NASA Technical Memorandum 101483

Channelized Coplanar Waveguide: Discontinuities, Junctions, and Propagation Characteristics

Rainee N. Simons Case Western Reserve University Cleveland, Ohio

and

George E. Ponchak, Konstantinos S. Martzaklis, and Robert R. Romanofsky Lewis Research Center Cleveland, Ohio

Unclas G3/33 OlS(EU99

Prepared for the 1989 IEEE MTT-S International Microwave Symposium Long Beach, California, June 13-15, 1989

. . I

https://ntrs.nasa.gov/search.jsp?R=19890011801 2020-02-14T18:21:19+00:00Z

I W

CHANNELIZED COPLANAR WAVEGUIDE: DISCONTINUITIES, JUNCTIONS, AND PROPAGATION C H A R A C T E R I S T I C S

Rainee N. Simons* Case Western Reserve U n i v e r s i t y

C leve land , Oh io 44106

and George E. Ponchak, K o n s t a n t i n o s S . M a r t z a k l i ~ . ~ and Rober t R . Romanofsky

N a t i o n a l Ae ronau t i cs and Space A d m i n i s t r a t i o n Lewis Research Cen te r C leve land , Oh io 44135

SUMMARY

A new v a r i a n t o f CPW wh ich has been termed chan- n e l i z e d CPW, CCPW. i s p resen ted . Measured and com- p u t e d 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 re p resen ted . Lumped e q u i v a l e n t c i r c u i t e lement va lues f o r a CCPW open c i r c u i t and r i g h t ang le bend have been o b t a i n e d . CCPW power d i v i d e r j u n c t i o n s and a coax-to-CCPW in-phase, r a d i a l power d i v i d e r a r e a1 so presen ted .

INTRODUCTION

Cop lanar waveguide, CPW, on a d i e l e c t r i c sub- s t r a t e c o n s i s t s of a c e n t e r s t r i p conduc to 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 on e i t h e r s i d e ( 1 ) . A v a r i a n t of CPW i s grounded cop lana r waveguide, GCPW, wh ich has an a d d i t i o n a l ground p l a n e on t h e o p p o s i t e s i d e o f t h e s u b s t r a t e t o f a c i l i t a t e h e a t removal and packag ing ( 2 ) . These t r a n s m i s s i o n l i n e s have s e v e r a l advantages wh ich make them i d e a l l y s u i t e d fo r microwave i n t e g r a t e d c i r c u i t s . The d i sadvan tage o f CPW and GCPW i s t h a t t h e s t r u c - t u r e can s u p p o r t s p u r i o u s modes bes ides t h e CPW mode s i n c e t h e t r a n s v e r s e d imens ions may be sev- e r a l wave lengths .

T h i s paper p r e s e n t s a new v a r i a n t o f CPW. The new s t r u c t u r e has s i d e w a l l s which, t o g e t h e r w i t h t h e ground p l a n e , c o n s t i t u t e s a channel and hence i s a p p r o p r i a t e l y termed as channe l i zed cop la - n a r waveguide, CCPW. A s h i e l d i n g s t r u c t u r e may be used to f u r t h e r c o n f i n e t h e e l e c t r o m a g n e t i c f i e l d s . T h i s s t r u c t u r e i s shown i n F i g . 1 . The e n c l o s u r e o f t h e CPW t r a n s m i s s i o n l i n e e l i m i n a t e s r a d i a t i o n loss and s p u r i o u s s u r f a c e modes c r e a t e d a t d i s c o n - t i n u i t i e s . A l s o , because t h e b a s i c t r a n s m i s s i o n l i n e s t r u c t u r e i s CPW, CCPW m a i n t a i n s t h e i n h e r e n t advantages o v e r m i c r o s t r i p for easy shun t as w e l l as s e r i e s moun t ing o f a c t i v e and p a s s i v e components

CCPW must be des igned to suppress t h e d i e l e c t r i c f i l l e d r e c t a n g u l a r waveguide mode, t h e m i c r o s t r i p mode, and t h e r e c t a n g u l a r coax mode. The channel w i d t h . 28. i s chosen such t h a t t h e r e c t a n g u l a r waveguide mode i s c u t o f f . The m i c r o s t r i p and r e c - t a n g u l a r coax modes a r e suppressed by t h e p r o p e r s e l e c t i o n o f t h e s lo t w i d t h , W . t h e c e n t e r s t r i p

To m a i n t a i n a s i n g l e CPW mode of p r o p a g a t i o n ,

*NASA Res iden t Research Assoc ia te . $ P r e s e n t l y a t t h e U n i v e r s i t y o f Akron, Akron,

Ohio 44325.

w i d t h , S, and t h e s u b s t r a t e t h i c k n e s s , D. The r a t i o s WID and S / D must be s u f f i c i e n t l y smal l t o suppress t h e m i c r o s t r i p mode. The r a t i o W/8 must be sma l l t o suppress t h e r e c t a n g u l a r coax mode.

T h i s paper p resen ts lumped e lement c i r c u i t models for seve ra l CCPW 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 lement va lues as a f u n c t i o n o f f r e - quency. 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 a r e an open c i r c u i t and a r i g h t ang le bend. The measured f requency dependence o f t he e f f e c t i v e d i e l e c t r i c cons tan t , c ( e f f ) , and t h e un loaded q u a l i t y f a c t o r , Q, a r e a l s o p resen ted f o r CCPW l i n e s f a b r i c a t e d on ~ ( r ) = 2.220.02 RTIDuro id 5880, & ( r ) = 6 . 0 t 0 . 1 5 R T / D u r o i d 6006, and c(r) = 10.220.25 3M Epsi lam-10 s u b s t r a t e s . Th is i s f o l l o w e d by t h e d e s i g n and c h a r a c t e r i z a t i o n o f a CCPW T - j u n c t i o n and 1-to-3 in-phase, matched power d i v i d e r . L a s t l y , t h e pe r - formance o f a nove l Coax-to-CCPH in-phase, N-way r a d i a l power d i v i d e r c i r c u i t i s p resen ted .

METHOD OF MEASUREMENTS

A r e s o n a t o r techn ique s i m i l a r t o t h a t des- c r i b e d by R i c h i n g s (3 ) and Stephenson and E a s t e r ( 4 ) was used. The X /4 end coup led s tubs c o u l d n o t be e tched o f f as i n t h e case o f m i c r o s t r i p s i n c e t h i s would a l t e r t h e CCPW open end parame- t e r s . Hence, a f o u r r e s o n a t o r s e t had t o be f a b r i - c a t e d for each f requency t o de te rm ine t h e end e f f e c t s . T h i s w i l l c o n t r i b u t e some e r r o r s t o t h e r e s u l t s because t h e r e s o n a t o r l e n g t h s and gaps w i 1 1 n o t be i d e n t i c a l f o r t h e two X / 2 and X resona- t o r s . The c i r c u i t d imens ions were measured t o =0.0002 i n . The gaps were v a r i e d t o m a i n t a i n a c o u p l i n g c o e f f i c i e n t , p, l e s s than 1 . For most o f t h e r e s o n a t o r s e t s p 0 . 3 . T h i s i s a s u f f i c i e n t c o n d i t i o n t o m in im ize t h e l o a d i n g of t h e r e s o n a t o r f o r t r a n s m i s s i o n l i n e s w i t h r e p o r t e d i n t h i s paper . The Q was de te rm ined th rough a t e c h n i q u e g i v e n i n Ref . 5 .

0's 1 100 as a r e

EFFECTIVE DIELECTRIC CONSTANT

The & ( e f f ) was measured o v e r t h e f requency range of 3 t o 18 GHz fo r seve ra l u n s h i e l d e d CCPW l i n e s and t h e r e s u l t s a r e shown i n F i g . 2 . The CCPW l i n e s have been modeled u s i n g Cohn 's tech - n i q u e ( 6 ) and t h e c ( e f f ) i s p l o t t e d f o r each CCPW l i n e . c ( e f f ) o f grounded CPW c a l c u l a t e d from t h e c l o s e d form e x p r e s s i o n o f Ghoine and N a l d i (7) i s a l s o p l o t t e d fo r compar ison.

1

OWOlNAL PAGE IS OF POUR QUALITY

c ( e f f ) was measured f o r i l nsn ie lded CCPW l i n e s f a b r i c a t e d on s u b s t r a t e s w i t h D i n the range o f 0 .062 to 0.250 i n . The CCPW parameters S . W , 28, and c ( r ) were h e l d f i x e d a t 0 .045. 0 .010, 0.200, and 2 . 2 i n . r e s p e c t i v e l y . No v a r i a t i o n i n c t e f f ) was observed f o r t he t h i c k e r s u b s t r a t e s , W/D 1 / 1 2 . 5 . c ( e f f ) o f t h e t h i n n e r s u b s t r a t e , W/D = 116. was 0.7 pe rcen t h i g h e r than t h e o t h e r measured cases; t h i s may be due t o t h e m i c r o s t r i p mode.

E f f e c t o f Cover H e i q h t

c ( e f f ) was measured f o r s h i e l d e d CCPW l i n e s w i t h cove r h e i g h t s o f H = D , 20. and 40. Resona- t o r s were t e s t e d w i t h c ( r ) , D, S , and W equal t o 2 . 2 , 0.125, 0 .045 , and 0 .010 i n . r e s p e c t i v e l y . Resonators were a l s o f a b r i c a t e d on 0 = 0 .050 i n . , ~ ( r ) = 6 and 10.2 s u b s t r a t e s . I n a l l t h e cases, t he change i n c ( e f f ) from t h e u n s h i e l d e d case was n e g l i g i b l e .

LOSS MEASUREMENTS

F i g u r e 3 shows t h e measured Q f o r r e s o n a t o r s o f l e n g t h x as a f u n c t i o n o f S f o r a f i x e d f r e - quency and c(r). The Q o f t h e u n s h i e l d e d reso- n a t o r s decreases w i t h i n c r e a s i n g S i n d i c a t i n g an i n c r e a s e i n r a d i a t i o n loss. The s h i e l d i n g enc lo - su re e l i m i n a t e s t h e r a d i a t i o n loss as ev idenced by t h e h i g h e r 0.

F i g u r e 4 shows t h e measured Q o v e r t h e f r e - quency range of 3 t o 18 GHz f o r X r e s o n a t o r s b o t h w i t h and w i t h o u t s h i e l d i n g . The r e d u c t i o n i n Q w i t h i n c r e a s i n g f requency f o r t h e u n s h i e l d e d case i s due t o t h e i n c r e a s e i n r a d i a t i o n loss. Wi th s h i e l d i n g , t h e Q i s observed t o i n c r e a s e w i t h f requency due t o t h e r e d u c t i o n o f r a d i a t i o n l o s s . A change i n t h e cove r h e i g h t f rom H I 20 t o H = D showed no measurable d i f f e r e n c e i n Q. The e f f e c t o f v a r y i n g D i n t h e range of 0.062 t o 0.250 i n . on Q was measured. No measurable v a r i a t i o n i n Q o v e r t h e f requency range o f 8 t o 18 GHz was observed.

OPEN END LINE E X T E N S I O N

When a CPW l i n e i s t e r m i n a t e d i n an open c i r - c u i t , t h e r e i s an excess f r i n g i n g o f t h e e l e c t r o - magne t i c f i e l d s wh ich g i v e s r i s e t o a capac i tance , C f (8). This c a p a c i t a n c e i s e q u i v a l e n t t o a s h o r t l e n g t h o f , a t r a n s m i s s i o n l i n e , Lo, t e r m i n a t e d i n a p e r f e c t open c i r c u i t . The open end l i n e e x t e n s i o n for t h e u n s h i e l d e d CCPW de-embedded from t h e reso- n a t o r d a t a i s shown as a f u n c t i o n o f f requency i n F i g . 5 . There was no v a r i a t i o n i n Lo for resona- t o r s w i t h a cove r h e i g h t of

R I G H T ANGLE BEND

H 2 20.

A CCPW r i g h t ang le bend and i t s e q u i v a l e n t c i r c u i t a r e shown i n F i g . 6 . The capac i tance , C. i s c r e a t e d by t h e accumu la t i on o f excess charge a t t h e c o r n e r s i n t h e two s l o t s and t h e r e s u l t i n g excess e l e c t r i c f i e l d s t o t h e ground p l a n e . The c u r r e n t f low i n t e r r u p t i o n c r e a t e s t h e excess

induc tance dh icn can be equated t o a l e n g t h o f tran;mis;ion l i n e , L . R a d i a t i o n f rom the co rne r i: rep resen ted by the shunt r e s i s t a n c e . The e q u i v - a l e n t c i r c u i t parameters w e r e found th rough resona- t o r technic lues and a re shown i n Tab le I .

CHANNELIZED CPW MATCHED T-JUNCTION

A CCPW matched T - j u n c t i o n was f a b r i c a t e d . A t t he T - j u n c t i o n . t he c h a r a c t e r i s t i c impedance, Z 1 . of t he two s i d e arms a r e i n o a r a l l e l and t h e n e t impedence t h e f o r impedance dance, ZO. o f The i n s e r t i o n f i x t u r e l o s s , g r e a t e r than

CHANNEL

i n p u t arm sees i s 2112. T h e r e f o r e , match ing , t he c h a r a c t e r i s t i c impe- t h e feed l i n e w a s s e t equal t o 2112. l o s s o f t he j u n c t i o n , i n c l u d i n g t e s t i s 0.5 dB and the r e t u r n l o s s i s 0 dB f rom 3 t o 6 GHz.

ZED CPW MATCHED 1-TO-3 IN-PHASE POWER D I V I D E R

A CCPW matched 1-to-3 tn-phase power d i v i d e r was f a o r i c a t e d . An i m p o r t a n t requ i remen t f o r a power d i v i d e r i s t h a t t h e s i g n a l emerging f r o m t h e o u t p u t p o r t s i s i n phase. I n o r d e r t o ach ieve t h i s , t h e p a t h l e n g t h between t h e s i d e arms and the t h r u arm must be e q u a l i z e d . T h i s i s ach ieved by t a p e r i n g t h e c e n t e r conduc to rs o f t h e t h r e e o u t - p u t l i n e s and t h e i n p u t l i n e so t h e y meet a t a p o i n t . The t a p e r a l s o f a c i l i t a t e s impedance match- i n g o f t h e i n p u t p o r t t o t h e o u t p u t p o r t s . For t h e oc tave bandwid th o f 3 t o 6 GHz, a maximum amp l i t ude imba lance o f 1 d6 was measured. The i s o l a t i o n between o u t p u t p o r t s was 9 dB and t h e i n p u t r e t u r n l o s s was g r e a t e r t han 10 dB.

COAX-TO-CHANNELIZED CPW I N - P H A S E N-WAY RADIAL POWER DIVIDER

A coax-to-CCPW in-phase, four -way r a d l a l power d i v i d e r i s shown i n F i g . 7 . The j u n c t i o n i s formed by t h e i n t e r s e c t i o n o f f o u r CCPW l i n e s . Power i s coup led t o t h i s j u n c t i o n f r o m a c o a x i a l c a b l e whose

o u t e r conduc to r i s s l o t t e d a l o n g t h e t d i r e c t i o n t o form f o u r coup led t r a n s m i s s i o n l i n e s . The cen- t e r p i n of t h e c o a x i a l l i n e meets t h e i n t e r s e c t i n g CCPW c e n t e r conduc to rs w h i l e t h e f o u r coup led o u t e r conduc to rs meet t h e CCPW ground p lanes . T h e r e f o r e , t h e e l e c t r i c c u r r e n t a t t h e open end o f t h e coax i s d i v i d e d i n t o the fou r CCPW l i n e s as i l l u s t r a t e d i n F i g . 8 . T h i s arrangement has t h e advantage o f h o l d i n g ground p lanes a t t h e same p o t e n t i a l and e x c i t i n g t h e f o u r CPW l i n e s i n equal a m p l i t u d e and phase. The a m p l i t u d e and t h e phase ba lance f o r t h i s c i r c u i t o v e r a 2 t o 18 GHz band a r e w i t h l n 0 .5 dB and 1 " r e s p e c t i v e l y ; t h e i s o l a t l o n i s 10 d6 between t h e o u t p u t p o r t s .

CONCLUSIONS

T h i s paper p resen ts a new v a r i a n t o f CPW which has been termed CCPW. Measured p r o p a g a t i o n char - a c t e r i s t i c s for CCPW a r e p resen ted and compared w i t h computed va lues . E q u i v a l e n t c i r c u i t compo- nen t va lues a r e p resen ted f o r an open c i r c u i t and a r i g h t a n g l e bend. CCPW power d i v i d e r j u n c t i o n s and a nove l coax-to-CCPW in-phase, r a d l a l power d i v i d e r a r e a l s o d e s c r i b e d .

2

1 . C.P. Wen, "Cop lanar Waveguide: A Surface S t r i o T ransmiss ion L i n e S u i t a b l e for

Frequency, GHz

2 . 9 7 4.92 9 . 7 4

13.49 17.84

Exper imen ta l Techniques f o r Deterrni n i n g 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 o f mm-Have M i c r o s t r i p L i n e s , " NASA TP-2899. 1989.

L, m i 1

22.622 26.241 30.972 27.867 31.794

N o n r e c i p r o c a l Gyromagne t i c Dev i ce Appl i ca- t i o n s . " I E E E Trans . Microwave Theory Tech., 6 . R.N. Simons. "Suspended Coupled S l o t l i n e v o l . MTT-17. no. 12, pp. 1087-1090, Dec. 1969. U s i n g Double Layer D i e l e c t r i c . " I E E E Trans.

Microwave Theory Tech., v o l . MTT-29. no. 2 . 2 . Y.C. Sh ih . and T. I t o h . " A n a l y s i s of DO. 162-165, Feb. 1981.

C I Y O , pF R

4.21 9 4.353 3.192 2.950 3 . a48

- . . ConductorLBacked Cop1 anar Waveguide ," E l e c t r o n . L e t t . , v o l . 18. no. 12, 7. G. Ghione and C . N a l d i . "Parameters o f pp . 538-540, June 10, 1982.

Method for D e t e r m i n i n g t h e I m p o r t a n t Prop- e r t i e s o f M i c r o s t r i p T ransmlss ion L i n e s , " 8. R . N . Simons and G . E . Ponchak. "Mode l i ng o f

Cop lanar Waveguides w i t h Lower Ground P lane . " E l e c t r o n . L e t t . , v o l . 19, no . 18,

3. J.G. R i c h i n g s , "An Accu ra te Exper imen ta l pp . 734-735, Sept . 1 , 1983.

Q, r a d i a t i o n

m

53,142.5 245.18 122.70 237.6

The Marcon i Review, v o l . 37, no. 195, pp . 209-216. f o u r t h Q u a r t e r 1974.

Some Cop lanar Waveguide D i s c o n t i n u i t i e s , " IEEE Trans . Microwave Theory Tech., v o l . 3 6 , no. 12. O D . 1796-1803. Dec. 1988. . r r

4 . I.M. Stephenson, and 8 . E a s t e r , "Resonant Techniques for E s t a b l i s h i n g t h e E q u i v a l e n t C i r c u i t s o f Smal l D i s c o n t i n u i t i e s i n M ic ro - ~ ~~

s t r t p . " E l e c t r o n . L e t t . , v o l . 7 , no. 10, pp. 582-584, Sept . 23, 1971.

TABLE I. - CPW R I G H T ANGLE BEND DISCONTINUITY

[(S = 0.045 i n . , W = 0.010 i n . , ~ ( r ) = 2.2, 28 = 0.200 i n . ) . ]

3

7

t

w n W 2 V c

kf L L W

1

CONDUCTOR PATTERN -

3 - s = 0.045 IN. w = 0.01 IN. D = 0.0125 IN. 2B = 0.2 IN. [61

[71

2 - 0 -[wI)I

I

+ 2B -4 FIGURE 1. - SCHEMATIC ILLUSTRATING A CHANNELIZED

COPLANAR WAVEGUIDE (CCPW).

350

E, = 10.2 s = 0.02 IN. w = 0.015 IN.

0 D = 0.05 IN. 23 = 0.1 IN. 0

-

s = 0.02 IN. w = 0.015 IN. D = 0.05 IN. 2B = 0.1 IN. 0 -

E, = 2.2 [71

E , = 2.2 w = 0.01 IN.

2B = 0.2 IN. r SHIELDED D = 0.125 IN.

F = 10 GHz / ( H = 2D) - I

/ o

r UNSHIELDED 250

200 300E 10 20 30 40 50 60 70

CENTER CONDUCTOR WIDTH. S, MILS-

FIGURE 3. - REASURED UNLOADED QUALITY FACTOR Q FOR CHANNELIZED CPW AS A FUNCTION OF THE CENTER CON- DUCTOR WIDTH. WITH AND WITHOUT A SHIELDING ENCLOSURE,

4

Er = 2.2

s = 0.045 I N t w = 0.01 I N .

c

r SHIELDED // (H = 2D)

D = 0.125 I N .

2B = 0.2 I N .

r U N S H I E L D E D

I 2 4 6 8 10 12 14 16 18

FREQUENCY, GHz - FIGURE 4 . - MEASURED UNLOADED QUALITY FACTOR Q FOR

CHANNELIZED CPW AS A FUNCTION OF THE FREQUENCY, WITH AND WITHOUT SHIELDING.

4 25

0

E, = 2.2

s = 0.045 I N .

w = 0.01 I N .

D = 0.125 IN.

2B = 0.2 I N .

g = 0.015 I N . -

I I I I I I I ." 2 4 6 8 10 12 14 16 18

FREQUENCY. GHz-

FIGURE 5. - EXPERIMENTALLY DETERMINED OPEN CIRCUIT EQUIVALENT END-EFFECT LENGTH AS A FUNCTION OF THE FREQUENCY.

I P I

1 I

IP' ( A ) (B)

FIGURE 6. - SCHEMATIC. (A) A CHANNELIZED CPW RIGHT-ANGLED BEND, (B) LUMPED EQUIVALENT CIRCUIT FOR THE BEND.

5

FIGURE 7. - COAX-TO-CHANNEL I ZED CPW I N-PHASE, FOUR-WAY, RADIAL POWER DIVIDER, ASSEMBLED VIEW.

,-COAXIAL LINE WITH II I 1

I 1 1 1 11 ,/ SLOTTED OUTER

CCPW 7- 4; ! /’ CONDUCTOR

/

OUTPUT -COAXIAL

LINE OUTPUT

PORT #3

F CCPW CCPW <

PORT #5 (B)

FIGURE 8. - ELECTRIC FIELD (F) DISTRIBUTION AT THE END OF THE SLOTTED COAXIAL LINE. EQUIVALENT CIRCUIT OF THE JUNCTION SHOWING THE INPUT RF CURRENT (7) BEING DIVIDED INTO THE FOUR PORTS.

6 ORI~NAL PAGE IS OF POOR QUALm

Nat~ond Aaonwbco and Report Documentation Page 1. Roport No.

NASA TM-101483 2. Government Accession No.

7. Author@)

17. Key Words (Suggested by Author@))

Rainee N. Simons, George E. Ponchak, Konstantinos S. Martzaklis, and Robert R. Romanofsky

18. Distribution Statement

9. Performing Organization Name and Address

National Aeronautics and Space Administration Lewis Research Center Cleveland, Ohio 44135-3191

19. Security Classif. (of this report)

Unclassified

12. Sponsoring Agency Name and Address

National Aeronautics and Space Administration Washington, D.C. 20546-0001

20. Security Classif. (of this page) 121. No of pgages 22. Price'

Unclassified 1 A02

3. Recipient's Catalog No.

5. Report Date

6. Performing Organization Code

8. Performing Organization Report No.

E-46 16

IO. Work Unit No.

506-44-2C

11. Contract or Grant No.

13. Type of Report and Period Covered

Technical Memorandum

14. Sponsoring Agency Code

IS. Supplementary Notes

prepared for the 1989 IEEE MTT-S International Microwave Symposium, Long Beach, California, June 13-15, 1989. Rainee S. Simons, Case Western Reserve University, Cleveland, Ohio 44106 and NASA Resident Research Associate. George E. Ponchak and Robert R. Romanofsky, NASA Lewis Research Center. Konstantinos S. Martzaklis, NASA Lewis Research Center, presently at The University of Akron, Akron, Ohio 44325.

IS. Abstract

A new variant of CPW which has been termed channelized CPW, CCPW, is presented. Measured and computed propagation characteristics are presented. Lumped equivalent circuit element values for a CCPW open circuit and right angle bend have been obtained. CCPW power divider junctions and a coax-to-CCPW in-phase, radial power divider are also presented.

Microwave transmission line Coplanar transmission line Power divider Discontinuities

Unclassified - Unlimited Subject Category 33

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