NASA Technical Memorandum 100808

Modeling of Some Coplanar Waveguide Discontinuities

Rainee N. Simons and George E. Ponchsk Lewis Research Center Cleveland, Ohio

Prepared for the IEEE MTT-S International Microwave Symposium New York, New York, May 25-27, 1988

ORIG~NAL PAGE rs OE: POOR QUALITY

MODELING OF SOME COPLANAR WAVEGUIDE DISCONTINUITIES

Ra inee N . Simons and George E . Ponchak

. N a t i o n a l A e r o n a u t i c s and Space A d m i n i s t r a t i o n Lew is Research C e n t e r C l e v e l a n d

A BS TRACT

The p a p e r p r e s e n t s lumped e q u i v a l e n t c i r - c u i t mode ls for s e v e r a l c o p l a n a r wavegu ide d i s - c o n t i n u i t i e s such as an open c i r c u i t , a s e r i e s gap , and a symmet r i c s t e p , and t h e i r e l e m e n t v a l u e s as a f u n c t i o n of t h e d i s c o n t i n u i t y phys - i c a l d i m e n s i o n s . The model e l e m e n t v a l u e s a r e

m de-embedded from measured S-pa ramete rs . The f r e q u e n c y dependence o f t h e e f f e c t i v e d i e l e c - tric c o n s t a n t was measured and compared to com- p u t e d v a l u e s .

01

INTRODUCTION

A c o p l a n a r waveguide (CPW) o n a d i e l e c t r i c s u b s t r a t e ( 1 ) c o n s i s t s o f a c e n t e r s t r i p c o n d u c t o r w i t h s e m i - i n f i n i t e g round p l a n e s o n e i t h e r s i d e s ( F i g . I ) . C o p l a n a r wavegu ide o f f e r s s e v e r a l advan- t a g e s o v e r c o n v e n t i o n a l m i c r o s t r i p l i n e : i t f a c i l - i t a t e s easy s h u n t as w e l l as s e r i e s m o u n t i n g of a c t i v e and p a s s i v e d e v i c e s , i t e l i m i n a t e s t h e need for wrap -a round and v i a - h o l e s , and i t has a low r a d i a t i o n l o s s . These, as w e l l as s e v e r a l o t h e r a d v a n t a g e s , make CPW i d e a l l y s u i t e d fo r m ic rowave i n t e g r a t e d c i r c u i t a p p l i c a t i o n s ( 2 . 3 ) . However , v e r y l i t t l e i n f o r m a t i o n i s a v a i l a b l e i n t h e l i t e r a - t u r e o n d i s c o n t i n u i t y mode ls for CPW ( 4 . 5 ) . T h i s l a c k o f s u f f i c i e n t d i s c o n t i n u i t y mode ls f o r CPW has l i m i t e d t h e e x t e n t of a p p l i c a t i o n s f o r CPW i n m ic rowave c i r c u i t d e s i g n .

T h i s p a p e r p r e s e n t s for t h e v e r y f i r s t t i m e lumped e l e m e n t e q u i v a l e n t c i r c u i t mode ls fo r v a r i - ous d i s c o n t i n u i t i e s , t o g e t h e r w i t h t h e i r e l e m e n t v a l u e s as a f u n c t i o n of t h e d i s c o n t i n u i t y p h y s i c a l d i m e n s i o n s . These e l e m e n t v a l u e s a r e de-embedded from measured s c a t t e r i n g p a r a m e t e r s o f t h e d i s c o n - t i n u i t i e s . The d i s c o n t i n u i t i e s c h a r a c t e r i z e d i n t h i s p a p e r a r e a s e r i e s gap i n t h e c e n t e r conduc- to r , a s y m m e t r i c s t e p i n t h e c e n t e r c o n d u c t o r , and an open c i r c u i t fo r two d i f f e r e n t c e n t e r c o n d u c t o r w i d t h s .

The c h a r a c t e r i s t i c impedance f o r b o t h geome- t r i e s was 50 R . The f r e q u e n c y dependence o f t h e e f f e c t i v e d i e l e c t r i c c o n s t a n t , c ( e f f ) , was a l s o measured and i s compared to computed v a l u e s from t h e l i t e r a t u r e .

O h i o 44135

DE-EMBEDDING DISCONTINUITY SCATTERING P A R A M E T E R S

P r e c i s i o n CPW c a l i b r a t i o n s t a n d a r d s such as open c i r c u i t s , s h o r t c i r c u i t s , and 50 R matched l o a d s for c a l i b r a t i n g an a u t o m a t i c n e t w o r k a n a l y z e r ( A N A ) a r e c u r r e n t l y n o t a v a i l a b l e . C o n s e q u e n t l y , a t w o - t i e r de-embedding t e c h n i q u e w h i c h has been used s u c c e s s f u l l y to c h a r a c t e r i z e a c t i v e d e v i c e s such a s GaAs MESFET's ( 6 , 7 ) was used to c h a r a c t e r i z e t h e CPW d i s c o n t i n u i t i e s . The t w o - t i e r de-embedding t e c h n i q u e c o n s i s t s o f c a l i b r a t i n g t h e A N A u s i n g p r e c i s i o n c o a x i a l s t a n d a r d s and t h e n u s i n g t h e c a l - i b r a t e d ANA t o c h a r a c t e r i z e t h e t e s t f i x t u r e . A CPW c i r c u i t whose c h a r a c t e r i s t i c s a r e known i s p l a c e d i n t h e t e s t f i x t u r e d u r i n g t h e f i x t u r e c h a r - a c t e r i z a t i o n . The CPW c i r c u i t c o n s i s t s o f a u n i - form s e c t i o n of a 50 R CPW l i n e t e r m i n a t e d a t b o t h ends by a l i n e a r l y t a p e r e d CPW l i n e w h i c h p r o v i d e s impedance m a t c h i n g to a p a i r o f c o a x i a l c o n n e c t o r s . Thus, t h e CPW l i n e a r t a p e r s and t h e c o a x i a l connec- tors form a p a r t o f t h e t e s t f i x t u r e and a r e c h a r - a c t e r i z e d i n i t i a l l y . The c h a r a c t e r i z a t i o n i s done b y m e a s u r i n g t h e f o u r s -pa ramete rs o n an HP8510 A N A . The t e s t f i x t u r e w i t h a CPW c i r c u i t o n 0 .125 i n . RT-5880 D u r o i d i s shown i n F i g . 2 .

A m i x e d l u m p e d - d i s t r i b u t e d e q u i v a l e n t c i r c u i t t o p o l o g y t o model t h e f i x t u r e was d e v e l o p e d b y t a k - i n g i n t o c o n s i d e r a t i o n t h e p h y s i c a l n a t u r e o f t h e t e s t f i x t u r e and t h e CPW c i r c u i t . The c o a x i a l con- n e c t o r s w e r e r e p r e s e n t e d by a s e c t i o n of a l o s s y t r a n s m i s s i o n l i n e c o n s i s t i n g o f lumped e l e m e n t s i n s e r i e s w i t h a s m a l l s e c t i o n o f a c o a x i a l l i n e . The t a p e r e d CPW s e c t i o n was mode led as a m u l t i p l e sec- t i o n s t e p p e d impedance t r a n s f o r m e r . EEsof Touch- s t o n e ' s ( 8 ) model o f CPW as a l o s s l e s s t r a n s m i s s i o n l i n e whose p r o p a g a t i o n c h a r a c t e r i s t i c s a r e d e s c r i b e d b y Gh ione and N a l d i ( 9 ) was used t h r o u g h o u t t h e m o d e l i n g e x p e r i m e n t .

t h e n o p t i m i z e d t o match t h e measured S p a r a m e t e r s u s i n g t h e EEsof Touchs tone c i r c u i t a n a l y s i s and o p t i m i z a t i o n p r o g r a m s . The c i r c u i t model i s shown i n F i g . 3 . F i g u r e 4 shows t h e measured and mode led S11 and 521 c h a r a c t e r i s t i c s for t h e t e s t f i x t u r e and t h r u l i n e . T h i s model was t h e n used t o de-embed t h e d i s c o n t i n u i t y c h a r a c t e r i s t i c s from t h e f i x t u r e c h a r a c t e r i s t i c s . The measured r e t u r n loss w i t h t h e 50 R CPW c i r c u i t i n p l a c e i s b e t t e r t h a n 16 db o v e r t h e f r e q u e n c y r a n g e 0 . 0 4 5 t o 18 GHz. However , for

The e l e m e n t s o f t h e e q u i v a l e n t c i r c u i t were

1

t h e p u r p o s e o f de-embedding t h e d i s c o n t i n u i t y e q u i v - a l e n t c i r c u i t p a r a m e t e r s , a 1 GHz band c e n t e r e d a t 6 GHz was chosen .

EFFECTIVE DIELECTRIC CONSTANT

The c ( e f f ) i s d e t e r m i n e d from t h e p h y s i c a l l e n g t h o f a p a i r o f s e r i e s - g a p c o u p l e d s t r a i g h t r e s o n a t o r s w h i c h a r e t e r m i n a t e d i n a s h o r t c i r c u i t and t h e measured r e s o n a n t f r e q u e n c i e s as d e s c r i b e d i n ( 1 0 ) . F i g u r e s 5 ( a ) and ( b ) show c ( e f f ) f o r 50 R CPW w i t h two d i f f e r e n t s t r i p w i d t h s o v e r t h e f r e q u e n c y r a n g e o f 3 to 18 GHz. F i g s . 5 ( a ) and ( b ) i s c t e f f ) computed u s i n g t h e e x p r e s s i o n s i n ( l ) , ( 9 ) . and ( 1 1 ) . Good ag reemen t i s o b s e r v e d between t h e measured and computed r e s u l t s above 6 GHz. The c ( e f f ) does n o t appear to be a s t r o n g f u n c t i o n o f t h e c e n t e r s t r i p w i d t h f o r CPW l i n e s o f t h e same impedance.

Also shown i n

CPW OPEN CIRCUIT

A CPW open c i r c u i t i s f o r m e d b y e n d i n g t h e c e n t e r s t r i p a s n o r t d i s t a n c e b e f o r e t h e s l o t e n d s , t h e r e b y c r e a t i n g a g a p , g l , as shown i n F i g . 6 . An e l e c t r i c f i e l d e x i s t s a t t h e open c i r c u i t between t h e t e r m i n a t e d c e n t e r s t r i p and t h e s u r r o u n d i n g g r o u n d c o n d u c t o r and hence g i v e s r i s e t o a c a p a c i - t i v e r e a c t a n c e . T h i s r e a c t a n c e i s seen a t a p l a n e c o i n c i d e n t w i t h the open end o f t h e c e n t e r s t r i p . Thus t h e a p p a r e n t p o s i t i o n o f t h e open c i r c u i t i s beyond t h e p h y s i c a l end o f t h e c e n t e r s t r i p . The open c i r c u i t c a p a c i t a n c e , COC, i s a p a r a l l e l combi- n a t i o n o f t h e c a p a c i t a n c e due t o t h e f r i n g i n g f i e l d s a c r o s s t h e gap , g l , and t h o s e a c r o s s t h e s lo t , W . The gap dependen t c a p a c i t a n c e v a r i e s p r o p o r t i o n a l l y as l / g l . The s lot dependen t c a p a c i t a n c e i s c o n s t a n t . F i g u r e 7 p r e s e n t s t h e de-embedded open c i r c u i t capac- i t a n c e , COC, as o b t a i n e d from t h e measured S- p a r a m e t e r s .

SERIES GAP I N THE CENTER CONDUCTOR

A s e r i e s gap o f l e n g t h g i n t h e c e n t e r con- d u c t o r o f a CPW i s shown i n F i g . 6 . The gap i s mode led as a lumped P i - n e t w o r k c o n s i s t i n g o f a cou- p l i n g c a p a c i t a n c e , C 2 , and two f r i n g i n g c a p a c i - t a n c e s , C1. Ana logous to t h e open c i r c u i t , t h e c a p a c i t a n c e a c r o s s t h e gap , C2, d e c r e a s e s p r o p o r - t i o n a l l y as l / g . The f r i n g i n g c a p a c i t a n c e , C1, i n c r e a s e s from t h e CPW l i n e c a p a c i t a n c e for g = 0 t o t h e open c i r c u i t s a t u r a t i o n c a p a c i t a n c e fo r l a r g e 9 . F i g u r e 8 shows t h e de-embedded c a p a c i - t a n c e s o b t a i n e d from t h e measured S-pa ramete rs as a f u n c t i o n o f t h e gap w i d t h g .

STEP CHANGE I N T H E WIDTH OF CENTER CONDUCTOR

A s t e p change i n w i d t h o f t h e c e n t e r c o n d u c t o r o f CPW i s shown i n F i g . 6 . The s t e p d i s c o n t i n u i t y p e r t u r b s t h e no rma l CPW e l e c t r i c and m a g n e t i c f i e l d s w h i c h g i v e r i s e t o a d d i t i o n a l r e a c t a n c e s . These a d d i t i o n a l r e a c t a n c e s a r e assumed t o be lumped and l o c a t e d i n t h e p l a n e o f t h e s t e p d i s c o n t i n u i t y . The m o d e l i n g e x p e r i m e n t s show t h a t t h e r e a c t a n c e s can be mode led as a s h u n t c a p a c i t a n c e C s . The i n f l u e n c e o f t h i s c a p a c i t a n c e i s to e f f e c t i v e l y l e n g t h e n t h e l o w e r impedance CPW l i n e t o w a r d s t h e h i g h e r impedance CPW l i n e . F i g u r e 9 shows C s as

a f u n c t i o n o f t h e n o r m a l i z e d s t e p w i d t h . n o r m a l i z e d s t e p change, 5 1 \ 5 2 , i n c r e a s e s , C s app roaches t h e open c i r c u i t s a t u r a t i o n c a p a c i t a n c e .

DISCUSSIONS

As t h e

A l t h o u g h t h e r e s u l t s p r e s e n t e d i n t h i s p a p e r appear t o be s e l f c o n s i s t e n t , a m e n t i o n o f t h e a c c u r a c y of t h e d a t a i s r e q u i r e d . The two p o r t c i r c u i t e l e m e n t mode ls a r e more a c c u r a t e t h a n t h e one p o r t c i r c u i t e l e m e n t mode ls . T h i s i s because t h e two p o r t mode ls a r e based on a l l f o u r S- p a r a m e t e r s v e r s u s a s i n g l e S-parameter fo r t h e one p o r t m o d e l s . F u r t h e r m o r e , t h e open c i r c u i t model i s a f u n c t i o n of t h e phase of S 1 1 o n l y . t h e open c i r c u i t de-embedded c a p a c i t a n c e i s s e n s i t i v e to phase e r r o r s . To m i n i m i z e t h e phase e r r o r s , s e v e r a l p r e c a u t i o n s were t a k e n . A l l measurements were made i n t h e f r e q u e n c y range a t wh ich t h e meas- u r e d p r o p a g a t i o n c o n s t a n t was c l o s e t o t h a t used by T o u c h s t o n e . I n a d d i t i o n , t h e l i n e l e n g t h from t h e open c i r c u i t t o t h e t r a n s i t i o n was k e p t s h o r t t o m i n i m i z e t h e d i f f e r e n c e i n e l e c t r i c a l l e n g t h between t h e measured and t h a t used by T o u c h s t o n e .

To t a k e i n t o a c c o u n t t h e e r r o r s i n t r i n s i c i n

T h e r e f o r e ,

p r i n t e d c i r c u i t b o a r d f a b r i c a t i o n , a l l l i n e l e n g t h s were measured t o a t e n t h o f a m i l . Even w i t h t h e s e p r e c a u t i o n s , t h e e r r o r i s b e l i e v e d t o be 5 p e r c e n t fo r t h e open c i r c u i t d a t a . F u r t h e r t e s t i n g o f a l a r g e r sample o f c i r c u i t s s h o u l d y i e l d more com- p l e t e and a c c u r a t e r e s u l t s .

CONCLUSIONS

The p a p e r p r e s e n t s for t h e v e r y f i r s t t i m e lumped e q u i v a l e n t c i r c u i t mode ls for t h e f o l l o w i n g CPW d i s c o n t i n u i t i e s : an open c i r c u i t , a s e r i e s gap i n t h e c e n t e r c o n d u c t o r and. a symmet r i c s t e p i n t h e c e n t e r c o n d u c t o r . The model e l e m e n t v a l u e s a r e de-embedded from t h e measured S-pa ramete rs and p r e - s e n t e d as a f u n c t i o n o f t h e d i s c o n t i n u i t y p h y s i c a l d i m e n s i o n s . The measured f r e q u e n c y dependence o f c ( e f f ) i s a l s o compared t o computed v a l u e s and f o u n d to be i n good ag reemen t above 6 GHz.

REFERENCES

C.P. Wen, " C o p l a n a r Waveguide, A S u r f a c e S t r i p T r a n s m i s s i o n L i n e S u i t a b l e Fo r N o n r e c i D r o c a l G y r o m a g n e t i c D e v i c e App l i c a t i o n s , " I E E E T r a n s . M ic rowave Theory T e c h . , v o l . M T T - 1 7 , p p . 1087-1090, Dec. 1969.

G y r o m a g n e t i c D e v i c e App l i c a t i o n s , " I E E E T r a n s . M ic rowave Theory T e c h . , v o l . M T T - 1 7 , p p . 1087-1090, Dec. 1969.

R . E . S tegens and D . N . A l l i s s . " C o p l a n a r Micro- wave I n t e g r a t e d C i r c u i t for I n t e g r a t e d Subsys- tems , " MSN Mic rowave S y s t . News, v o l . 1 7 ,

D . Neu f and S . S p o h r e r . " U l t r a s m a l l M I C M i x e r

p p . 84 -96 , O C t . 1 9 8 7 .

D e s i g n e d f o r ECM' A p p l i c a t i o n s , " MSN Mic rowave S y s t . News, v o l . 15, p p . 70-82, O c t . 1985.

K.C. G u p t a , R . Garg , and R . Chadha, Computer- a i d e d D e s i g n of Mic rowave C i r c u i t s . Dedham: A r t e c h House I n c . , 1981, Chap. 6 .

ORIGINAL PAGE IS OE POOR QUALI'W

ORIGINAL PAGE IS QE m R QUALITY

5. R.K. Hoffmann, Handbook of microwave integrated circuits. Norwood: Artech House Inc., 1987, Chap. 13.

6. R . Lane, "De-embedding Device Scattering Param- eters," Microwave J . , vol. 2 7 , pp. 149-156, Aug. 1984.

7. G.E. Elmore and L . J . Salz, "Quality Microwave Measurement of Packaged Active Devices," Hewlett-Packard J., vol. 38, pp. 39-48, Feb. 1987.

8. EEsof Touchstone Reference manual, Version 1.5, EEsof Inc., Mar. 1987.

9. G. Ghione and C. Naldi. "Analytical Formulas for Coplanar Lines in Hybrid and Monolithic MICs," Electron. Lett., vol. 20, pp. 179-181 Feb. 1984.

10. T.C. Edwards, Foundations for Microstrip Cir- cuit Desiqn. New York: John Wiley 8, Sons, 1981. Chap. 7.

1 1 . R.N. Simons, "Suspended Coupled Slotline Usinq Double Layer Dielectric," IEEE Trans. Micro- wave Theory Tech., vol. MTT-29, pp. 162-165, Feb. 1981.

H

I t

FIGURE 1. - CROSS-SECTION OF THE COPLANAR WAVEGUIDE IN THE TEST FIXTURE.

3

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FIGURE 2. - TRANSITION BETWEEN A 50-OHM CPW AND COAXIAL CONNECTORS USING A LINEAR TAPER TRANSFORMER.

lRATlON PI ANF- 'i * I

p 1 p p 2 I

ANA CALlL _ _ - - DE-EMBEDDING PLANES ,-ANA CALIBRATION PLANE

FIGURE 3. - A LUMPED ELEMENT EQUIVALENT CIRCUIT MODEL OF THE TRANSITION BETWEEN THE 50-OHM CPW AND COAXIAL CONNECTOR.

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1, = 5 . 5 GHz f 2 = 6 .3 GHz

FIGURE 4. - MEASURED (MEASCPW) AND MODELED (MODCPW) S-PARAMETERS OF THE TRANSITION BETWEEN CPW AND COAXIAL CONNECTOR.

5

Er = 2 . 2

H = 0.72 I N .

2B = 1 .0 I N . W = 0.010 I N .

- COMPUTED ----- MEASURED D = 0.125 I N .

2 . 2

2.0 u + - 2, = 50 R y t 1 .8 J U w . 2 %

S / ( S + 2W) = 0.9 &

f 1.6 W

t; 5 1.4 W U U

1.2

1 .o ( A ) S = 0.178 I N , , W = 0.010 I N .

2 1.8

y ~ 1 . 6 . cc c ,

L l A J

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t;? 1 . 2 -

5 1 .0

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- WEN7 r S l M O N S

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ORIGINAL PAGE IS OF POOR QUALITY

6

CPW DISCONTINUITY

P I

I

f !I w

P'

W I I

f

T I1 I S W

P i P i

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OPEN T O C p,

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FIGURE 6. - COPLANAR WAVEGUIDE DISCONTINUITIES AND THEIR LUMPED ELEMENT EQUIVALENT CIRCUIT MODEL.

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2 - 1 5 L z V

0 4 V

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~

I N .

0.011 0.009

5 10 15 20 2 5 30 OPEN END GAP WIDTH, 91, MILS

FIGURE 7. - DE-EMBEDDED LUMPED FRINGING CAPACITANCE FROM MEASURED SCATTERING PARAMETERS AS A FUNCTION OF THE OPEN END GAP WIDTH.

7

.20

.15

LL a i

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r\ 0.011

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- 0.009 t

1 0 20 30 40 50 60 GAP WIDTH. g, M I L S

FIGURE 8. - DE-EMBEDDED LUWED FRINGING AND COUPLING CAPACITANCE FROM HEASURED SCATTER I NG PARMETERS AS A FUNCTION OF GAP WIDTH.

.

W1, IN.

0.011 0.009

Er = 2.2 D = 0 . 1 2 5 IN. H = 0.72 IN.

d 2B = 1.0 IN.

Z,, = 50 Q S1/(S1 + 2W) = 0.9

s2 + 2w2 = s1 + 2W1

I I 1.5 2.0 2.5 3.0 0

NORMALIZED STEP WIDTH, S1/S2

FIGURE 9. - DE-ERBEDDED LUMPED SHUNT CAPACITANCE FROM HEASURED SCATTERING PARAMETERS AS A FUNCTION OF THE NORMALIZED STEP WIDTH.

8

NASA

NASA TM-100808 4. Title and Subtitle

Report Documentation Page

5. Report Date

Space Aam#n#slral#on

1. Report No. I 2. Government Accession No. I 3. Recipient's Catalog No.

Mode l i ng o f Some Cop lanar Waveguide D i s c o n t i n u i t i e s

7. Author@)

Rainee N . Simons and George E . Ponchak

6. Performing Organization Code

8. Performing Organization Report No.

E-3981

7. Key Words (Suggested by Author@))

Cop 1 anar wavegu i de ; D i s con t i nu i t i e s ; M i c r o w a v e / m i l l i m e t e r wave t r a n s m i s s i o n l i n e s

10. Work Unit No.

506-44-2C 9. Performing Organization Name and Address

11. Contract or Grant No. N a t i o n a l A e r o n a u t i c s and Space A d m i n i s t r a t i o n Lewis Research Cen te r C leve land , O h i o 44135-3191

13. Type of Report and Period Covered

18. Distribution Statement

U n c l a s s i f i e d - U n l i m i t e d S u b j e c t Category 32

2. Sponsoring Agency Name and Address

9. Security Classif. (of this report) 20. Security Classif. (of this page) 21. No of pages

Uncl ass i f i ed U n c l a s s i f i e d 10

N a t i o n a l A e r o n a u t i c s and Space A d m i n i s t r a t i o n Washington, D.C. 20546-0001

22. Price'

A 0 2 ,

Techn ica l Memorandum 14. Sponsoring Agency Code -

~

5. Supplementary Notes

Prepared for t h e I E E E MTT-S I n t e r n a t i o n a l Microwave Symposium, New York, New York, May 25-27, 1988.

6. Abstract

The paper p r e s e n t s lumped e q u i v a l e n t c i r c u i t models for s e v e r a l c o p l a n a r wave- g u i d e d i s c o n t i n u i t i e s such as an open c i r c u i t , a s e r i e s gap, and a symmetr ic s t e p , and t h e i r e lement va lues as a f u n c t i o n o f t h e d i s c o n t i n u i t y p h y s i c a l dimen- s i o n s . The model e lement v a l u e s a r e de-embedded from measured S-parameters. The f requency dependence o f t h e e f f e c t i v e d i e l e c t r i c c o n s t a n t was measured and compared t o computed va lues .