in standard transmission line procedure we will assume a definite input current and voltage, and calculate the output current and voltage from the constants of the line0 As the line sections are already reduced to infinitesimal sections we may neglect the shunt elements in the computation of the effect or the series elements and vice versa.

6. In each section of the line the voltage is decreased be- caus3 of the series impedance and the current decreased by the action of the shunt admittance and the stray capacitance., In order to simplify the derivation It wJ.ll now be assumed that the current and voltage are sinusoidally distributed in the axial direction (Z) except in the calculation of the effective series inductance and the effects of the stray capacitance* This is a very good approximation as the lines have a very low loss and in fact will later bo assumed lossless to further simplify the rssulting equations,,

7. Noting that a dot over the quantity is used to denote a vector the equations of the voltage drop across an infinitesimal section of line and the shunt current may be written as

>dv(w",t) = RKw'StMw"-^ j m(w)£ i(w,,t)dw,| dw" (1)

V' =-- *o

and

u-°

-di(w",t) = Gv(v"it)dw"+ci. v(w,/fc)dw"+f/c(v)ij v(w",t)

~v(v%tj] dw'j dw"u where v = alternating component of the voltage,

i = alternating component of the current, R = resistance per unit length (mhos/meter)

(2)

G = conductance per unit length (mhos/meter; p = capacitance to core per unit length (far^

sjj(^j s nm&ual inductsnce per unit length between two of T*in« TeriffthdiTand dZ^

Cp = capacitance to core per unit length (farads/meter)9 mutual inductsnce per unit length between two elementary sections of line length dZ and dZ* separated by a distance w (henries/meter)«

w = (z«~z+f «»f) «= w» - v"

w"= z+r let i = linax sy-P j«#(t-i')

V and v s Vmax exp 3w(t-w»)

V where 0 » 2«V - 2*f

A

V « velocity of propagation*

•«•<»,.. . -•- . *-s- £:. . i<lu.»«. ••*• «w-:'f* -A.-.-?- '-^Mur-v-v - ». - . . b4Hft

NAVORD Report 3759

Let us look at J m(w) * i(w",t)dw,J

» iu>l /m(w) exp j u;(t-v') dw»,

* .jwl exp jw (t-w^) | m(w) expfj Vw)dw,

« jmi L(*>), <* (It)

where L(u>) = / m(w) expf ju'v ><*w, (5) v /^ v '" >

thus L&6 la the Fourier transform of m(w)

8o This problem may he simplified considerably by the follow- ing approximation., Let us assume that the i>adial depth of the winding pb << *? ajud in fact is ao small that (r,~r) —*> 0. In other words we assume we have a single layer solenoid wound with wire whose diameter is ^0 Thia assumption has been experimentally verified as will be shown later« In practice $ would have a lower limit of about 0.07" and pb upper limit abTJut 0.012" so that r' would vary from 0.06V to 0.076"«,

9« The parameter w then becomes a function of the axial sepa- ration between the reference turn and all other turns. This problem has oeen solved . The authors replaced the coil with a thin cylindrical sheet of radius s over which flows a current sheet in the axial direction

Is = I0 exp(-pZ) per unit length

where $ * 2ir

The solution of equation (5) was given as

L(<£) = felT (m)) K, OrD)l L_ (*> v L - X -1- X .'

where 1^ and K± are modified Bessel Functions of the first and sscoixu xxj.nc» * p

LQ » inductance of the line at low frequencies (henries/meter)„ D * mean line diameter (meters)„ ;, « axial wave length along the line (meters).

10o We now determine the capacitance coupling to the n th coll by considering the effect of ths nearest neighboring coils onlyQ Inasmuch as the variable of Integration in equation (2) is w° f

•MOBs; - • ..•„ — «. ••••••>. u t., * 'mms--' •» T . 3.m '•'.<**»*&.

HAVORD Report J759

one can take the differentiation sign out of the Integral thus

/cCw) * |v(v»,t) ~v(w»,t)j dv« -

iL 7 c(w) fvCw-jt) -v(w',t)l dvr'o (7J 5

11 o As the capacitance por unit length is constant equation (7) becomes

Ml

^ JL /[v(w\t) -v(w',t)] dw« (8)

Where C«. » stray capacitance between two adjacent turns and Of. m stray capacitance/unit 3.engthc

•-»* .*>*•>- .«... •^>>«ssss»BBNw,'*a3ta*i-**)<«*'«»«:-

Oo

7(w",t

J ) ~v(w»,t) ,- d »»s-(vn,-n-i -vn) -f-<vn.„ -vn).f.(vn,1 -vn)

„(vn^nil) ^ <vn -vn^. p ) ~(vn =vn..fp+i) (9)

!£ the n th turn had "been on the inside boundary

v(w»»,t) - v(vv',t)"]d^v'= - f(vn=.D -vft) - (vn - vn+1) = (vn .7n

•>(vn -vn^pi-lJ.

If the n th turn had been on the outside boundary fr -> r

Jjv(w",t)-v(w''?L) dw's- / (vn-p-,i -vn)~f-fvn^p -vn)-f (Vn.,a vn)

(vn 'Vn^p)J . Expanding by means of a Taylor series for the voltage of the adjacent turn in reference t>~> that of its neighboring turn and substituting x for w'

*+p)

(10)

(11)

vn+ 1- vn i

vn«l = vn

v. A b dtfjj .... b£ dfyn . /. . . . . Ux 2,! dx2"

6 ^n^.b2 d2v dx* dX ^2'

n „ • • * o «

vn+ p- vn + o-U b ifauL&A _L *' d2{vn +Jfci). , dx

vn»p— vn-p + b (dvr «.+. i J b2 dTVn-n 4 1 )

dx ^* dx^

a

2, dx

vn ip4-vn4 p.- 2 t b ?nt^* §, dT^±P-2# ax 2

•*) D • O O

dx<

b^ d3

© o O

(12)

(13)

(14)

(15)

(16)

(17) dx ° ;; dx^

Vn + p + l = vnfP + b |^n + p).|.|f. 4?2 (vn + p)+.^£3(vni..p) (IS

Substituting equation (14) in equation (18) we obtain

•"•*W»«*SH«»»«JHi^^ '«"'- •»«***«••- J-USsfifc?"**.*. .sriiMitaw****1*' S

a—• «. IM.Ii. I IH.

rn* p+1 = vn+o~H~k &-(V-p-lM— ilL(v T> b£ d^ (v .A

f> o ©

a « t « I (19)

Collecting terms

Wf vntP-.Vr- 21 ^-^n.f-p-l)f ^b£ flLCv^^jL ^ _d3 (^ ^ UA ox* 3 dxJ

, 2b4 d4. rvnAn *),.. (20)

Substituting equation (14) in equation (18)

rn+Ptl = vn-fp-2-i.^ feW+p-2*f^- ^ Wzlf

+ ab^i ^g^fp-2^ - . Ja2|S^(^p.2v *

tife^V- 1 o « +• 2b4

Collecting terms

v

3

2 *2

<*i-(v 1 dx^

vn+p^2^ • ' ' f,n (2i;

•aWl-Vp.2+311 A-(vn+p_2)+|b£ ^(vn+p.2) ^3 jl3 ( j UJi 2 dx-5

+ 24 •gprvn-fp-2<>-f<> • • • •

Substituting equation (17) in equation (22) Vn+p+l = *|rntp~34.4j2 4-(v^P"3U &£ ^<Vn+p-3L26J&L dL(v a O r dx • J < dx2 " '3 dx3^Vntp-»3J

\—<-/

29b4 d4 (v 0). J dx

6

(23)

»#U»--«s^* * • •'*£"•>• tJWH millli l1jBK»Bi#»^«g?J»W»'iWltr'^1' ?

P'HI—MO Ml — HH I •• •••••III' •!•••• ' III! !• I II WWII—i I |i>imw .'III—I

In similar fashion

•f ~P^ ^J ^nfp, 4)..;. |pl SLCVaj.p.4) ^- • • • • <<4

vn+pfls.vntp-5f.& fl-(vnfp-5>+ M- d|2<vntp~5)

180b3 d3 (v ^ c) . lQ80b4 d4 <v . A) L. /off. dx^ -•*-'• 24 dx

Thus

4.1 = vn+n.^.L.7b __ 3> ? 2 dx

^n4P4-ls vn+p~6jJ2l |-:(vn.,.p. 6kl5£ ^Cvn4,p..6<

^ Wa =* fe(Vn"p+l)f £: ^(vn-P+D- 2 67/

±H?^ gj(vn,p-6),||^i g,<v„+p-^+- - • (26) ]

etc until we get a scries for vnfpt>1 in terras of vn<,

similarly

vn-p~l r vn p -* J_(v ) fc£ 4::^(vn.p) -fcL d3 (vn.p) ax "2 ax*- 3 dxi

h4 *4 , > (27) £— fl_T(vncsp) 4 dx4

_ b ra-.(vn-.Pf 1) =b £,(vn»pfl)4 ft2 fll-Cvn-P+l). . . . . I J dx dx* ' 2 dx-3 j

+ £552(vn-pti: - bfl3 (vn„pti)^|S ^(vn^pfl^ H

- f ffe('»-Ptl> ~ "^W^ •Vl'j^vn .p+i> - J =(2C

L J L' J

ums$ammmm»''i

•*- •«—'••'-•- *'-'-:-"~:m- 7-7— v.-:V~..-«fttiUMl

ax ^ dx^ ' 3 dx3

, 17?J4 d4 (v O (29)

dx n 2 dx^ ^ 5^3 d3 (Vn,p^)

dx-3 (30)

-rvn.p^ - lb ^(vn.,p+3)+6b2 j2 <vn.pj3) . |8b3 «3 <n,.>p^)

trv.4 (3D

^ZSL. £,<vn.p+3). dx

sVn,.p+4 - & &.(vn.p^UgliS d£ (Vn.^4) - 53b3 dL,;v ^4) dx ' 2 dx2 " j Av^ dx3

-4 ,4 -LL'iL <* (vn nj4.) i p-?< O o • o o

(32) 12 dx* "

etc until we get. a series for vn„ -y in terras of vQ

If q is the number of turns removed from the reference turn a gonerel expression would be

v„tqi,"n * & ^(vn ) f. S.?. [<£_ - A7J|£L(vn

where

h3f f bJ &L E •3 I

2 WMMM

&L-<vn) • V )

41 I •••••••gl »ri i dx^

... b5fa5 D*1d5 (V ^

I"" J"" Af.O q<3

J2 (q~3)u

*4 01 mai

3 J^O |2

q'4

JfljJl- r 3J Q >; 4

cf=o q'4

1 2 (q-3)2

q>>4 J- 21

2 q^3

8

(33)

.... .„ .:. -....< '( -V .,•• <Vfc * iSta •BMBMMWMWWWWB»*C*^JW^4«-»^' '•

<T D \ -.0 o <4

/sr2 (q-3)3 0^,4 3.

— iv

For^an inside turn using equations (9) and (33)

J/v(w",t) -vCw' ,t)fdw,^G)(P+,l) d_ vn, b2 (o-KL)2 -A' :'i£- v., -£ L J I dx "+ "IT^ j dx? n

b3 (D-M)3 ~B»/dI, » b4

t-

(pfl)4 -c'/ £L v o » o * o

dx"* 'M—- i JL [ 21

A d2

jdX^

"\ t 1 £H ' BiJ » d^ xr

jr ]S3 u

b4 |p4 -C" d4 v 7 dx^ n • a a a b d V-<b2 d2 vn

dx ^'2T* Bx2'

b3 d3 Vni&4 d vn- 31 dx-i M-3 dx4 n

. o J. b d 'n+ b2 d2 v

d* " J 2l dl2 n

x. 1^ -jfil. v . V^ _d4 v 4 . ui)b <L v ^3J dx3 n\i dx4 n ' dx n

x £f|! -A"] ^ vn4blj£ -B'«7 d3 v b4[^ -c«

J-b(p^l) d_ vnJ.b2. [(p-ft)2 ,\'flldl. vr,D

3|(pfl) i d.x ' | 2~ dx2 "M ft~"

7«4 *n. .. « • •

J -B"'M v

4 7" 4 b^" j(o-fl) <•)<•••! a

CO V1 I dx4 (

!dx 75 n

U (34)

JL v(w",t) -v(v(,t) dvJ1 ~ - J b2 j 4^ii4gt4 ,A*/d2

/ J / ~~i 2> Ux n

— l)l=-

=C* d^ v , b4 |4p-i + 3r,3 tl2t£±Sp±4 ~c* rl-jr.3 ' : 4"

d4 V 1 dx • \ (35)

where f0 p<2 A* < 4 if p - 2

}8 p/,3

C* will not bo needed later and is not tabulated

.iv-stii--.*- •.'•S-JMBs. ^. •. — a. . »• •*"» '*»• Jt-^'^^^iMBB^SSMWWWi^aWiMSfci; ^^•W«='-- ^3M ,<»ffe-»... .»•- •"

> ^saggwawgawwHwiiaiw • ,r~. .. -J(l,.-^-?i-.-.«»

}

Prom an inside boundary turn using equations (10) and (33)

v(w«,t) -v(w<9t};dw'~ kPb d_ v ,,bf p2 . A»7 d2 vn

I """ to ' [5T J d? ^ fe -B« Jd3 vn , b4 [p4 „c„1 d4 v b d v

/ 3' /dx3 < / 4j /dx4 T dx

Kk£ flL vn i. VJ d3 v . b4 d4 *• dx«= - j>3 clx-^ ' 41 dx«

Pb A,, v *L.teL. ~A«i df, vn.b3 ^B«']dL yn4j£ j> ~ci4 vr

I _J CiX<

jJ>Cja±l)JL vn,b^Ll)2 -A"']dfL v b3 f(pi-l)3 »B'"]d3 v 1 dX I I 5i I ^,,9 ~f-=~ ~-~ —=~r n

3° J^x (dx2 ...

4 A ^ , i > 4 _r>Hi|' J*

ff

, b" Cp+i)'' -C»']ti' ^ j dx4 }

(36]

Jjv(w",t)-v(w' ,t) I dw»- - f(p*2) bd v.b2 Hp2* 2u-K> ^Id2 v

s b r

where

dx-

A** [ 0 P ^2 r *J 2 if p - 2 v..

foi* an outside boundary turn using equations (11) and 03)

Jv(w"t) -v(w.'t) [dwL - )~(pfl)bcL vn > """""~ dx s7 J I

,b2 (pfl)2 -A'jd2 v r,3 (ofl)3 „B' d3 v /2! dx* j i» dx3

, fil p^i)4 -C'/dL -V. . . .o^bd v , b2 |>

I 10

(i l,a^

? f

dx ,k

" •-• - ' •--• - • •* - - < " -**.^

.^..-, : •**. s«B^»&!WWaii^ll««*BWsrsflP»-?

•

b3 Hi »B»^ vn ,£ U.c«]d 3J dxJ •\3 •nJ.iL. |£_ -C"[" V 1 I 4J Idx4

b d vnfif £L vn - lb3 £ vni*4 cl4 v dx d:c 3 J cb° ax

, £b d_ VjabSfpS -A-'Jdf vn , b3 p3 _B.i d3._ vn

3-' dx-5

r. 4»

•C d4 v

dxH C • 9 I (38)

jv(w"t) -v(v;»,t) | dw»ss - ) -(p+2) bd_ v ,/D2 I ~* "dx "' !

3p->2p-H2 - A°* d11" v„ -TJ n

b3 >3-3P

2.3P -B°*f£. v b*[3 p^W -4P4-2

3.' |dx:i J 4«

-where Aot v 0

(6

p < 2 p ; 2 o ?,3

2

dx

o*id4 vr/ dx^ (

J

(39)

? C°*l£L vnt

To a first approximation we may neglect all terms higher than the second derivative if the phase shift per turn is small..

(40) urn

e<»

v(w",t) -v(w't) dw1- b2£p2f p^i)2 -A*7d2 vn for an inside t

j jdx2

(41) :-b(pf2) d_ V

dx n ~«

for inner boundary turn.

3P^f2p-f2 ~A* (H v

2 J 'idx*1

ifo(w",t) -v<w»,t) dw'r: b(of?) d_ v - b2/3P?'7 2pf2 -A°* | d_2 v„ -~L ' J dx 21 I dx- for outside bondary turn (42)

I*© If P^.3 and substituting w" for x 1 r

.. £Xk

v(w"^) v(v;'t) jdw?~ jb(p?2) d_ v f b2 3p2f 2p^-2 -A* id2 vn • ' - - ' fdw^

(43)

QW i 2J

b2(p-2)| (n^pfl)2 -A* JdJL vn - b(p^) d_ vu

b2 bsfi^oi^ ~r j d2 vn ] | 2: j dF2 f 11

*• .^u.-.

1 |v(\v",t) -v(v?a,t) dwE- •- .)b2(2p3^-p2 -2 A0) d£._ vA

where An:r 8p -4 P > 3

(44)

For the special case of a 2 layer coil DO

v(w",t) -v(w',t) I dw'-«14b^ dT_. vn LL i * dw'2

,', )f"v(w%t) -v(w',t)| dw'- Kb2 d5_o = K yL b2 v

(45)

(46)

where K is given in Table. 1.

TABLE I

Number of Layers 1 2 3 4 5 6 7 8 9

10

K j.

14 43 116 239 424 633 1028 1471 2024

A plot of K vs the number of layers appears in Figure 3«

Equations 1 and 2 then become for sinusoidal applied voltages as in equation 3-

J <*E - ri .|,.](4L4L(^ (47)

jfcft - Gv^jC* (Co^J^bKgti V

(48) V

If These equations are those of an ordinary distributed constant 1

L : L CM)

L * c0

C4q)

(50)

12

,. ,„ . • . • • V • » **> *•£*• •'-•;. "^»»» ••»-«,**n»>.«ipm«^. . •' ••=•• .-•• •

If the line Is now assumed to be lossless, the well Known solution of the transmission line equations of interest ares

time delay (per unit length) T =yLC (sec/meter) met p **• » it

phase shiftzQ) -UJHLC (rad/meter)

characteristic impedance z( YC (ohms)

(5D (52) (53) J° Y C

Inserting equations (6), (4c) and (50) Inequation (51) we obtain

/I To/

H 2*1 U2£) % (ffi)) i l-i/^f £LJ£ i (54) •"A \T* J

where TO^V/L0CO? is the low frequency time delay. Substituting in equation (54) for ^ we obtain

/if- 21., (3TD) *! (2jB) [lf<» <W '; (55)

where 4 Ct Kb f. IK (56)

12o It is thus apparent that the stray ctpacitance between turns, G+, is multiplied by a fsctor K0 For a single layer line (K = 1) the effect of this capacitance is negligible,. For a 3 or more layer line K has been increased many times and actually is large enough to compensate for the decrease of Inductance with frequency as far as time delay is concerned» It is true that the characteristic impedance will suffer from this compensation, as it does with all other known compensation measures in delay lines. However the time delay is in general far more critical than characteristic impedance. This stray capacitance actually becomes our compensation and these lines are thus called self-compensated lines0

13 • & plot of $0 from equation (55) is shown in Figure **o It will be observed that for a given delay line with q>o, 3;

o decreases as the frequency increases to some minimum value and then increases without limit,, If the maximum variation in time delay is prescribed q may be determined«>

l*f<, "If the variation from a linear phase characteristic is no more than 1/2 radian in a frequency range of .1

3 x pulse length

.. „••*.., '-' •**. "'' ** '**' '-».' iU^waMEE»~; • . . I -

NAVORD Report 5759

there will probably be no serious loaa of signal detail©"8 "If the variation from a linear phase characteristic is as much as one radian in a frequency range of 1

3~: "^ulaeTTengih" complete loss of signal detail may be expected, o If a syst-em is to pass pulses of duration T the approximate bandwidth is made"

P • 1 • (57)

Prom the above, however, v/e require that the deviation from linearity in 2/3 of the bandwidth given by equation (57) shall not be more than 1/2 radian*

15* Thus, if a pulse whose duration was 0.166 microsecond was to be passed, the phase distortion would have to be less than 1/2 radian up to 2 megacycles• This corresponds to a total error in time delay (T-T0) of 0o0l|. microseconds, Thus, if the total delay was 1 microsecond the error could be ]+#<>

T 16. Let us arbitrarily allow the m curve to go as much above io

1, for a given value of q, as the curve did go below 1© Thus, from Figure i|, we can secure the % variation in time delay vs q. This curve appears as Figure 5» Thus, in the example of the last paragraph q must be greater than 0*55• Figure 6 is a plot of % variation in time delay vs (, "^. -)max° Tbe valuo °* was obtained from Figure \\. where the* T/To curve orosses the maximum error in T allowable in upward direction. Figure 7 shows (^ )n«>y vs q from Figures 5 s^d 6*

A 17* The variation In time delay of these multilayer self* compensated lines are very similar to single layer lines with compensation patches?,

i8o The design equations of multilayer lines may now be stated.

Rewriting equation (56) as

C 8 >fCt Keb farads/meter, (58) o —^ )

and using Ct - ^ ^2^^ r^— farads, (59)

7F J b^a" where Kg is the relative dielectric constant of the insulation on the wire, we finally get

•

0o » k-jf 2Kg £ 0Kb rg— farads/meter„ (60)

D /2~q J S^a ThSs Is a convenient form to relate the compensation capacitance (C*) to the capacitance to ground (c ) as we have equations to

Ik

NAVORD Report 3759

relate to CQ to the physical dimensions of the line,

Co " 2<rrKed go farada/meter, (6l)

where K^ is the dielectric constant; of the insulation between the core and the winding,

Do la the core diameter,

and D^ la the diameter of the core plus the inaulationo

19o This almple formula is applicable In most multilayer linos, but it should be noted that there is a capacitance formed by the insulation on the wire itself. As the dielectric constants are not, in general, the same, more exact results may be secured by considering both mediums10. In most cases however equation (61) la accurate enough.

2Qo She inductance of a long solenoid is given by the well known expression

L. » TTN2 D2MC (henries/meter), (62) o j-

where N la the number of turns per meter<>

21o From Figure 4 *•* is obvious that some variation in time delay is unavoidable• This variation in time delay is a vari- ation in phase response (see equations (51) and (52))„ It is well known that any variations in the amplitude or phase response of a system will alter the wave form of the output signal of the systemso From the method of paired echoesA1 we know that amplitude distortion produces distortion symmetrical about the center of the pulse, while phase distortion produces antl« symmetrical distortion of the pulse. The response of a unit impulse passed through several kinds of amplitude distortion is shown in Figure 3s Frosi some measurements made on the amplitude distortion of these lines with sinusoidal signals applied, it appears that the response of these lines resembles (c) through much of the range with e sharper drop at so*ae higher frequency where the amplitude is already very low©

22 o The phase distortion of an uncompensated and self "compensated line is shown in Figure 9<> The phase distortion approaches the form indicated in Figure 10o Ths response to a unit impulse is also shown In Figure 10 if the phase error is assumed sinusoldalo The response is altered by the echo or impulse overshoot. The magnitude•*•* of this echo is

Jl (££) JrT*11 ' (63) 3-5

KAVOBD Report 3759

where J-, ia the E®ssel Function of the first kind and 1st order, j is the Bessel Function of the first kind and Oth order, °

23. It is thu3 apparent that the amplitude distortion produces symmetrical overshoot echoes and phase distortion produces anti- symmetries! overshoot echoes. Measurements of amplitude and phasa distortion echoes on typical lines used in this report are shown in Table II. This table demonstrates that phase dis- tortion is causing most of the overshoot in most of the lines wound.

2*f. Thus with the aid of equations (5l). 153), (60), (6l). (62), (57) and statement below equation (57), and Figures 3, ** and 5 this type of line may be designed. Lines have been wound when the average number of layers was not an integer. In this case the value of X was read from Figure 3 for the average number of layers. No difference in performance of these lines has been noticed.

25* In general, lines have been bank wound with layers from 2 through 5 and wire sizes from 32 through k? with several kinds of insulation. These lines have had Impedances from 2.000 ohms through 10,000 ohms and time delays from 2.5 to over 3$ micro- seconds per meter. Examples are given in Table II. Experi- mental evidence to substantiate the theory developed in this section will be given.

Line Construction

26. The lines were wound on 3/l6 inch diameter polystyrene cores 12 Inches long. These cores were given several coats of silver conducting paint to form the ground strip. Although the cores could be slotted after an overnight drying period a much cleaner cut was made if the drying period was several days. The cores were axially slotted forming 36 thin strips, each strip being about 0.015 inch wide. The slots were about 0.003 inch wide. A one inch length of the core was left unslotted to facilitate the connection of the external ground lead. The core was covered with a layer of insulating material to give the re- quired winding-to-core capacitance. A piece of thin teflon tape was wound around the core. A number of small pieces of scotch cellophane tape held the teflon on the core until the line was wound. The scotch tape was removed piece by piece as the line was wound.

27. The winding was done on a lathe. In order? to provide uniform wire tension, both to secure a good winding and to pre- vent breakage, a wire feeding device was used. The wire feeding device and the slotting device are shown in Figure 11. The wire tension was adjustable over a range of about 10 to 70 grams. The tension was continuously indicated by a pointer.

16

u«n

NAVORD Report 3759

28o A wire guide attached to the longitudinal feed of the lathe was placed about 1/16 Inch from the core, which was chucked In the lathe* The longitudinal travel of the wire guide could be ao low as 0*, 00066 inoh per turno As this distance Is a fraction of the wire diameter, the result was a multiple layered coll approximating a bank winding. The far end of the core was attached to a counter chucked in the tall° stock * A steel drill rod was Inserted through a hole In the core for rigidity. A 10 Inch long winding was wound on the core* Lines have been wound with speeds varying from about 200 to 800 rpm0

29« A magnified view of the end of the line showing details of construction appears In Figure 12„

Measurement s

309 The method for determining the characteristic impedance of these delay lines was baaed upon the fact that no re- flections occur in an Idealized delay line terminated In character1stic impedance. The value of the characteristic impedance in a praotlcal case involving complex waves must therefore be compromised for minimum reflections over the band of frequencies for whioh the line is designed to operate* The lines were terminated at the input as well as the output to minimize any possible secondary reflections at the input* A suitable means of determining the effective characteristic impedance when the line is used to delay rectangular pulses is to feed the pul&e itself Into the delay line and to adjust the terminating impedances for minimum reflections* A block diagram illustrating the experimental method for determining the characteristic Impedance of these delay lines and for recording the response of the delay lines to rectangular pulses appears in Figure 13c The pulse generator was of the delay line type© RO-65/U delay line cable was used* This pulse generator was triggered by a La vole type LA~592A pulse generator* A Hewlett Packard type 212A pulse generator was used on oocasion in observing the response of the lines to pulses of greater than 1 microsecond duration,, A Tektronix type 517 oscilloscope was used, The oscilloscope sweep was triggered by the input pulse* A camera, mounted on the oscilloscope, was used to record the input and output wave shapes of the delay line, A video amplifier was placed between the delay line and the pulse generator. The load impedance of the video amplifier was made equal to the characteristic impedance of the liner A diagram of the video amplifier appears in Figure 14*

310 The pulse distortion and attenuation were also measured with the same equipment* The oscilloscope camera was used to record the wave forms of both the input and output signals and the measurements were made directly from the photographs as the sweep of the type 517 oscilloscope is quite linear and the sweep time in milli»microseconds per centimeter quite accurate.

:

- 3

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NAVORD Report 3759

32e The vertical gain was kepi; constant for both input and output pulses so that attenuation measurements could be made from the photographs•

33o The delay time as well as the rise time and fall time was likewise measured on the oscilloscope,. The delay time was defined as the time between the mid-point of the leading edge of the input and output wave forms• The rise and fall tlmea were defined as the time duration between the 10# and 90$ values of the pulse amplitude• The pulse duration was defined as the time between the $0% values. The attenuation was measured by comparing the amplitudes of the input and output pulses*

3I+0 Although the pulse response of the lines was Used as a measure of their ability, some sinusoidal data were taken,, In crder to determine the validity of the equations, a line was connected to a r*f. signal generator through a 10,000 ohm resistor as shown in Figure 15* The Tektronix 517 oscilloscope was used as a VTVM» With the line short circuited, the frequen» cies at which the impedance of the line was a minimum, was noted. The line was thus electrically A, 3 h

2 TT etc longo The measure*

ments were repeated with the line open circuited, the line then being £, 3 A , 5 A etc* long electrically* Prom this data* the

measured values of LQ. and 0o at low frequencies, and the physical dimensions of the line. irD could be calculated*

T Experimental Results

35o Photographs of the input and output wave forms for several short lines appear in Figure 16* All input pulses are 1 micro* second duration* Line A has an average of i|«7 layers of AWO ijlF wire and was I065 inches long v/ith a delay of 1-03 micro° seconds* This line had a bad reflection occurring near the middle of the line as can be observed* Line B has If.'layers of AWO I4JLF wire and was 2*14J. inches long with a delay of 0*6 microsecond* Line C has 3 layers of AWG 39F wire and «as 2«=»3/fy- inches long and had a delay of 1017 microseconds0 The last row of photographs are the input and output wave forms observed using a 15 foot piece of RGt=>65/TJ cable which had a delay of 0<>7 microsecond* The gain of the scope was kept constant in each line ao that the attenuation in the lines may be oboervedo

36* Photographs of the inputs output and Input and output wave forms superimposed for another line appear in Figure 17o Line D has 3 layers of AWO IflHF wire and was 9*75 inches long* It had a delay of 2,1 microseconds* In the photograph of input and output wave forms superimposed come small variations are observed in the base lixra* Those not originating with the pulse Itself (due to finite passband and compensation limitations) probably occur due to minor reflections from discontinuities in the linec

£8

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HAVORD Report 3759

Reflections of this magnitude are present in most of the lines wound* For comparison purposes the response of a k6 foot piece of RG-65/U cable is shown as well as a 3 foot piece of General Electric 1100 ohm cable.

37. Examples of lines wound with other insulated wires appear in Figure 18, All these lines are wound with 3 layers of AWG *+l wire with different types of insulation. Line F was wound with heavy formex insulation (Kg = 3.1). line F was wound with Sprague Electric Company Ceroc ST insulation (assumed Kg = 3). This wire has an inorganic ceramic insulating coating thinly deposited on copper wire with an overlay of teflon* Line G was wound with Sprague Electric Company Ceroc 200 insulation (assumed K© • 3). This wire has an overlay of silicon instead of teflon out otherwise the same as Ceroc ST. Line H Is a teflon insulated wire (Kg « 2) of Hitemp Wires, Incorporated. In general the characteristics of all these lines are similare Due to the lower dielectric constant of the teflon, line H has a higher characteristic impedance and a shorter delay per unit length.

38. Lines have been wound with size AWG h? wire. The pulse response of such a line appears in Figure 19. It will be noted that the attenuation for this line is considerably greater than those previously mentioned. This is due to the increased ohmic resistance of this very small wire. Extreme care had to be used in winding lines with this small wire.

39B The response of a higher impedance line is shown in Figure 20. This line had characteristic impedance of 10,000 ohms. The response of another line to pulses of various durations is shown in Figure 21.

M). An attempt was made to check Figure h by the method outlined in section 17. The measurements made on line C is shown in Figure 22. The crosses indicate open circuit measurements and the circles indicate short circuit measurementsf a comparison of Figure 22 and Figure h indicates that q is about 0.**. From measurements of capacity to ground the value of q was found to be 0.605o The error is considered to be well within experimental limits when one considers that there was no means of accurately placing each turn in accordance with the geometrical pattern assumed in the theoretical derivation. Measurements were also made on several other lines and the discrepancy of these lines was about the same as the one shown.

*H. Characteristics of a line with longer delay are shown in Figure 23. This line was 35-1/2 inches long and had a delay of 7.35 microseconds. As a comparison a 112 foot section of RG-65/U cable is shown. This cable had a delay of 5ob" micro- seconds. It is apparent that the rise time of this line is considerably better than that of RG-65/U cable even though its delay is considerably longer„ Several bad reflections are apparent due to wire breakage and improper winding.

&*,, • • *

19

oytrMi*1 *

NAVORD Report 3759

*f2. The rise times of several of the lines which were more or less identical have been plotted In Figure 2h, The data points on curve are indicated with crosses. The data points for RG-65/U cable are indicated by circles. From this curve it is apparent that the rise time of self- compensated lines and RG-65/U cable are about equal at a delay tiiae of about 3.? microseconds and at longer delays the self-compensated line is considerably better.

**3« More data on the lines shown in all the photographs appears in Table II. The cut-off frequency is computed from the rise timell.

*o = P.W? CM Tr

CONCLUSIONS

MH Experimental evidence has shown good agreement with the theoretical analysis within experimental error.

*f5« It is observed that these multilayer self^-compensated, bank wound lines have considerably longer delays per axial inch, have considerably reduced attenuations for the same delay time, but suffer from more internal reflections- For short delays (up to about 2 microseconds) the rise time is considerably poorer. This, of course, means lower cut-off frequencies. At delays of greater than h microseconds, however^ the rise time is considerably better than RG-65/U. This is attributed to the fact that the output pulse of these lines remains largely unchanged as the time delay increases, while RG-65/U cable has an exponential rise and fall with a flat top.

h6. Experimental evidence indicates little variation of attenuation with different wire insulating materials. A higher dielectric constant material on the wire would give increased compensation and thus give even greater delays per unit length*

h7. It appears that the attenuation of these lines can be re- duced somewhat and fewer minor reflections obtained if a better winding technique can be developed to approach more closely a true bank wound line.

20 '«* Mi -f * *-: «'--*"*""'* r.;^-*-^^ '_ •' ' •'••'.

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AMPLITUDE DISTORTION OF SYSTEM SYSTEM RESPONSE TO UNIT IMPULSE

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WITH NO PHASE DISTORTION ON THE RESPONSE

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NAVORD REPORT 3759

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COMPENSATED ^DESIRED CURVE

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FIG. 9 PHASE SHIFT vs FREQUENCY

PHASF DISTORTION OF SYSTEM SYSTEM RESPONSE TO A UNIT IMPULSE

FIG. 10 EFFECTS OF A SINUSOIDAL PHASE DISTORTION

WITH NO AMPLITUDE DISTORTION ON THE RESPONSE

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LAVOIE LA-592A

PULSE 6EN

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UNDER TEST

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FIG. 13 BLOCK DIAGRAM OF MEASURING EQUIPMENT

NAVORD REPORT 375S

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NAVORD REPORT 3739

RF SIGNAL

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FIG. 15 BLOCK DIAGRAM OF EQUIPMENT

FOR OPEN AND SHORT CIRCUIT DATA

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NAVORO REPORT 3759

INPUT OUTPUT

r^A

LINE A —H U—

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IJ65 IN. LONG, 4.7 LAYER BANK WOUND LINE USING 41 FORMEX INSULATED WIRE (TOTAL DELAY L03/*SEC)

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FIG. 16 PULSE RESPONSE OF SEVERAL BANK WOUND LINES AND A SHORT LENGTH OF RG-65/U DELAY LINE CABLE

NAVORD REPORT 3759

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INPUT OUTPUT INPUTS OUTPUT

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FIG. 18 COMPARISON OF SEVERAL 3 LAYER BANK WOUND LINES FOR VARIOUS TYPES OF INSULATION ON A.WG. 41 WIRE

NAVORO REPORT 3759

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NAVORD REPORT 3759

OUTPUT SNPUT AND OUTPUT

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0.2 fl SEC PULSE

0.3 fl SFC PULSE

0.5 fl SEC PULSE

1.0 fl SEC PULSE

2.4 fl SEC PULSE

FIG. 2! PULSE RESPONSE OF A LINE

TO VARIOUS PULSE DURATIONS

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NAVORD REPORT 3759

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FIG. 24 PLOT OF RISE TIME vs TIME DELAY FOR SELF COMPENSATED LINES AND RG-65/U DELAY CABLE

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DISTRIBUTION

Copies

Chief 9 Bureau of Ordnance , Navy Department Attn: Re, Re6 1

Rexg, Re2b, Relj., R«9 2

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|

Director, Naval Research Laboratory 2 Washington 20, Do C, Attn: Technical Information Officer

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Johns Hopkins university, Radiation Laboratory 1 Baltimore. Maryland

Director, Colas Signal Laboratory, SCEL 1 Ft, Monmouth, New Jersey

Chief* Engineering and Technical Division 1 Office of the Chief Signal Officer Department of Defense, Washington 25s Do Co

Bell Telephone Laboratories 1 Murray Hill, New Jersey

Naval Ordnance Test Station (NOTS) 1 Inyokern, California

Naval Ordnance Laboratory 1 Corona, California

Diamond Crdnanoe Fuze Laboratory 1 Washington 25 „ Do Co

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IIA.VORD Report 3759

Copies

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ervices Technical Information ~"H

&m Because of oar limited supply, you are requested to return this copy WHEN XT HAS SERVED YOUR PURPOSE so that it may be made available to other requesters. Your voapewXion will be appreciated.

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