A Broad Frequency Band Non-Reflecting Termination for Free Space Electromagnetic Waves

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PURDUE UNIVERSITY

TH IS IS TO CERTIFY THAT TH E T H E S IS P R E P A R E D U N D E R MY S U P E R V IS IO N

BY

James Wilson Green* j r .

entitt.eu

A BROAD FREQUENCY BAND NON-REFLECTING TERMINATION FOR FREE SPACE ELECTROMAGNETIC WAVES

COM PLIES W ITH T H E U NIV ERSITY R E G U L A T IO N S O N GR A DU ATIO N T H E S E S

A N D IS A PPR O V ED BY ME A S F U L F IL L IN G TH IS PAR T O F THE R EQ UIREM ENTS

F O R THE D E G R E E O F

Doctor

of

P hilosophy

P r o f e s s o r in C h a r g e o f Th e s is

H ead of S chool or D epartm ent

TO TH E L IB R A R IA N :---IS A c JT TH IS T H E S IS B B S O K TO B E R EG A R D E D A S CON FIDENTIA L.

GRAD. SCHOOL FORM 9—3-49—1M

A BROAD FREQUENCY BAND NON-REFLECTING TERMINATION FOR FREE SPACE ELECTROMAGNETIC WAVES

A Thesis Subm itted to th e F a c u lty of Purdue U n iv e rs ity by James W ilson Green, J r . In P a r t i a l F u lfillm e n t of t h e Requirem ents f o r th e Degree of D octor of Philosophy June, 1950

ProQuest Number: 27714066

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uest ProQuest 27714066 Published by ProQuest LLC (2019). C opyright of the Dissertation is held by the Author. All rights reserved. This work is protected against unauthorized copying under Title 17, United States C o d e M icroform Edition © ProQuest LLC. ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106 - 1346

ACKNOWLEDGMENT

The au th o r g r a te f u lly acknowledges th e encouragement and a s s is ta n c e o f P ro fe sso r George R. Cooper under whose super­ v is io n t h i s a n a ly s is was c a r r ie d o u t and th e many* h e lp fu l su g g estio n s made by P ro fe s so rs R. P. S isk in d and E. M. Sabbagh.

TABLE OF CONTENTS

Page ABSTRACT......................................................................................................

i

INTRODUCTION.........................

.

1

.................................................................

7

THE TWO FILM TERMINATION

THE THREE FILM TERMINATION.....................................................................li* THE N FILM TERMINATION......................................................................... 25 DESIGN FORMULAS.............................

36

FILM CHARACTERISTICS.................................. THE GENERAL ANGLE OF INCIDENCE

.

1*5

........................................................53

L in ear P o la r iz a tio n i n th e P lan e o f I n c i d e n c e .........................53 L in ear P o la riz a tio n Normal t o th e P lane

of In cid en ce . .

Wave Guides and T ransm ission L ines . . . . . . . . . . . CONCLUSIONS..........................................

56 61 65

APPENDIX - CALCULATIONS AND D A T A ........................................................ 6 8 BIBLIOGRAPHY AND CITED REFHRENCES........................................................ 78 V I T A ...............................................................................................................

LIST OF FIGURES

F ig u re

Page

1.

Frequency C h a r a c te r is tic of S in g le Film T erm ination . . .

2.

T ransm ission Line E q u iv alen t of M u lti-film T erm ination

3.

The Two Film T erm ination

In

Frequency C h a r a c te r is tic of th e Maximally F l a t Two Film T e r m i n a t i o n ......................................................

12

A dm ittance Loci as a F unction o f Frequency - Two Film T erm ination ................................. • • • • •

13

5.

3 .

5

................................................

8

6.

The Three Film T e r m i n a t i o n .................................................................15

7.

Frequency C h a r a c te r is tic of Three Film Term ination

8.

Adm ittance Loci a s a Function o f Frequency-Three Film T e rm in a tio n ...............................................................

9.

. . .

22 21*.

V oltage D is tr ib u tio n - S in g le Film T e r m i n a t i o n .......................27

10.

V oltage D is tr ib u tio n - Two Film T e rm in a tio n .........................

11.

V oltage D is tr ib u tio n - Three Film T e rm in a tio n ...........................29

12.

Frequency C h a r a c te r is tic of S ix Film T erm ination

13.

Film D esig n atio n s f o r Use w ith D esign E q u a tio n s ...................... 38

ll*.

P ercentage Band Width Over Which R e fle c te d Energy I s 26 db D o w n ..................................

1*3

15.

Cross S e c tio n of a Conducting Film

1*7

16.

R e fle c te d Energy as a F u n ctio n of th e Angle o f In c id e n c e . E i n th e Plane of In cid en ce . .....................

55

Frequency C h a r a c te r is tic o f S ix Film T erm ination. Angle o f In cid en ce 30 d e g re e s. E in Plane o f I n c i d e n c e ..........................................

57

17.

. . . .

. . . . . . . . . . .

28

35

18.

R e fle c te d Energy as a F unction of Angle o f In cid en ce. E Normal to Plane o f In cid en ce ............................................59

19.

Frequency C h a r a c te r is tic of S ix Film T erm ination. Angle of In cid en ce 30 D egrees. E Normal t o Plane of In cid en ce .....................

60

LIST OF TABLES

Table 1*

Performance D ata on S ev eral Four Film T erm inations

2.

Film R e sista n c e s i n Ohms f o r T erm ination o f Free Space W a v e .........................

. . .

A BROAD FREQUENCY BAND NON-REFLECTING TERMINATION FOR FREE SPACE ELECTROMAGNETIC WAVES

By James W ilson Green, J r . AN ABSTRACT T his d i s s e r t a t i o n c o n s titu te s th e i n i t i a l d is c lo s u re of a p r in c ip le o f d e sig n o f r e s i s t i v e , n o n - re f le c tin g electro m ag n etic wave te rm in a tio n s f o r u se over a b ro ad band of fre q u e n c ie s#

The

te rm in a tio n c o n s is ts o f a mmfoer of r e s i s t i v e elem ents mounted i n th e tra n sm iss io n medium a t e q u a lly spaced in te r v a ls of oneq u a rte r w avelength a t th e nominal d esig n frequency#

The elem ent

f a r t h e s t from th e so u rc e h as an exceedingly sm all r e s is ta n c e which may be co n sid ered as e s s e n t i a l l y zero#

The v alue

of r e s is ta n c e

a s s o c ia te d w ith th e o th e r elem ents i s such a s to make th e desig n frequency v o lta g e or e l e c t r i c f i e l d a t each elem ent p r o p o rtio n a l to

%» “

F

where N i s an in te g e r equal t o th e nunfoer o f r e s i s t i v e elem en ts, excluding th e f i n a l zero r e s is ta n c e elem ent, and K i s an in te g e r d e sig n a tin g th e p a r t i c u l a r elem ent under c o n sid e ratio n # D esign form ulas a re p re se n te d to en ab le t h i s p r in c ip le to be t r a n s l a t e d in to a c tu a l d e s ig n .

Perform ance of v a rio u s term in a-

ii

tio n s as a fu n c tio n of frequency and o f an g le o f in c id e n c e i s c a lc u la te d . An a n a ly s is of th e c h a r a c te r is tic s of th e film s r e q u ire d f o r th e te rm in a tio n in d ic a te s them to be p r a c t i c a l . The a p p lic a tio n o f th e p r in c ip le to n o n - re f le c tin g term in a­ tio n s f o r wave g uides and tra n sm iss io n l i n e s i s p o in te d o u t, and th e t h e o r e t ic a l perform ance i s analyzed.

A BROAD FREQUENCY BAND NON-REFLECTING TERMINATION FOR FREE SPACE ELECTROMAGNETIC HAVES

S e c tio n I INTRODUCTION This re s e a rc h , u n d ertak en to d esig n a broad freq u en cy band n o n - re f le c tin g te rm in a tio n f o r f r e e space electro m ag n etic waves, soon in d ic a te d th e d e s i r a b i l i t y , i f n o t th e n e c e s s ity , t h a t broad band be in te r p r e te d i n th e sense t h a t i t i s u s u a lly a p p lie d to microwave devices*

T his i n t e r p r e t a t i o n d ir e c te d subsequent

in v e s tig a tio n and a n a ly s is tow ard achieving t h e d e sig n through th e u se of a s e r ie s of t h i n energy d is s ip a tin g film s p laced normal to th e d ir e c t io n o f p ro p a g a tio n of th e wave.

S* A. S chelkunoff 1

has d isc u sse d th e u se o f a s in g le film f o r an e f f e c tiv e te rm in a tio n o f a wave guide and Razno and Whinnery^ have in d ic a te d a lo g ic a l e x te n sio n to in c lu d e th e te rm in a tio n of a f r e e space wave.

The

c h a r a c t e r is t i c s of such a s in g le f ilm and th e spacing re q u ire d between th e f ilm and a p e r f e c tly conducting su rfa c e which forms th e f i n a l elem ent of th e te rm in a tio n a re developed i n th e in d ic a te d r e fe r e n c e s .

1 2

S. A. S ch elk u n o ff, E lectro m ag n etic Waves, D. Van Nostrand C o., New York. 191*3. Ramo and Whinnery, F ie ld s and Waves i n Modem R adio, John W iley and Sons, New York.

2

This s in g le f ilm te rm in a tio n i s frequency c r i t i c a l .

The

sp acin g betw een t h e f ilm and th e p e r f e c tly conducting s u rfa c e which forms th e f i n a l te rm in a tio n must be e x a c tly a q u a rte r of a wave­ le n g th i n th e medium i n which th e wave i s pro p ag atin g i f a th e o r e ti­ c a lly p e r f e c t n o n - r e f le c tin g te rm in a tio n i s t o r e s u l t .

The

freq u en cy c h a r a c t e r is t i c o f a s in g le f ilm te rm in a tio n f o r a p lan e wave p ro p a g atin g on a normal to th e f ilm s u rfa c e has been c a lc u la te d and i s shown i n F ig . 1 . To in c re a s e th e frequency band over which th e te rm in a tio n i s e s s e n t i a l l y n o n - r e f le c tin g , i t i s lo g ic a l to employ a network which d i s t r i b u t e s t h e energy d is s ip a tio n

among

s e v e ra l p o in ts

o r su rfa c e s in s te a d o f d is s ip a tin g i t a t a s in g le s u r f a c e .

In

s h o r t, a su c c e ss io n o f f il m s , each of which absorbs a p o r tio n of th e t o t a l energy i n th e in c id e n t wave, o f f e r s a p o s s ib le s o lu tio n t o t h e broad freq u en cy band c h a r a c t e r i s t i c d e s ire d i n th e te rm in a tio n . There a re s e v e ra l a l t e r n a t iv e s i n th e d e sig n of a s e r ie s o f f ilm s . 1)

Each film may have i d e n t i c a l c h a r a c te r is tic s b u t

t h e i r sp acin g v a ry in accord w ith a f u n c tio n which p ro v id e s th e maximally f l a t frequency c h a r a c t e r is t i c d e s ir e d . 2)

A c o n sta n t spacing between th e f ilm s may b e main­

ta in e d b u t t h e s u rfa c e r e s i s t i v i t y o f each vary i n accord w ith a fu n c tio n which p r o tid e s th e maximally f l a t frequency c h a r a c t e r is t i c d e s ir e d . 3)

A com bination of 1) and 2 ) .

3

2 ,6

2 .4

1.6

1.4

1.2

5 FREQUENCY

FIG. I.

6

.7

.6

n o r m a lized

FREQUENCY SINGLE

.9 TO

1.0

1.1

DESIGN

1.2

1.3

1.4

FREQUENCY

CHARACTERISTIC OF FILM TERMINATION.

1.5

k

The tra n sfo rm e r a c tio n o f th e q u a r te r wave l i n e and th e req u irem en t f o r a p e r f e c tly conducting f i n a l elem ent seemed adequate re a so n t o channel subsequent a n a ly s is in l i n e w ith ( 2 ) above^.

T his d e c is io n does n o t r u le out a design based on (1 )

o r ( 3 ) b u t i t i s b e lie v e d t h a t r e s u l t s o b tain ed j u s t i f y t h i s ch o ic e . F u rth e r a n a ly s is and d e sig n s o lu tio n s a r e based on th e f ilm network shown i n F ig . 2. Note t h a t an a r b i t r a r i l y la r g e number of film s may be u sed , t h a t th e spacing between su c c e ssiv e film s i s one q u a r te r of a w avelength a t th e d e s ig n freq u en cy , and t h a t th e f i n a l elem ent in th e network i s a p e r f e c tly conducting s u rfa c e . The p receed in g d e s c r ip tio n and g e n e ra l d is c u s s io n en ab le t h e d esig n problem to b e s u c c in tly s ta te d :

determ ine th e s u rfa c e

r e s i s t i v i t y o f each o f an a r b i t r a r i l y la r g e number o f p a r a l l e l r e s i s t i v e f il m s , p la c e d normal to th e d ir e c tio n of p ro p ag atio n of a p lan e e lec tro m a g n e tic wave, and spaced -Aw ith t h e l a s t f il m

—-

a t a d e sig n freq u en cy ,

from th e p a r a l l e l s u rfa c e o f a p e r f e c t

co n d u cto r, so as t o in s u re t h a t : 1)

a t th e d e sig n freq u en cy , th e in p u t impedance to

th e network s h a l l equal th e impedance of f r e e space, 2)

a t fre q u e n c ie s o th e r th a n th e d e sig n freq u en cy ,

th e in p u t impedance to th e network s h a ll d i f f e r from th e impedance o f f r e e space bo th i n phase and m agnitude by a minimum degree f o r th e number o f film s a r b i t r a r i l y chosen.

3

R. M. Fano and A. W. Lawson, Microwave F i l t e r s Using Quarter-wave Coupling, P ro. IRE. Vol. 35, November, 191*7.

5

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6

A d i r e c t g e n e ra l s o lu tio n to t h i s d esig n problem ap p earin g rem o te, a m athem atical a n a ly s is o f a two f ilm netw ork i s f i r s t c a r r ie d th ro u g h .

The th r e e f il m d e sig n problem i s th e n so lv e d to

a v ery c lo s e approxim ation.

F in a lly , from th e s o lu tio n s to th e one,

tw o, and th r e e f ilm netw orks, a s u r p r is in g g e n e r a liz a tio n f o r th e a r b i t r a r i l y la r g e number o f f ilm s i s o bserved.

Using t h i s g e n e ra li­

z a tio n , a te rm in a tio n employing 15 film s i s d esig n ed and i t s perform ance computed w ith v e ry g r a tif y in g r e s u l t s . fo rm u las a r e th e n worked o u t.

U sable d e sig n

The g en eral c h a ra c te r of s u ita b le

f ilm s w ith p a r t i c u l a r em phasis on th e p r a c t i c a l n a tu re o f s a t i s ­ f a c to r y film s i s covered i n S e c tio n VI.

C o n sid era tio n i s given in

S e c tio n V II to the problem o f waves in c id e n t a t o th e r th a n normal in c id e n c e . The impedance concept suggested by S. A. Schelkunoff^ i s used e x c lu s iv e ly and d iss ip a tio n L e s s tra n s m is s io n l i n e r e la tio n s h ip s a re employed to determ ine impedance le v e ls a t network c ro ss s e c tio n s .

^

I b id .

F ootnote 1 , page 1 .

7

S ectio n I I THE TWO FILM TERMDMION The tra n sm iss io n l i n e and lumped elem ent e q u iv a le n t of th e two f ilm network i s shorn i n F ig . 3 . For any v alu e o f

equal to o r l e s s th a n th e c h a r a c te r is ti c

impedance of th e U n e , Rc , th e r e i s a corresponding v a lu e of Rg which w ill make th e in p u t impedance, d e sig n frequency*

7.±nf

equal to Rc a t th e

Any v alu e of R^ so chosen and used i n co n ju n ctio n

w ith th e corresponding v alu e o f Rg w i l l broaden th e frequency c h a r a c t e r is t i c o f th e te rm in a tio n .

However, as th e frequency changes

from th e d esig n freq u en cy , and th e e q u a lity between Z i n and Rc i s n o t m ain tain ed , th e s e le c te d v alu e of R^ w i l l in flu e n c e m a te r ia lly th e e x te n t to which Z j_n d i f f e r s from Rc , i n bo th phase and m agnitude, f o r a given change i n freq u en cy . Since Rg i s c o n s ta n t, th e v a r ia tio n i n phase and m agnitude of Z in o ccurs as a r e s u l t o f th e v a r ia tio n o f so lv e f o r

2.y

Thus, i f we

Z 3 i n term s of R j, Rc , and th e freq u en cy f , determ ine

f o r what v a lu e o f R^ th e v a r ia tio n i n th e phase and th e m agnitude o f Z 3 i s m inim ized, we w i l l have determ ined th e v alu e of R^ f o r optimum band-w idth of th e term in atio n *

Using th e w e ll known

r e la tio n s h ip e x is tin g on a d is s ip a tio n le s S tra n sm iss io n l i n e ? ,

Zs = r c Z r, * %

ta^ s ..

(x)

Rc + j Z R t a n ^ s 5

King Mimno and Wing, T ransm ission L in e s, A ntennas, and Wave G uides, McGraw-Hill, New York* 19kS* ~

8

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