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Cascode voltage switch logic circuits Chu, Kan Man 1986

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CASCODE VOLTAGE SWITCH LOGIC CIRCUITS by Kan Man Chu B. Eng. (Hons) , McGi 11 University, 1984 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF ELECTRICAL ENGINEERING We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o the r e q u i r e d s t a n d a r d THE UNIVERSITY OF Apr i I © Kan Man BRITISH COLUMBIA 1986 Chu, 1986 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y a v a i l a b l e for reference and study. I further agree that permission for extensive copying of t h i s thesis for s c h o l a r l y purposes may be granted by the head of my department or by his or her representatives. It i s understood that copying or p u b l i c a t i o n of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of ti^C7^icAu ^ipCy. The University of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date 2- A A ) p-6  10 /1Q\ A b s t r a c t Cascode v o l t a g e s w i t c h (CVS) l o g i c i s a CMOS c i r c u i t t e c h n i q u e which has p o t e n t i a l advantages over c o n v e n t i o n a l NAND/NOR l o g i c i n terms of c i r c u i t d e l a y , l a y o u t d e n s i t y , power d i s s i p a t i o n and l o g i c f l e x i b i l i t y . T h i s t h e s i s p r e s e n t s two new p r o c e d u r e s f o r c o n s t r u c t i n g d i f f e r e n t i a l CVS c i r c u i t s t o p e r f o r m random l o g i c f u n c t i o n s . The f i r s t p r o c e d u r e makes use of a Karnaugh map and t h e second p r o c e d u r e i s a t a b u l a r method based on the Quine-McCluskey approach. Both s t a t i c and dynamic c i r c u i t t e c h n i q u e s employing t h e CVS l o g i c c o n c e p t a r e d i s c u s s e d . Some w i r i n g and l a y o u t methods based on t h e o r e t i c a l graph models a r e p r e s e n t e d t o ensure the w i r a b i l i t y of CVS c i r c u i t s . An 8x8 NORA CVS m u l t i p l i e r has been d e s i g n e d u s i n g t h e 3um CMOS t e c h n o l o g y of N o r t h e r n Telecom. The c h i p measures 4mm by 4mm and s i m u l a t i o n s i n d i c a t e t h a t i t can be run a t a throughput r a t e of 50MHz. i i T a b l e of C o n t e n t s A b s t r a c t i L i s t of f i g u r e s i v L i s t of T a b l e s x Acknowledgement x i 1 . I n t r o d u c t i o n 1 1.1 G e n e r a l background 1 1 .2 O b j e c t i v e 3 1.3 T h e s i s o u t l i n e 4 2. T h e o r e t i c a l a s p e c t s of CVS l o g i c 6 2.1 CVS l o g i c d e s i g n p r o c e d u r e s 6 2.1.1 SCVS t r e e d e s i g n 6 2.1.2 DCVS t r e e d e s i g n 9 2.1.2.1 D e s i g n by i n t u i t i o n 10 2.1.2.2 K-map pr o c e d u r e ..17 2.1.2.3 T a b u l a r method 25 2.2 W i r i n g and l a y o u t of CVS t r e e s 36 2.2.1 O n e - d i m e n s i o n a l t r e e l a y o u t method 36 2.2.2 Two-dimensional t r e e l a y o u t method 37 2.3 T e s t i n g schemes f o r DCVS c i r c u i t s 42 3. C i r c u i t t e c h n i q u e s w i t h CVS l o g i c 49 3.1' s t a t i c c i r c u i t t e c h n i q u e s 49 3.1.1 C o n v e n t i o n a l CVS c i r c u i t s i n NMOS and CMOS 49 3.1.2 D i f f e r e n t i a l s p l i t - l e v e l CMOS l o g i c 53 3.2 Dynamic CVS c i r c u i t t e c h n i q u e s 57 3.2.1 Domino CMOS l o g i c 57 3.2.2 NORA CMOS l o g i c 68 i i i 3.3 Performance comparisons of CMOS f u l l a d ders 77 4. A h i g h speed CVS p i p e l i n e d m u l t i p l i e r d e s i g n 84 4.1 A l g o r i t h m and a r c h i t e c t u r e 84 4.2 C e l l t y p e s and t h e i r c i r c u i t s 97 4.3 P r o c e s s and speed c r i t e r i a 106 4.4 S i m u l a t i o n s of the c e l l s 111 4.5 Input and ou t p u t c o n s i d e r a t i o n s 121 4.6 F l o o r p l a n and c e l l l a y o u t 133 5. C o n c l u s i o n 137 REFERENCES 138 APPENDIX A: SPICE l i s t i n g s f o r s i m u l a t i o n of f u l l a d ders 144 APPENDIX B: SPICE o u t p u t s f o r s i m u l a t i o n of m u l t i p l i e r c e l l s 160 APPENDIX C: L a y o u t s of some major c e l l s of t h e m u l t i p l i e r 169 L i s t of T a b l e s T a b l e Page 2.1 T y p i c a l l i s t format f o r the t a b u l a r method 27 2.2 T y p i c a l format f o r a 1 0 - l i s t 27 2.3 The 1 0 - l i s t of a 3 - b i t magnitude comparator 30 2.4 The prime i m p l i c a n t t a b l e of the 1 0 - l i s t of T a b l e 2.3 31 2.5 The 1 - l i s t and i t s m i n i m a l sum f o r t h e magnitude comparator 33 2.6 The 0 - l i s t and i t s m i n i m a l sum f o r t h e magnitude comparator 34 3.1 Comparison of s i m u l a t i o n r e s u l t s f o r d i f f e r e n t t y p e s of f u l l a d ders 78 4.1 A t r u t h t a b l e of the m u l t i p l e x e r a r r a y 89 4.2 The d i s t r i b u t i o n of d i f f u s i o n nodes f o r t h e CVS t r e e i n F i g . 4 . 1 7 116 L i s t of f i g u r e s F i g u r e Page 2.1 A t y p i c a l S C V S c i r c u i t s t r u c t u r e i n NMOS 7 2.2(a) A S C V S c i r c u i t f o r the f u n c t i o n f = AB'C +AB'D' +AE +F' ...8 2.2(b) Another S C V S c i r c u i t f o r the f u n c t i o n f 8 2.3 The s t r u c t u r e of a D C V S c i r c u i t 11 2.4 D C V S e x c l u s i v e - o r c i r c u i t s 13 2.5(a) DCVS c i r c u i t f o r the f u n c t i o n c ^ g 1 + P J C Q 1 5 2.5(b) R e c u r s i v e D C V S s t r u c t u r e f o r the f u n c t i o n c = g + p c „ 15 n n n n-1 2.6(a) The DCVS t r e e and i t s s y m b o l i c r e p r e s e n -t a t i o n f o r the f u n c t i o n P = x. x_ ... x 16 1 2 n 2.6(b) D C V S i m p l e m e n t a t i o n f o r the f u n c t i o n f 1 = P 1 Y + P 2 Y ' 1 6 2.6(c) D C V S i m p l e m e n t a t i o n f o r t h e f u n c t i o n 2.7(a) E n c i r c l e m e n t of the K-map f o r the c a r r y - o u t f u n c t i o n of a f u l l adder 18 2.7(b) D C V S i m p l e m e n t a t i o n of the c a r r y - o u t of a f u l l adder 18 2.8(a) The K-map of F i g . 2 . 7 ( a ) , but w i t h d i f f e r e n t e n c i r c l e m e n t s 20 2.8(b) The D C V S t r e e r e s u l t i n g from t h e 10-loops of F i g . 2 . 8 ( a ) 20 2.8(c) The complete D C V S t r e e r e s u l t i n g from F i g . 2 . 8 ( a ) 20 vi 2.9(a) K-map f o r the f u n c t i o n Q = x' x' x' x V + 1 2 3 4 x ( x„ + x„ + x ) showing the 10- and 1 2 3 4 01 - e n c i r c l e m e n t s ...23 2.9(b) DCVS c i r c u i t c o r r e s p o n d i n g t o the 0 1 - l o o p 23 2.9(c) The complete DCVS c i r c u i t 23 2.10(a) An a l t e r n a t i v e e n c i r c l e m e n t arrangement f o r the K-map of F i g . 2 . 9 ( a ) 24 2.10(b) The c i r c u i t r e s u l t i n g from F i g . 2 . 1 0 ( a ) . Compare t h i s c i r c u i t w i t h t h a t i n F i g . 2 . 9 ( c ) 24 2.11 The b a s i c DCVS t r e e s t r u c t u r e as i t would d e v e l o p from a t a b u l a r l i s t 26 2.12 The sh a r e d DCVS t r e e c i r c u i t c o r r e s p o n d i n g t o t he 1 0 - l i s t of T a b l e 2.4 32 2.13 The complete DCVS t r e e f o r the 3 - b i t magnitude comparator 35 2.14(a) A SCVS t r e e f o r the c a r r y l o o k - a h e a d f u n c t i o n 38 2.14(b) The c o r r e s p o n d i n g E u l e r p a t h from F i g . 2 . 1 4 ( a ) 38 2.14(c) A 1-D l a y o u t of the c i r c u i t i n F i g . 2 . 1 4 ( a ) 38 2.15(a) A DCVS h a l f adder c i r c u i t 39 2.15(b) The E u l e r p a t h from F i g . 2 . 1 5 ( a ) 39 2.15(c) The l a y o u t of a h a l f adder 39 2.16 A 2-D l a y o u t of the c i r c u i t i n F i g . 2 . 1 4 ( a ) 41 2.17(a) A DCVS f u l l adder c i r c u i t 43 2.17(b) A 2-D l a y o u t of the f u l l adder 43 2.18 A 3 - i n p u t NAND gate w i t h i l l e g a l i n p u t s 46 2.19 An i l l e g a l s t a t e d e t e c t o r f o r DCVS t r e e s 46 v i i 2.20 A f a u l t d e t e c t i o n scheme f o r DCVS c i r c u i t s 47 3.1(a) The g e n e r a l s t r u c t u r e of SCVS c i r c u i t s 50 3.1(b) A s t a t i c NMOS SCVS c i r c u i t w i t h reduced l o g i c swing 50 3.2 Another SCVS c i r c u i t c o n f i g u r a t i o n i n NMOS 51 3.3 A s t a t i c SCVS c i r c u i t i n CMOS 51 3.4(a) A s t a t i c DCVS c i r c u i t i n NMOS .54 3.4(b) A s t a t i c DCVS c i r c u i t i n CMOS 54 3.5 A g e n e r a l s t r u c t u r e of DSL c i r c u i t s 56 3.6(a) The i n t e r c o n n e c t i o n method of DSL c i r c u i t s 58 3.6(b) The i n t e r c o n n e c t i o n method of DCVS c i r c u i t s 58 3.7(a) A dynamic SCVS gat e 59 3.7(b) A dynamic DCVS gate 59 3.8 A SCVS domino ga t e w i t h a feedback d e v i c e T2 61 3.9 A SCVS domino ga t e w i t h p r e c h a r g e d i n t e r n a l nodes 61 3.10(a) A SCVS domino NAND gate 64 3.10(b) A DCVS domino NAND gate 64 3.11 An l a t c h e d domino c i r c u i t 65 3.12 An example c o n s t r u c t i o n f o r a g l i t c h - f r e e domino l o g i c b l o c k 67 3.13(a) A c l o c k e d CMOS r e g i s t e r 69 3.13(b) The l a s t s t a g e of a CVS p i p e l i n e d s e c t i o n 69 3.14(a) A N-type RCCMOS r e g i s t e r 71 3.14(b) A P-type RCCMOS r e g i s t e r 71 v i i i 3.15(a) A NORA 0 - s e c t i o n w i t h a SCVS t r e e 71 3.15(b) A NORA 0 - s e c t i o n w i t h a DCVS t r e e 71 3.16 The t i m i n g diagram f o r a 0 ' - s e c t i o n c a s c a d e d t o a 0 - s e c t i o n 73 3.17 A p i p e l i n e d s t a g e which p r o v i d e s d i f f e r e n t i a l o u t p u t from s i n g l e - e n d e d i n p u t s 74 3.18 A t i m i n g c o n s t r a i n t a d d i t i o n a l t o F i g . 3 . 1 6 i f t he p i p e l i n e d s t a g e i n Fig.3.17 i s used 76 3.19 A s t a t i c CMOS f u l l adder 79 3.20 A c o n v e n t i o n a l NORA f u l l adder 81 3.21 A m o d i f i e d NORA f u l l adder 82 4.1 The NORA p i p e l i n e scheme and i t s t i m i n g 86 4.2 The a r c h i t e c t u r a l scheme of an 8x8 m u l t i p l i e r 92 4.3 The c e l l l e v e l scheme of a re c o d e r a r r a y 93 4.4 The c e l l l e v e l scheme of a m u l t i p l i e r a r r a y 93 4.5 The c e l l l e v e l scheme of a c a r r y save a r r a y 94 4.6 The c e l l l e v e l scheme of an 1 6 - b i t adder 96 4.7 A r e c o d e r c e l l C1 and i t s t r u t h t a b l e 99 4.8 The DCVS c i r c u i t s f o r the f u n c t i o n s 2X. and D sub 99 3 4.9 A DCVS c i r c u i t t o g e n e r a t e t h e m u l t i p l e x e d outpads ...... 101 4.10 The h a l f adder and f u l l adder b l o c k s and t h e i r l o g i c a l f u n c t i o n s 102 4.11 The b l o c k diagrams and l o g i c a l f u n c t i o n s of c a r r y l ook-ahead c e l l s 102 i x 4.12 An a l t e r n a t i v e c o n s t r u c t i o n of c i r c u i t s i n F i g . 2 . 5 ( a ) and (b) 104 4.13(a) A d e l a y stage w i t h s i n g l e - e n d e d o u t p u t 105 4.13(b) A d e l a y s t a g e w i t h complementary o u t p u t s 105 4.14(a) A lumped model of a CVS c i r c u i t 108 4.14(b) A s i m p l i f i e d RC model of a CVS c i r c u i t 108 4.15 Contour l i n e s of r e l a t i v e d e v i a t i o n e{p,-y) i n Ref .[39] 112 4.16(a) A c a p a c i t i v e model f o r t h e output l o a d 112 4.16(b) A lumped RC model f o r t h e out p u t l o a d 112. 4.17 A c i r c u i t example f o r f i n d i n g the c r i t i c a l d i s c h a r g i n g p a t h 116 4.18(a) A NORA s t a g e w i t h s i n g l e - e n d e d output 119 4.18(b) A NORA s t a g e w i t h complementary o u t p u t s 119 4.19 The s t a g e s of t h e p i p e l i n e d m u l t i p l i e r 122 4.20(a) A t y p i c a l gate p r o t e c t i o n s t r u c t u r e f o r i n p u t pads 124 4.20(b) A c r o s s s e c t i o n of the p r o t e c t i o n s t r u c t u r e i n F i g . 4 . 2 0 ( a ) 124 4.21 The sche m a t i c of a b a s i c c e l l of s t a g e #1 125 4.22 The out p u t s t a g e of t h e m u l t i p l i e r . The numbers i n d i c a t e t he w i d t h s (jim) of the t r a n s i s t o r s 125 4.23 The t h r e e t y p e s of c o n t a c t placement i n ou t p u t pad d e s i g n 128 4.24 The c r o s s s e c t i o n of a CMOS i n v e r t e r w i t h p a r a s i t i c t r a n s i s t o r s shown 131 x 4.25 The l a t c h - u p modes of a CMOS d r i v e r 131 4.26 A l a y o u t of o u t p u t pad which h e l p t o p r e v e n t l a t c h - u p 132 4.27 An abnormal power-up sequence f o r a CMOS i n v e r t e r 134 4.28 The a d d i t i o n of an d i o d e t o p r e v e n t l a t c h - u p ....134 4.29 The f l o o r p l a n of the m u l t i p l i e r 135 x i Acknowledgement The a u t h o r wishes t o thank P r o f e s s o r D a v i d L. P u l f r e y f o r h i s p a t i e n t s u p e r v i s i o n and h i s v a l u a b l e s u g g e s t i o n s on t h i s p r o j e c t . I am a l s o g r a t e f u l t o Tommy Luk and Gai v a n Chang f o r t h e i r e f f o r t s i n h e l p i n g l a y out p a r t of the m u l t i p l i e r c h i p i n the c o u r s e of a f o u r t h y e a r u n d e r g r a d u a t e p r o j e c t under the a u t h o r ' s s u p e r v i s i o n . S p e c i a l thanks go t o my p a r e n t s f o r t h e i r encouragement throughout t h i s work. F i n a n c i a l a s s i s t a n c e from the N a t u r a l S c i e n c e s and E n g i n e e r i n g Research C o u n c i l of Canada i s g r a t e f u l l y acknowledged. x i i 1 CHAPTER 1 : INTRODUCTION 1.1 GENERAL BACKGROUND Random l o g i c design t r a d i t i o n a l l y u t i l i z e s NAND/NOR gates as b a s i c b u i l d i n g elements. The advantage of t h i s simple b u i l d i n g block approach i s that each stage has power gain and generates good l o g i c l e v e l s t h a t assure l a r g e noise margins. While t h i s produces good r e s u l t s , i t i s a l s o e x c e s s i v e i n terms of area and power. Furthermore, long c h a i n s of these gates w i l l r e s u l t i n long l o g i c d e l a y s , h i g h power consumption, and waste of c h i p a r e a . A new approach [ 1 ] i s to combine cascode d i f f e r e n t i a l p a i r s of NMOS de v i c e s i n t o c o m b i n a t i o n a l l o g i c t r e e networks capable of p r o c e s s i n g complex Boolean f u n c t i o n s w i t h i n a s i n g l e c i r c u i t d e l a y . T h i s type of c i r c u i t with a t r e e network of s t a c k i n g t r a n s i s t o r s i s c a l l e d a cascode v o l t a g e switch (CVS) c i r c u i t . CVS c i r c u i t s can be c l a s s i f i e d i n t o two types, namely, si n g l e - e n d e d (SCVS) and d i f f e r e n t i a l (DCVS). SCVS l o g i c gates c o n s i s t of one bi n a r y t r e e , with t r u e or complemented forms of input v a r i a b l e s , and provide only one form of output v a r i a b l e . The complement of the output v a r i a b l e can be obtained through an i n v e r t e r . On the c o n t r a r y , DCVS l o g i c gates c o n s i s t of two i n t e r r e l a t e d or d i s j o i n t e d b i n a r y t r e e s , which g i v e s i m u l t a n e o u s l y both the tr u e and complement outputs. 2 The i m p l e m e n t a t i o n of random l o g i c d e s i g n w i t h CVS l o g i c has many advantages over the c o n v e n t i o n a l NAND/NOR l o g i c a p p r o a c h . The most o b v i o u s advantage i s i n d e v i c e c o u n t ; i t appears t h a t DCVS c i r c u i t s w i l l u s u a l l y r e q u i r e fewer t r a n s i s t o r s , of both n- and p - t y p e , than the two l e v e l NAND/NOR i m p l e m e n t a t i o n [ 1 ] . D e v i c e redundancy i s n a t u r a l l y reduced by the f u n c t i o n a l power of the d i f f e r e n t i a l l o g i c t r e e . SCVS l o g i c can be r e a l i s e d i n NMOS t e c h n o l o g y a l s o . A r e c e n t example of t h i s i s a l a r g e l e v e r a g e c i r c u i t i n which a l a r g e number of d e l a y s t a g e s have been compressed i n t o a s i n g l e CVS gate [ 2 ] . A l t h o u g h t h i s CVS c i r c u i t has an i n c r e a s e d s t a c k h e i g h t , t h e e l i m i n a t i o n of l o n g ^ c h a i n s of g a t e s r e s u l t s i n f u r t h e r advantages i n bo t h d e n s i t y , power and perfo r m a n c e . Another g e n e r a l advantage of DCVS i s t h e i n c r e a s e of l o g i c f l e x i b i l i t y t h a t i s a f f o r d e d , e s p e c i a l l y i n t h o s e i n s t a n c e s where some complex f u n c t i o n must be implemented i n domino CMOS. A c o n s t r a i n t of u s i n g CMOS c i r c u i t s t o form a domino c h a i n a r i s e s t h r o u g h h a v i n g t o ensure t h a t a l l the i n p u t s t o the domino c h a i n a r e s i g n a l s of the "domino g a t e " t y p e , i . e . , s i g n a l s which a r e a t ground p o t e n t i a l d u r i n g p r e c h a r g e [ 3 ] . I f no t , c h a r g e s may l e a k away from a p r e c h a r g e d node, r e s u l t i n g i n a wrong s i g n a l p r o p a g a t i n g a l o n g t h e domino c h a i n . Thus, s t a n d a r d domino l o g i c s u f f e r s from t h e f a c t t h a t i n v e r t i n g l o g i c g a t e s cannot be implemented. However, c l o c k e d DCVS p r o v i d e s 3 complementary o u t p u t s and t h e r e f o r e overcomes t h i s r e s t r i c t i o n [ 1 ] . 1.2 OBJECTIVE Cascode v o l t a g e s w i t c h (CVS) l o g i c i s a newly-proposed MOS l o g i c f a m i l y [ 1 ] . I t s advantages of reduced c i r c u i t d e l a y , a r e a s a v i n g and low power d i s s i p a t i o n have been r e c o g n i z e d and i t may be t h a t CVS l o g i c w i l l r e p r e s e n t a s i g n i f i c a n t new d i r e c t i o n i n NMOS/CMOS l o g i c d e s i g n . W i t h t h e s e a t t r a c t i v e p r o s p e c t s i n mind, t h r e e a s p e c t s of CVS l o g i c a r e examined i n t h i s t h e s i s . F i r s t , t h e o r e t i c a l i s s u e s such as c i r c u i t d e s i g n methodology and l a y o u t t o p o l o g y a r e i n v e s t i g a t e d and r e n d e r e d u s e f u l t o IC d e s i g n e r s . A r e c e n t CVS l o g i c d e s i g n method [ 4 ] uses an a l g e b r a i c d e c o m p o s i t i o n and f a c t o r i z a t i o n t e c h n i q u e , and complex l o g i c can be implemented by t h i s c o m p u t e r - a i d e d a p p r o a c h . However, two o t h e r d e s i g n methods a r e d e v e l o p e d here t o g i v e more i n s i g h t i n t o c i r c u i t b e h a v i o u r . W i r i n g and l a y o u t d e s e r v e s p e c i a l a t t e n t i o n i n CVS c e l l d e s i g n . A l a y o u t s t y l e i s p r e s e n t e d t o ensure a r e a e f f i c i e n c y and c e l l c o m p a c t i o n . Second, v a r i o u s c i r c u i t t e c h n i q u e s e m p l o y i n g t h e CVS l o g i c c o n c e p t a r e e v a l u a t e d and compared w i t h c o n v e n t i o n a l t e c h n i q u e s . U t i l i z i n g t h e domino and NORA (NO RAce) t e c h n i q u e s , the CVS 4 l o g i c i s shown t o be s u p e r i o r t o o t h e r l o g i c f a m i l i e s i n terms of c i r c u i t speed and l o g i c f l e x i b i l i t y . T h i r d , the i m p l e m e n t a t i o n of CVS l o g i c i n a CMOS t e c h n o l o g y i s shown t o be f e a s i b l e t h r o u g h a s p e c i f i c d e s i g n example. A p i p e l i n e d 8x8 b i t m u l t i p l i e r has been c o n s t r u c t e d u s i n g CVS l o g i c , i n o r d e r t o demonstrate how the f o r e g o i n g t h e o r i e s and p r i n c i p l e s can be i n c o r p o r a t e d i n t o a p r a c t i c a l d e s i g n . The d e s i g n d i f f i c u l t i e s of t r a d i t i o n a l dynamic c i r c u i t s , such as l o g i c b l o c k c o n s t r u c t i o n and d e l a y time p a r t i t i o n i n g , a r e shown t o be r e l i e v e d i n CVS l o g i c . 1.3 THESIS OUTLINE Ch a p t e r One i n t r o d u c e s the background and c u r r e n t work on Cascode V o l t a g e S w i t c h (CVS) l o g i c . Some advantages of CVS l o g i c a r e d i s c u s s e d . The f i r s t s e c t i o n of Chapter Two p r o p o s e s two new approaches t o CVS l o g i c d e s i g n , one i s a Karnaugh map method and t h e o t h e r i s a t a b u l a r method. S p e c i f i c examples u s i n g t h e s e p r o c e d u r e s a r e g i v e n . The second s e c t i o n d i s c u s s e s two d i f f e r e n t a p proaches t o t h e l a y o u t of CVS l o g i c t r e e s : a o n e - d i m e n s i o n a l method based on a graph model and a t w o - d i m e n s i o n a l method where the number of v a r i a b l e a l i g n m e n t s a r e maximized. The t h i r d 5 s e c t i o n p r e s e n t s a t e s t i n g scheme u t i l i z i n g the s e l f - t e s t i n g and f a u l t - s e c u r e p r o p e r t i e s of DCVS t r e e s . C h apter Three summarizes the s t a t i c and dynamic c i r c u i t t e c h n i q u e s which c o u l d a p p l y t o CVS l o g i c . Problems such as c h a r g e - s h a r i n g and c l o c k skew c o n s t r a i n t s a r e i n v e s t i g a t e d . A comparison of t h e s e c i r c u i t t e c h n i q u e s i s c a r r i e d out by s i m u l a t i o n s . Chapter Four i s devo t e d t o the d e s i g n of an 8x8 CVS p i p e l i n e d m u l t i p l i e r . The d e t a i l s of c h i p a r c h i t e c t u r e and i n d i v i d u a l c e l l i m p l e m e n t a t i o n s a r e p r e s e n t e d . S i m u l a t i o n s a r e done t o ens u r e t h a t each p i p e l i n e s t a g e meets the speed c o n s t r a i n t . The problems a s s o c i a t e d w i t h t h e I/O i n t e r f a c e , such as t r a n s i s t o r w i d t h / l e n g t h r a t i o d e g r a d a t i o n and l a t c h - u p , a r e d i s c u s s e d . C o n c l u s i o n s a r e drawn and s u g g e s t i o n s a r e made i n the l a s t C h a p t e r . 6 CHAPTER 2 : THEORETICAL ASPECTS OF CVS LOGIC 2.1 CVS LOGIC DESIGN PROCEDURES 2.1.1. SCVS Tree D e s i g n A s i m p l e r e a l i z a t i o n of a SCVS c i r c u i t i n NMOS t e c h n o l o g y c o n s i s t s of a d e p l e t i o n l o a d d e v i c e , a p a i r of i n v e r t e r b u f f e r s and a b i n a r y t r e e (or SCVS t r e e ) , as shown i n F i g . 2 . 1 . The SCVS t r e e i s d e s i g n e d such t h a t node Q i s d i s c o n n e c t e d from ground when the i n p u t c o n t r o l v e c t o r x = ( x , . . . , x ) i s the f a l s e 1 n v e c t o r of the s w i t c h i n g f u n c t i o n f ( x ) , and node Q i s grounded when x i s the t r u e v e c t o r . G i v e n a Boolean e x p r e s s i o n , which can be a minterm e x p r e s s i o n or m i n i m a l sum, of a l o g i c a l f u n c t i o n , a c o r r e s p o n d i n g SCVS t r e e s t r u c t u r e i s sought. G e n e r a l l y , t h i s k i n d of network can be d e s i g n e d u s i n g f a c t o r i z a t i o n t e c h n i q u e s [ 4 ] . For example, the s w i t c h i n g f u n c t i o n f = AB'C + AB'D' + AE + F' can be f a c t o r i z e d as f = A[B'(C+D')+E]+F', and i t s c o r r e s p o n d i n g SCVS t r e e can be r e a l i z e d as i n e i t h e r F i g . 2 . 2 ( a ) o r ( b ) . These c i r c u i t s can be shown t o be c o r r e c t because each p o s s i b l e p a t h from node Q t o ground c o n t r i b u t e s t o one p r o d u c t term i n the e x p r e s s i o n f o r f . SINGLE RAIL OR DUAL RAIL CONTROL SIGNALS i g . 2 . 1 A t y p i c a l SCVS c i r c u i t s t r u c t u r e i n NMOS 8 J 1 j LOAD/BUFFERS f 2 • i ^ NOOE Q <-Ot f • f F i g . 2 . 2 ( a ) A SCVS c i r c u i t f o r t h e f u n c t i o n f =AB'C+AB'D'+AE+F' LOAD/BUFFERS NODE Q B X 7 F i g . 2 . 2 ( b ) A n o t h e r SCVS c i r c u i t f o r t h e f u n c t i o n f 9 The s t r u c t u r e i n F i g . 2 . 2 ( a ) i s more a p p r o p r i a t e when a s t a t i c f u l l CMOS c i r c u i t t e c h n i q u e i s used. The nodes w i t h l a r g e r s h a r e d p a r a s i t i c c a p a c i t a n c e a r e c l o s e r t o the p u l l - u p l o a d d e v i c e and thus d e c r e a s e t h e r i s e t i m e . However, f o r dynamic t e c h n i q u e s which r e q u i r e p r e c h a r g i n g (such as domino CMOS), the s t r u c t u r e i n F i g . 2 . 2 ( b ) i s b e t t e r s i n c e s h a r e d nodes a r e c l o s e r t o t h e ground and thus reduce t h e d i s c h a r g i n g t i m e . 2.1.2 DCVS Tree Design The d e s i g n of DCVS c i r c u i t s i s c o n s i d e r a b l y more d i f f i c u l t t h an t h a t of SCVS c i r c u i t s . The o n l y e x i s t i n g p r o c e d u r e f o r t h e d e s i g n of DCVS t r e e s i s an a l g e b r a i c t e c h n i q u e based on t h e i d e n t i f i c a t i o n of s u b - e x p r e s s i o n s common t o two or more Bo o l e a n f u n c t i o n s [ 4 ] . The d e c o m p o s i t i o n and f a c t o r i z a t i o n t e c h n i q u e s i n v o l v e d i n t h i s approach a r e q u i t e m a t h e m a t i c a l . As suc h , t h e method does not p r o v i d e t h e i n s i g h t i n t o c i r c u i t b e h a v i o u r which i s o f t e n i m p o r t a n t f o r IC d e s i g n e r s . S e c t i o n ( l ) which f o l l o w s s u g g e s t s a few i n t u i t i v e methods t o approach some of t h e d e s i g n p r o b l e m s . S e c t i o n s ( 2 ) and (3) i n t r o d u c e two o t h e r methods, which a r e much s i m p l e r and more p r a c t i c a l t h a n d e s c r i b e d i n [ 4 ] , f o r c o n s t r u c t i n g DCVS t r e e s . The f i r s t p r o c e d u r e u t i l i z e s t h e p i c t o r i a l n a t u r e of the Karnaugh map. T h i s h a n d - p r o c e s s i n g method i s shown t o be an 10 e f f i c i e n t a pproach t o r e a l i z i n g low d e v i c e - c o u n t c i r c u i t s f o r f u n c t i o n s of up t o f i v e or s i x v a r i a b l e s . However, the c o m p l e x i t y of K-maps sudd e n l y i n c r e a s e s when more than f i v e v a r i a b l e s a r e c o n s i d e r e d . A c c o r d i n g l y , a second p r o c e d u r e which has a u n i f o r m p r o c e d u r a l c o m p l e x i t y f o r n - v a r i a b l e s , has been d e v e l o p e d . The method i s t a b u l a r i n n a t u r e and i s a m o d i f i e d form of the Quine-McCluskey method [ 7 ] . Note t h a t a u n i q u e , one-to-one c o r r e s p o n d e n c e between a Boolean e x p r e s s i o n and a DCVS t r e e s t r u c t u r e does not e x i s t [ 6 ] . Thus, the above d e s i g n p r o c e d u r e s can produce s e v e r a l t r e e s t r u c t u r e s t o r e a l i z e a p a r t i c u l a r l o g i c o p e r a t i o n . A l s o f o r a g i v e n s t r u c t u r e , some of t h e i n p u t v a r i a b l e s may be a l l o w e d t o p e r m u t a t e . The two DCVS d e s i g n p r o c e d u r e s proposed here can be used t o implement any Boolean f u n c t i o n , p r o v i d e d the a p p r o p r i a t e t r u t h t a b l e s a r e known. Examples of CMOS d e s i g n s which have been i n v e s t i g a t e d i n t h i s t h e s i s i n c l u d e adder c e l l s , magnitude c o m p a r a t o r s and m u l t i p l i e r c i r c u i t s . 2.1.2.1 D e s i g n by I n t u i t i o n D i f f e r e n t i a l cascode s w i t c h c i r c u i t s u s u a l l y c o n s i s t of a p u s h - p u l l l o a d , and a p a i r of i n t e r r e l a t e d b i n a r y d e c i s i o n t r e e s (or DCVS t r e e s ) , as shown i n F i g . 2 . 3 . 11 * 1 DUAL RAIL CONTROL SIGNALS X n PUSH-PULL LOAD OUTPUTS DCVS TREE ^ G N D F i g . 2 . 3 T h e s t r u c t u r e o f a DCVS c i r c u i t 12 The DCVS t r e e i s p r o p e r l y d e s i g n e d such t h a t : 1. When t h e i n p u t v e c t o r x = ( x , x ) i s the t r u e 1 n v e c t o r of the s w i t c h i n g f u n c t i o n Q ( x ) , node Q i s d i s c o n n e c t e d from ground and node Q' i s c o n n e c t e d t o ground by a unique c o n d u c t i n g p a t h t h r o u g h the t r e e ; 2. When x= ( x 4 x ) i s t h e f a l s e v e c t o r of Q ( x ) , the 1 n r e v e r s e h o l d s . A s i m p l e example i s a 2-way e x c l u s i v e - o r DCVS gat e shown i n F i g . 2 . 4 ( a ) . The f u n c t i o n a l i t y of t h i s c i r c u i t can be e a s i l y v e r i f i e d by t r y i n g a l l the p o s s i b l e c o m b i n a t i o n s of t h e i n p u t v e c t o r s . However, we can a l s o v e r i f y t he c i r c u i t by o b s e r v i n g the s e t of unique p a t h s from nodes Q and Q* t o the ground. The se t of p a t h s a t t a c h e d t o node Q" c o r r e s p o n d s t o t h e e x p r e s s i o n x i x'^ + x'^ x^ which i s e q u a l t o Q ( x ) , w h i l e f o r node Q the e x p r e s s i o n Q'(x) = x ^ x'^ + x j X 2 * Sometimes the DCVS t r e e can be c o n s t r u c t e d e a s i l y by i n t u i t i o n , e s p e c i a l l y f o r th o s e k i n d s of Boolean f u n c t i o n s w i t h a r e c u r s i v e n a t u r e . F o r i n s t a n c e , a 3-way XOR t r e e (see F i g . 2 . 4 ( b ) ) can be b u i l t by r e p l a c i n g the x 2 , x ' 2 p a i r i n F i g . 2 . 4 ( a ) w i t h a n o t h e r 2-way XOR t r e e . F i g . 2 . 4 ( c ) shows a g e n e r a l s t r u c t u r e f o r an n-way XOR t r e e , w i t h a s t a c k i n g h e i g h t e q u a l t o n. 13 LOAD ( c ) n-way XOR gate F i g . 2 . 4 DCVS e x c l u s i v e - o r c i r c u i t s 14 Another i n t e r e s t i n g example of Boolean f u n c t i o n s w i t h r e c u r s i v e n a t u r e a r i s e s i n the c a r r y l o o k - a h e a d c i r c u i t [ 5 ] , G i v e n a r e c u r s i v e e x p r e s s i o n c = g + p c ( f o r n=1 , 2 , 3 , . . . ) , n n n n-1 we c o n s t r u c t a c i r c u i t t o have c and c' as o u t p u t s , w i t h i n p u t n n v e c t o r e q u a l t o ( 9 n ' 9 ' n 9 1 ' 9 ' l ' P n ' P ' n P 1 ' P ' l ' C 0 ' C ' o K F i r s t of a l l , the f u n c t i o n c = g + p c„ can be r e a l i z e d as 1 y 1 M O the c i r c u i t i n F i g . 2 . 5 ( a ) , and i s t h e b a s i c c i r c u i t f o r the r e c u r s i o n . F i g . 2 . 5 ( b ) shows a g e n e r a l s t r u c t u r e of t h e c i r c u i t f o r c , w i t h a s t a c k i n g h e i g h t e q u a l t o 2n+1. n For B o olean e x p r e s s i o n s c o n s i s t i n g of o n l y a few p r o d u c t terms, i t i s easy t o c o n s t r u c t the DCVS t r e e n e t w o r k s . C o n s i d e r a s i m p l e f u n c t i o n P = •••• x n ? t n e c o r r e s p o n d i n g s t r u c t u r e and i t s s y m b o l i c r e p r e s e n t a t i o n a r e shown i n F i g . 2 . 6 ( a ) . U s i n g F i g . 2 . 6 ( a ) as the b a s i c b u i l d i n g b l o c k , we can c o n s t r u c t more complex f u n c t i o n s f = P y + P„ y" and f = P + P„ , 1 .1 1 2 1 2 1 2 where P 1 , a r e two d i f f e r e n t p r o d u c t terms, and y, y' are l i t e r a l s . T h e i r s t r u c t u r e s a r e shown i n F i g . 2 . 6 ( b ) and (c) r e s p e c t i v e l y . F i g . 2 . 5 ( a ) DCVS c i r c u i t f o r t h e f u n c t i o n c = g + P 1 LOAO BLOCK (n-i) — _ r I BLOCK J . (n) F i g . 2 . 5 ( b ) R e c u r s i v e DCVS s t r u c t u r e f o r t h e f u n c t i o n c n = 9n + Pn cn-1 16 P P > HE F i g . 2 . 6 ( a ) The DCVS t r e e and i t s s y m b o l i c r e p r e s e n t a t i o n f o r the f u n c t i o n P *= x 1 x 2 .... x n 1 Ik! F i g . 2 . 6 ( b ) DCVS implement-a t i o n f o r t h e f u n c t i o n f i = p i y + p 2 y' F i g . 2 . 6 ( c ) DCVS implement-a t i o n f o r t h e f u n c t i o n f 2 - P 1 + P 2 17 2 . 1 . 2 . 2 K-Map Pr o c e d u r e The i n p u t v a r i a b l e of a DCVS t r e e i s r e p r e s e n t e d by x. , f o r i = 1 , 2 , . . . , n . A l i t e r a l i s a v a r i a b l e x^ or i t s n e g a t i o n x'. . A cube i s a s e t P of l i t e r a l s such t h a t x. eP i m p l i e s 1 i x'. / P. l In a Karnaugh map of n v a r i a b l e s , t h e r e a r e 2 ° c e l l s , of which each r e p r e s e n t s a cube c o n s i s t i n g of e x a c t l y n l i t e r a l s . C e l l s t h a t c o n t a i n 1's a r e c a l l e d 1 - c e l l s ( s i m i l a r l y , 0 - c e l l s ) . A 1 - l o o p t h a t e n c i r c l e s two a d j a c e n t 1 - c e l l s e x p r e s s e s a cube w i t h one l e s s l i t e r a l than each of t h e cubes r e p r e s e n t i n g the o r i g i n a l 1 - c e l l ( s i m i l a r l y , - 0 - l o o p ) . Suppose t h a t two r e c t a n g u l a r 1 - l o o p s , each c o n s i s t i n g of 2 1 1 - c e l l s , a r e a d j a c e n t on a K-map. I f t h e s e 1 - l o o p s e x p r e s s cubes, say Cx and Cx' , 1 + 1 we get a new r e t a n g u l a r 1 - l o o p c o n s i s t i n g of 2 1 - c e l l s by com b i n i n g t h e two 1 - l o o p s , and the new 1 - l o o p e x p r e s s e s cube C ( s i m i l a r l y f o r t h e 0 - l o o p s ) . B e f o r e i n t r o d u c i n g the K-map a l g o r i t h m , we g i v e an example t o demonstrate some of t h e i d e a s , i . e . g i v e n the Boolean f u n c t i o n Q = x x ^ + x x + x „ x (which i s t h e form of t h e 1 2 2 3 3 1 c a r r y - o u t f u n c t i o n of a f u l l a d d e r ) , c o n s t r u c t t h e c o r r e s p o n d i n g DCVS t r e e . The K-map i s shown i n F i g . 2 . 7 ( a ) . The 1 - and 0-loops a r e e n c i r c l e d p r o p e r l y t o form t h e m i n i m a l c o v e r f o r the 1- and 0 - c e l l s r e s p e c t i v e l y . 18 F i g . 2 . 7 ( a ) E n c i r c l e m e n t o f the K-map f o r the c a r r y - o u t f u n c t i o n of a f u l l adder x 3 h x 2 hc p^Vx; XfHlJ^ ^ TptXl ^ X3 ~5 5 1 - t r e e 0 - t r e e Fig.2.7(b) DCVS i m p l e m e n t a t i o n o f t h e c a r r y - o u t of a f u l l adder 19 F i g . 2 . 7 ( b ) i l l u s t r a t e s t he r e s u l t i n g DCVS t r e e p a i r . The t r e e a t t a c h e d t o node Q' i s d e r i v e d from the 1 - c e l l s and i s c a l l e d t he 1 - t r e e . S i m i l a r l y , the 0 - t r e e i s d e r i v e d from the 0 - c e l l s and i s a t t a c h e d t o node Q. Note t h a t the 1- and 0- t r e e s a r e d i s j o i n t e d because the 1- and 0 - c e l l s have been grouped s e p a r a t e l y . T h i s DCVS c i r c u i t r e q u i r e s t e n N - d e v i c e s t o r e a l i z e the f u n c t i o n Q. The K-map p r o c e d u r e does more than j u s t c o n s t r u c t the two d i s j o i n t e d 1- and 0 - t r e e s . I t a l s o a l l o w s the maximum commonality between t h e s e two t r e e s t o be e x p l o r e d ; from t h i s a " s h a r e d " t r e e s t r u c t u r e l e a d i n g t o the m i n i m i z a t i o n of d e v i c e count can be d e v e l o p e d . Suppose a 1 - c e l l ( 0 - c e l l ) r e p r e s e n t i n g the cube x ^ and a 0 - c e l l ( 1 - c e l l ) r e p r e s e n t i n g the cube x ^ P s i m u l t a n e o u s l y e x i s t , then t h e c e l l c o r r e s p o n d i n g t o the cube P i s d e f i n e d as a 1 0 - c e l l ( 0 1 - c e l l ) . These 0 1 - c e l l s or 1 0 - c e l l s a c t as i n d i v i d u a l c e l l s of two d i f f e r e n t t y p e s . A 01 - l o o p ( 1 0 - l o o p ) can be formed by e n c i r c l i n g two or more a d j a c e n t 0 1 - c e l l s ( 1 0 - c e l l s ) . W i t h t h e s e c o n c e p t s added, we r e v i s i t t he p r e v i o u s example. The K-map shown i n F i g . 2 . 8 ( a ) has t h r e e t y p e s of e n c i r c l e m e n t s , namely, 0- l o o p , 1-loop, and 10-loop. The " s h a r e d " t r e e c o r r e s p o n d i n g t o the 10-loops i s f i r s t c o n s t r u c t e d ( F i g . 2 . 8 ( b ) ) , and t h e n more branches c o r r e s p o n d i n g t o t h e 1-loop and 0-loop a r e added t o form a complete DCVS t r e e ( F i g . 2 . 8 ( c ) ) . Note t h a t 20 x 2 x 3 0 1 00 01 11 10 h 1 1 I 10-loop i F i g . 2 . 8 ( a ) The K-map of F i g . 2 . 7 ( a ) , but w i t h d i f f e r e n t enc i r c l e m e n t s F i g . 2 . 8 ( b ) The DCVS t r e e r e s u l t i n g from t h e 10-l o o p s of F i g . 2 . 8 ( a ) F i g . 2 . 8 ( c ) The complete DCVS t r e e r e s u l t i n g from F i g . 2 . 8 ( a ) 21 o n l y e i g h t N - d e v i c e s a r e now r e q u i r e d , which i s two d e v i c e s fewer than t h e d i s j o i n t e d t r e e i n F i g . 2 . 7 ( b ) . However, the number of s t a c k e d l e v e l s i n c r e a s e s t o t h r e e . The K-map p r o c e d u r e c o n s i s t s of f o u r s t e p s : 1. I d e n t i f y f o u r d i f f e r e n t t y p e s of c e l l s i n the K-map, namely, 0 - c e l l s , 1 - c e l l s , 0 1 - c e l l s and 1 0 - c e l l s . 2. F i n d a m i n i m a l c o v e r f o r a l l the 0 1 - c e l l s . C o n s t r u c t the t r e e c o r r e s p o n d i n g t o t h i s m i n i m a l c o v e r . The v a r i a b l e s x^ i n each of the t r e e branches a r e a r r a n g e d from t o p t o bottom w i t h magnitude of i i n a s c e n d i n g o r d e r . Always c o n s t r u c t t r e e branches c o r r e s p o n d i n g t o l o o p s of s m a l l e r s i z e f i r s t . The t o p p a i r of c o n t r o l i n p u t s a r e x i a s s o c i a t e d w i t h node Q, and x'^ a s s o c i a t e d w i t h node Q'. The s o u r c e s of the t r a n s i s t o r s w i t h gate i n p u t s x i and x ^ ar e a l w a y s c o n n e c t e d t o g e t h e r . 3. From t h e prime i m p l i c a n t s of a l l the 1 0 - c e l l s , f i n d a m i n i m a l c o v e r such t h a t t h e t r e e so c o n s t r u c t e d may share some of t h e branches w i t h the t r e e i n s t e p ( 2 ) . C o n t r a r i l y t o s t e p ( 2 ) , the t o p p a i r of c o n t r o l i n p u t s a r e x'^ a s s o c i a t e d w i t h node Q, and x a s s o c i a t e d w i t h node Q'. 1 4. F i n d a m i n i m a l c o v e r f o r t h e r e m a i n i n g 0 - c e l l s and 1 - c e l l s . W h i l e c o n s t r u c t i n g the t r e e , always l o o k f o r the s h a r i n g of t r e e b r a n c h e s . The r o o t of t h e 0 - t r e e ( 1 - t r e e ) i s co n n e c t e d t o node Q (node Q'). 22 The above p r o c e d u r e may c r e a t e d i f f e r e n t t r e e s t r u c t u r e s i f x i ' s a r e permutated ( e . g . and x^ v a r i a b l e s a re i n t e r c h a n g e d ) . A l s o , t h e r e may be s e v e r a l ways t o choose a mi n i m a l c o v e r , and t o share t r e e b r a n c h e s . As an example, g i v e n a 4 - v a r i a b l e K-map as shown i n F i g . 2 . 9 ( a ) , a p p l i c a t i o n of s t e p s (1) and (2) g e n e r a t e s the t r e e s t r u c t u r e i n F i g . 2 . 9 ( b ) . F u r t h e r , a p p l y i n g s t e p (3) g e n e r a t e s th e complete DCVS t r e e i n F i g . 2 . 9 ( c ) . S t e p (4) has been s k i p p e d because t h e r e a r e no r e m a i n i n g 0 - c e l l s and 1 - c e l l s . A d i f f e r e n t way of e n c i r c l i n g t h e K-map, as shown i n F i g . 2 . 1 0 ( a ) , l e a d s t o a d i f f e r e n t t r e e s t r u c t u r e , see F i g . 2 . 1 0 ( b ) . Note t h a t the 1 0 - c e l l s a r e not c o v e r e d m i n i m a l l y i n t h i s m a n i f e s t a t i o n , and thus the s t a c k l e v e l i n some of the t r e e branches i s i n c r e a s e d . T h i s u n d e s i r a b l e f e a t u r e , combined w i t h the l a r g e p a r a s i t i c c a p a c i t a n c e s a s s o c i a t e d w i t h t h e numerous sha r e d s o u r c e and d r a i n c o n n e c t i o n s , i n d i c a t e s t h a t t h e c i r c u i t of F i g . 2 . 9 ( c ) would have s u p e r i o r e l e c t r i c a l performance t o t h a t of t h e c i r c u i t i n F i g . 2 . 1 0 ( b ) . For a DCVS c i r c u i t w i t h more than about s i x s t a c k e d l e v e l s , t h e performance may be re d u c e d because of c h a r g i n g and d i s c h a r g i n g the p a r a s i t i c d r a i n and so u r c e c a p a c i t a n c e s t h rough l o n g c h a i n s of t r a n s i s t o r s . So, f o r c i r c u i t s r e q u i r i n g h i g h speed, i t may be b e t t e r t o break up c o m p l i c a t e d l o g i c i n t o DCVS c i r c u i t s of s i x or l e s s v a r i a b l e s . I n such c a s e s , the K-map x, x 2Vaa oo 01 11 10 X 2 X 3 X 4 101-loOp; F i g . 2 . 9 ( a ) K-map f o r the f u n c t i o n Q = x ' 1 x ' 2 x ' 3 x ' 4 + x 1 ( *2 + x 3 + x 4 ) showing the 10- and 0 1 - e n c i r c l e m e n t s F i g . 2 . 9 ( b ) DCVS c i r c u i t F i g . 2 . 9 ( c ) The complete DCVS c o r r e s p o n d i n g t o the 0 1 - l o o p c i r c u i t 24 X 4 00 01 11 10 00 1 1 v 1 / 1) fo\ 01 0 0 0 11 1 1 1 10 V F i g . 2 . 1 0 ( a ) An a l t e r n a t i v e e n c i r c l e m e n t arrangement f o r t h e K-map of F i g . 2 . 9 ( a ) F i g . 2 . 1 0 ( b ) The c i r c u i t r e s u l t i n g from F i g . 2 . 1 0 ( a ) . Compare t h i s c i r c u i t w i t h t h a t i n F i g . 2 . 9 ( c ) 25 d e s i g n p r o c e d u r e may prove p a r t i c u l a r l y u s e f u l . 2.1.2.3 T a b u l a r Method The t a b u l a r method d e s c r i b e d here makes use of the Quine-McCluskey method [7] of f i n d i n g prime i m p l i c a n t s and t h e i r m i n i m a l c o v e r i n g s e t . A l i s t c o n v e n t i o n a l l y c o n s i s t s of two f i e l d s , namely; the i n p u t v e c t o r ( x x ) on the r i g h t 1 n and i t s d e c i m a l r e p r e s e n t a t i o n on t h e l e f t (see T a b l e 2.1). The i n p u t v e c t o r s a r e grouped i n t o r e c o r d s i n an a s c e n d i n g o r d e r of t h e i r i n d e x (number of 1's i n t h e i r b i n a r y r e p r e s e n t a t i o n ) . We s t a r t w i t h a 1 - l i s t ( l i s t c o n t a i n i n g 1's of the f u n c t i o n ) , and a 0- l i s t ( l i s t c o n t a i n i n g O's). From t h e s e two l i s t s , we g e n e r a t e a n o t h e r two l i s t s , namely; a 1 0 - l i s t and a 0 1 - l i s t . The mechanism i s analogous t o the g e n e r a t i o n of 1 0 - c e l l s and 01- c e l l s from the 1 - c e l l s and 0 - c e l l s i n the K-map approach. S e l e c t i o n of m i n i m a l c o v e r s from the 0 - l i s t , 1 - l i s t , 1 0 - l i s t and 0 1 - l i s t u s i n g a m o d i f i e d Quine- McCluskey p r o c e d u r e r e s u l t s i n a DCVS t r e e s t r u c t u r e shown i n F i g . 2 . 1 1 . The t a b u l a r p r o c e d u r e c o n s i s t s of f i v e s t e p s : 1. Draw a 1 - l i s t which c o n t a i n s a l l t h e t r u e v e c t o r s ( x^ x ) of t h e f u n c t i o n Q. The l i s t i s s u b d i v i d e d i n t o n r e c o r d s w i t h i n c r e a s i n g i n d e x i from t o p t o bottom. S i m i l a r l y , a 0 - l i s t w hich c o n t a i n s a l l the f a l s e v e c t o r s of 26 I L _ I T R E E I I DERIVED | I FROM 1 - LIST | I 1 T R E E DERIVED FROM 01 - LIST T R E E DERIVED F R O M 10 - LIST _ J I T R E E I DER IVED | FROM 0 - LIST _L I \ 7 F i g . 2 . 1 1 The b a s i c DCVS t r e e s t r u c t u r e as i t would d e v e l o p from a t a b u l a r l i s t 27 DEC1WI REPRESENTATION l i n n VECTOR OF 1MPU1 VECTOR X, x?- • • x n e.g. 1 0 0 1 4 1 0 0 3 0 1 1 6 1 1 0 o O o O e 0 o o o e > RECORD f RECORD j>i T a b l e 2.1 T y p i c a l l i s t format f o r the t a b u l a r method OECIrR REPRESENTATION REDUCED INPUT VECTOR OF REDUCED IWUT VECTOR e.g. 1 0 1 2 1 0 3 1 1 o O 0 0 0 0 > RECORD RECORD J>i T a b l e 2.2 T y p i c a l format f o r a 1 0 - l i s t 28 Q i s drawn. The r e c o r d w i t h index i i s n o t a t e d as r e c o r d i . 2. For i = 1 t o n: In t h e 1 - l i s t , each row s t a r t i n g w i t h x i = 1 w i t h i n r e c o r d i i s compared w i t h the rows w i t h i n r e c o r d i - 1 of the 0 - l i s t . I f the reduced v e c t o r ( x , x ) of the two 2 n rows i s the same, then check th e s e two rows i n the 1 - l i s t and 0 - l i s t r e s p e c t i v e l y and add a row e n t r y t o the 1 0 - l i s t . The format of t h e 1 0 - l i s t i s s l i g h t l y d i f f e r e n t and i s shown i n T a b l e 2.2. The v a r i a b l e x i i s no l o n g e r r e q u i r e d . 3. For i = 0 t o n - l : In the 1 - l i s t , each row s t a r t i n g w i t h x^ = 0 w i t h i n r e c o r d i i s compared w i t h the rows w i t h i n r e c o r d i+1 of the 0- l i s t . S i m i l a r l y , i f t h e reduced v e c t o r ( x_ ,..., x ) of 2 n the two rows i s the same, check t h e s e two rows and add a row e n t r y t o the 0 1 - l i s t . The format of t h e 0 1 - l i s t i s the same as t h a t of t h e 1 0 - l i s t . 4. A p p l y the Quine-McCluskey method of f i n d i n g prime i m p l i c a n t s t o the rows i n the 1 0 - l i s t and 0 1 - l i s t . S e l e c t a m i n i m a l c o v e r i n g s e t f o r each of the two l i s t s by row and column dominance p r o c e d u r e s , and l o o k f o r a maximum amount of s h a r i n g of t r e e b ranches when c o n s t r u c t i n g the c o r r e s p o n d i n g t r e e s . Thus, a " s h a r e d " t r e e i s b u i l t . 5. A p p l y t h e c o n v e n t i o n a l p r o c e d u r e o f s e l e c t i n g a minimal c o v e r i n g s e t f o r the unchecked rows i n t h e 0 - l i s t and 1- l i s t . C o n s t r u c t the t r e e s c o r r e s p o n d i n g t o the s e two 29 m i n i m a l sums, by a d d i n g more branches t o t h e "sha r e d " t r e e . Thus, a DCVS t r e e s t r u c t u r e of t h e form shown i n Fig.2.11 m a t e r i a l i s e s . As an example, c o n s i d e r the d e s i g n of a 3 - b i t magnitude comparator by the t a b u l a r method. The c i r c u i t compares two b i n a r y numbers, A= A^ A^ A and B= , and g i v e s an ou t p u t Q=1 whenever A>B. We a s s i g n t h e v a r i a b l e s e q u a l t o ( X , X , X , X , X , X ) 1 2 3 4 5 6 ( A 3 ' B 3 ' A 2 ' B 2 ' A 1 ' B 1 K Note: a d i f f e r e n t assignment w i l l l e a d t o a d i f f e r e n t t r e e s t r u c t u r e . By s t e p (1) of the p r o c e d u r e , we r e a d i l y t a b u l a t e t h e 1 - l i s t ( t o t a l l i n g 28 r o w s ) , and t h e 0 - l i s t (36 r o w s ) . A f t e r s t e p (2) i s performed, a 1 0 - l i s t as shown i n T a b l e 2.3 i s drawn. A p p l i c a t i o n of s t e p (3) i n d i c a t e s t h a t no 0 1 - l i s t can be g e n e r a t e d . By s t e p ( 4 ) , a prime i m p l i c a n t t a b l e as shown i n T a b l e 2.4 i s d e r i v e d from t h e 1 0 - l i s t , and the s e prime i m p l i c a n t s a c t u a l l y form a m i n i m a l c o v e r i n g s e t . The "s h a r e d " t r e e i s i l l u s t r a t e d i n F i g . 2 . 1 2 . By s t e p ( 5 ) , t h e unchecked rows of t h e 1 - l i s t and 0 - l i s t r e s u l t i n T a b l e s 2.5 and 2.6 r e s p e c t i v e l y . T h e i r c o r r e s p o n d i n g m i n i m a l sums worked out by the Quine-McCluskey method a r e a l s o i n d i c a t e d . The complete DCVS t r e e i s i l l u s t r a t e d i n F i g . 2 . 1 3 . 30 DECira REPRESENTATION REDUCED INPUT VECTOR OF REDUCED INPUT VECTOR *5 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 5 0 0 1 0 1 6 0 0 1 1 0 12 0 1 1 0 0 3 0 0 0 1 1 24 1 1 0 0 0 18 1 0 0 1 0 7 0 0 1 1 1 13 0 1 1 0 1 25 1 1 0 0 1 26 1 1 0 1 0 15 0 1 1 1 1 27 1 1 0 1 1 30 1 1 1 1 0 T a b l e 2 .3 T h e 1 0 - l i s t o f a 3 - b i t m a g n i t u d e c o m p a r a t o r 31 DECIMAL PRIME RtPHESENTmiW 0 1 3 M 5 6 ? 12 13 15 18 25 26 2? 30 IMPLICflNT N 5 x 6 X X x 2 X 3 x 5 -<6J X X *i *5J X X X *i x3J x„ X X X X *i x„ x5' X X X X *i XB X X X X *2 x 6 X X X X *2 x 3 x ;  x4 X X X X T a b l e 2.4 T h e p r i m e i m p l i c a n t t a b l e o f t h e 1 0 - l i s t o f T a b l e 2.3 F i g . 2 . 1 2 The s h a r e d DCVS t r e e c i r c u i t c o r r e s p o n d i n g t o t h e 1 0 - l i s t o f T a b l e 2.4 OECMRL REPRESENTATION INPUT VECTOR OF INPUT VECTOR *1 x 3 X 4 x 5 x 6 1 0 0 0 0 1 0 8 0 0 1 0 0 0 9 0 0 1 0 0 1 10 0 0 1 0 1 0 40 1 0 1 0 0 0 34 1 0 0 0 1 0 11 0 0 1 0 1 1 14 0 0 1 1 1 0 41 1 0 1 0 0 1 42 1 0 1 0 1 0 43 1 0 1 0 1 1 46 1 0 1 1 1 0 HIN1MRL sun = X 2 * 3 X 5 * 6 + W E X ' ) 6 + x ' X X ' 2 3 4 T a b l e 2.5 The 1 - l i s t and i t s m i n i m a l sum f o r t h e magnitude comparator OEIlrWL ftHiUtNlMtOI WW TECTOR «r imn ncroR *2 x5 x* x5 x B 16 0 1 0 0 0 0 20 0 1 0 1 0 0 1? 0 1 0 0 0 1 MB 1 1 0 0 0 0 21 0 1 0 1 0 1 22 0 1 0 1 1 0 28 0 1 1 1 0 0 19 0 1 0 0 1 1 52 1 1 0 1 0 0 19 1 1 0 0 0 1 29 0 1 1 1 0 1 23 0 1 0 1 1 1 53 1 1 0 1 0 1 54 1 1 8 1 1 0 60 1 1 1 1 0 0 51 1 1 0 0 1 1 31 0 1 1 1 1 1 61 1 1 1 1 0 1 55 1 1 0 1 I 1 63 1 1 1 1 1 1 niNiim. sun = *2yi *2*3*1 T a b l e 2.6 The 0 - l i s t and i t s m i n i m a l sum f o r t h e magnitude comparator 35 F i g . 2 . 1 3 The complete DCVS t r e e f o r t h e 3 - b i t magnitude c o m p a r a t o r 36 2.2 WIRING AND LAYOUT OF CVS TREES The h i g h f u n c t i o n a l d e n s i t y a c h i e v a b l e w i t h t h e c a s c o d e c i r c u i t t e c h n i q u e p o s e s a c h a l l e n g e f o r d e s i g n e r s t o f i n d c i r c u i t l a y o u t s w h i c h r e a l i z e t h e s e h i g h d e n s i t i e s w h i l e s t i l l b e i n g w i r a b l e . S e v e r a l a p p r o a c h e s a r e d i s c u s s e d h e r e t o c o m p a c t t h e t r e e l a y o u t and f a c i l i t a t e b u s s i n g b e t w e e n t r e e s . 2.2.1 O n e - D i m e n s i o n a l T r e e L a y o u t M e t h o d We f i r s t c o n s i d e r a l i n e a r , o n e - d i m e n s i o n a l l a y o u t s t y l e f o r a CVS c i r c u i t . T h i s o p t i m a l m e t h o d h a s b e e n u s e d t o l a y o u t AND-OR n e t w o r k s r e a l i z e d i n s t a t i c CMOS by means o f s e r i e s / p a r a l l e l c o n n e c t i o n s o f t r a n s i s t o r s [ 8 ] , T h e o r i g i n a l g r a p h m o d e l c o n s i s t s o f an n - s i d e d g r a p h r e p r e s e n t i n g t h e N-MOS s i d e o f t h e c i r c u i t a n d a p - s i d e d g r a p h f o r t h e P-MOS s i d e . H o w e v e r , d e s i g n i n g SCVS t r e e s r e q u i r e s o n l y t h e n - s i d e d g r a p h m o d e l . G i v e n a SCVS t r e e n e t w o r k , e d g e s a r e drawn c o r r e s p o n d i n g t o t r a n s i s t o r s a n d t h e y a r e c o n n e c t e d i n a manner a c c o r d i n g t o t h e c o n n e c t i o n s o f t r a n s i s t o r s i n t h e c i r c u i t . I f two e d g e s a r e a d j a c e n t i n t h e g r a p h m o d e l , t h e n i t i s p o s s i b l e t o p l a c e t h e c o r r e s p o n d i n g g a t e s i n p h y s i c a l l y a d j a c e n t p o s i t i o n s o f an a r r a y a n d h e n c e c o n n e c t them by a d i f f u s i o n a r e a . I f t h e r e e x i s t s an E u l e r p a t h , i . e . a s e q u e n c e o f e d g e s t h a t c o n t a i n s a l l t h e e d g e s 37 of the graph model, then a l l the d r a i n and the s o u r c e r e g i o n s can be c h a i n e d by d i f f u s i o n a r e a s . I f t h e r e i s no E u l e r p a t h , then the graph can be decomposed i n t o s e v e r a l subgraphs which have E u l e r p a t h s . In the l a t t e r c a s e , each E u l e r path c o r r e s p o n d s t o a c h a i n of t r a n s i s t o r s t h a t i s s e p a r a t e d from o t h e r such c h a i n s by a s e p a r a t i o n a r e a . Thus, a compact l a y o u t f o r a SCVS t r e e can be found by decomposing the c o r r e s p o n d i n g graph model i n t o a minimum number of E u l e r p a t h s t h a t c o v e r the graph model. F o r example, a SCVS t r e e shown i n F i g . 2 . 1 4 ( a ) has a E u l e r p a t h as i n ( b ) , and i t s l a y o u t i s i l l u s t r a t e d i n ( c ) . The same concept can be used t o l a y o u t some s i m p l e DCVS t r e e n e t w o r k s . C o n s i d e r a h a l f adder c e l l which c o n t a i n s two a d j a c e n t DCVS t r e e s ( F i g . 2 . 1 5 ( a ) ) . In o r d e r t o a r r a n g e two a d j a c e n t l i n e a r a r r a y s w i t h s t r a i g h t l i n e w i r i n g as shown i n F i g . 2 . 1 5 ( c ) , the E u l e r p a t h s i n (b) a r e chosen. The o n e - d i m e n s i o n a l method i s o n l y s u i t a b l e f o r l a y i n g out a few s m a l l CVS t r e e s a d j a c e n t t o each o t h e r . For c o n s t r u c t i n g l a r g e r c i r c u i t s such as t r e e macros, c o m p u t e r - a s s i s t e d , t w o - d i m e n s i o n a l l a y o u t methods s h o u l d be used [ 6 ] . 2.2.2 Two-Dimensional Tree Layout Method SCVS c i r c u i t s , e s p e c i a l l y t h o s e w i t h s e r i e s / p a r a l l e l (SP) o r d e r i n g s o f t r a n s i s t o r s , a r e more n a t u r a l l y r e a l i z e d as 38 C D E B F G A B-POLY / METAL DIFFUSION <7Gnd F i g . 2 . 1 4 ( c ) A 1-D l a y o u t o f t h e c i r c u i t i n F i g . 2 . 1 4 ( a ) F i g . 2 . 1 5 ( c ) The l a y o u t of a h a l f adder 40 t w o - d i m e n s i o n a l l a y o u t s than l i n e a r , o n e - d i m e n s i o n a l l a y o u t s [ 9 ] , The t r a n s i s t o r s which connect t o ground a r e p l a c e d on the bottom row of t h e t r e e . T r a n s i s t o r s c o n n e c t e d i n s e r i e s w i t h t h o s e i n the bottom row a r e p l a c e d on the second row, d i r e c t l y above the c o n n e c t i n g t r a n s i s t o r . T h i s p r o c e s s i s r e p e a t e d u n t i l the t o p row co n n e c t e d t o t h e l o a d d e v i c e s i s reached. The i n t e r n a l t r e e c o n n e c t i o n s may be made i n d i f f u s i o n because i t i n c r e a s e s the number of m e t a l w i r i n g t r a c k s a v a i l a b l e f o r making g l o b a l t r e e c o n n e c t i o n s . E s p e c i a l l y i n l a r g e c o l l e c t i o n s of SCVS t r e e s r e q u i r i n g a l a r g e number of e x t e r n a l c o n n e c t i o n s , the use of m e t a l t o p e r f o r m i n t e r n a l w i r i n g produces c o n g e s t i o n f o r the i n t e r - t r e e w i r i n g , which must n e c e s s a r i l y be made i n m e t a l . An example l a y o u t of the t r e e i n F i g . 2 . 1 4 ( a ) i s i l l u s t r a t e d i n F i g . 2 . 1 6 . I t i s w e l l known t h a t d i f f u s i o n i n t e r c o n n e c t i o n of t r a n s i s t o r s may have an impact on performance. However, i f t h e a d d i t i o n a l d i f f u s i o n i s kept t o a r e a s o n a b l e l e n g t h , t h e performance d e g r a d a t i o n can be more than o f f s e t by the i n c r e a s e i n d e n s i t y . A n o t h e r approach i s t o ease i n t e r - t r e e c o n n e c t i o n s by a r r a n g i n g c a r e f u l l y t h e i n d i v i d u a l t r e e s t r u c t u r e [ 6 ] . S t r a i g h t - l i n e w i r i n g between common v a r i a b l e s i n a d j a c e n t t r e e s i s e ncouraged, and t r e e s s h a r i n g common i n p u t s s h o u l d be kept t o g e t h e r . When w i r e s must t a k e j o g s t o make c o n n e c t i o n s , l a r g e p e n a l t i e s i n terms of w i r e l e n g t h and o v e r a l l l a y o u t p o r o s i t y may r e s u l t . I n o r d e r t o encourage v a r i a b l e b u s s i n g , s h a red F i g . 2 . 1 6 A 2-D l a y o u t of t h e c i r c u i t i n F i g . 2 . 1 4 ( a 42 v a r i a b l e s of t r e e s a r e p r e f e r e n t i a l l y p l a c e d i n the same row ( r a i l ) , e.g. t h e v a r i a b l e A on t h e t o p r a i l of the l a y o u t i n F i g . 2 . 1 7 ( b ) . The s e t of a l l o w e d t r e e c o n f i g u r a t i o n s i s g e n e r a t e d by i n t e r c h a n g i n g symmetric v a r i a b l e s , s w i t c h i n g v a r i a b l e s w i t h i n the same l e v e l t o o t h e r columns, and s l i d i n g v a r i a b l e s t o u n o c c u p i e d l e v e l s w i t h i n the t r e e [ 1 0 ] . The o p t i m a l s t r u c t u r e i s chosen by m a x i m i z i n g the number of a l i g n m e n t s between s h a r e d v a r i a b l e s of n e i g h b o u r i n g t r e e s . T h i s method i s s u i t a b l e f o r b oth DCVS and SCVS t r e e l a y o u t . An example i s t h e l a y o u t of a f u l l adder c e l l shown i n F i g . 2 . 1 7 . Note t h a t t h e s e t of v a r i a b l e s {A,B,C} a r e symmetric i n b oth of t h e l o g i c a l f u n c t i o n s and t h u s swapping v a r i a b l e s i n d i f f e r e n t r a i l s i s a l l o w e d . T h i s g r o u p i n g of common v a r i a b l e s i n a d j a c e n t t r e e s f u r t h e r compacts the l a y o u t . 2.3 TESTING SCHEMES FOR DCVS CIRCUITS Most s t r u c t u r e d d e s i g n p r a c t i c e s a r e b u i l t upon the concept t h a t , w i t h some a d d i t i o n a l c i r c u i t r y , a l l memory elements i n an IC can be t h r e a d e d t o g e t h e r i n t o a s h i f t r e g i s t e r . A c o n t r o l s i g n a l can s w i t c h t h e memory elements from t h e i r normal modes of o p e r a t i o n t o s h i f t r e g i s t e r mode. Then, the c u r r e n t s t a t e of the IC can be f r o z e n and s h i f t e d out f o r e x a m i n a t i o n . L e v e l - S e n s i t i v e Scan D e s i g n (LSSD) i s IBM's d i s c i p l i n e f o r SUM' SUM F i g . 2 . 1 7 ( a ) A DCVS f u l l adder c i r c u i t F i g . 2 . 1 7 ( b ) A 2-D l a y o u t of t h e f u l l adder 44 s t r u c t u r e d d e s i g n f o r t e s t a b i l i t y . "Scan" r e f e r s t o the a b i l i t y t o s h i f t i n t o or out of any s t a t e of the network. " L e v e l - s e n s i t i v e " r e f e r s t o c o n s t r a i n t s on c i r c u i t e x c i t a t i o n , l o g i c d e p t h , and the h a n d l i n g of c l o c k e d c i r c u i t r y . A key element i n t h e d e s i g n i s the " s h i f t r e g i s t e r l a t c h " (SRL), which has r e c e n t l y been implemented i n DCVS l o g i c [ 1 1 ] , We w i l l d e s c r i b e a c o n s i d e r a b l y d i f f e r e n t scheme f o r e x p l o i t i n g t h e s e l f - t e s t i n g p r o p e r t y of DCVS t r e e s [ 1 2 ] , A DCVS c i r c u i t has t h e unique p r o p e r t y of o n - l i n e t e s t a b i l i t y due t o the p r e s e n c e of complementary o u t p u t s f o r e v e r y t r e e . T h i s i n f o r m a t i o n may p r o v i d e b o t h s t u c k - a t and dynamic f a u l t c overage ( e . g . , due t o power g l i t c h e s or a l p h a p a r t i c l e s ) . A DCVS t r e e produces d i f f e r e n t i a l p a t h s from two nodes ( c a l l e d Q and Qbar, r e s p e c t i v e l y , and r e p r e s e n t e d by an o r d e r e d p a i r (Q,Q')) t o ground. Under f a u l t - f r e e o p e r a t i o n , o n l y one of two p a t h s t o ground i s a c t i v e , p r o d u c i n g a l e g a l (code space) o u t p u t (1,0) or ( 0 , 1 ) . I t i s known t h a t any s i n g l e f a i l u r e may cause t h e o u t p u t t o change s t a t e from one l e g a l s t a t e t o an i l l e g a l (non-code space) s t a t e such as (0,0) or (1,1) [ 1 2 ] . Thus, t h e d e t e c t i o n of an i l l e g a l s t a t e a t the out p u t of any t r e e i s a c l e a r i n d i c a t i o n of t h e presence of a f a u l t i n the t r e e . T h i s i s so c a l l e d t h e s e l f - t e s t i n g p r o p e r t y of DCVS t r e e s . A DCVS t r e e a l s o has a f a u l t - s e c u r e p r o p e r t y . I t can be shown t h a t a s i n g l e i l l e g a l i n p u t t o a f u n c t i o n i n g t r e e can o n l y 45 c a u s e t h e t r e e t o p r o d u c e e i t h e r an i l l e g a l o u t p u t o r c o r r e c t o u t p u t [ 1 2 ] . A DCVS t r e e c a n h a v e one o f i t s i n p u t s i n an i l l e g a l s t a t e , and p r o d u c e t h e c o r r e c t l e g a l o u t p u t i f i t s o t h e r i n p u t s a r e s u c h t h a t t h e o u t p u t i s i n d e p e n d e n t o f t h e i l l e g a l i n p u t . An e x a m p l e u s i n g a 3 - i n p u t NAND g a t e i s shown i n F i g . 2 . 1 8 . T h e r e f o r e , p l a c i n g t h e i l l e g a l s t a t e d e t e c t o r a t t h e o u t p u t s o f i n t e r n a l DCVS t r e e s , r a t h e r t h a n o n l y a t t h e l a t c h e s o f l o g i c a l b l o c k b o u n d a r i e s , c a n i n c r e a s e t h e e r r o r o b s e r v a b i l i t y . The i l l e g a l s t a t e d e t e c t o r c a n be an e x c l u s i v e - o r c i r c u i t shown i n F i g . 2 . 1 9 . The " e r r o r f l a g " i s p u l l e d down w h e n e v e r ( Q , Q ' ) i s e q u a l t o ( 0 , 0 ) o r ( 1 , 1 ) . A scheme w h i c h a l l o w s f a u l t s t o be l o c a t e d t o w i t h i n a s m a l l r e g i o n o f t h e c h i p i s shown i n F i g . 2 . 2 0 . T h i s i s v a l u a b l e t o h e l p d e b u g b o t h t h e p r o c e s s a n d t h e d e s i g n , and s e a r c h f o r f a u l t s i n t h e w h o l e c h i p . An e r r o r c a u s e s t h e c o r r e s p o n d i n g x a n d y l o c a t i o n s t o be e x c i t e d , a n d t h i s d a t a i s l a t c h e d a n d s e r i a l l y r e a d o f f t h e c h i p . N o t e t h a t t h e number o f a d d i t i o n a l p a i r s o f r e g i s t e r s r e q u i r e d f o r t h i s scheme i s t h e s q u a r e r o o t o f t h e number o f g r i d p o i n t s t o be l o c a t e d . T h e s y s t e m i s more o b s e r v a b l e t h a n when u s i n g t r a d i t i o n a l LSSD t e s t i n g , a n d t h e o n l y t e s t d a t a w h i c h n e e d s t o be s e n t o f f t h e c h i p i s t h e e r r o r f l a g s i g n a l . T h i s i s a c o n s i d e r a b l e e n h a n c e m e n t o v e r p s e u d o - r a n d o m s e l f - t e s t i n g , s i n c e no p a t t e r n ( c o m p r e s s e d o r o t h e r w i s e ) n e e d be s t o r e d o n - c h i p a n d t h e l e n g t h o f t h e t e s t i n g s e q u e n c e may be i n c r e a s e d o r d e c r e a s e d t o s u i t t e s t i n g n e e d s 0=0 I Q'=l O J f-B-I \7 (— C=0 F i g . 2 . 1 8 A 3 - i n p u t NAND gate w i t h i l l e g a l i n p u t s G h 0' >-TEST aocK HI ERRFLAG F i g . 2 . 1 9 An i l l e g a l s t a t e d e t e c t o r f o r DCVS t r e e s 4 7 SHIFT REGISTERS ; fK as S/fl "^SCAN OUT A NODE —* — 3 —* —5 —J —J —5 —) r n Fig.2.20 A f a u l t d e t e c t i o n scheme f o r DCVS c i r c u i t s 48 w i t h no m o d i f i c a t i o n t o the c i r c u i t needed. 49 CHAPTER 3 : CIRCUIT TECHNIQUES WITH CVS LOGIC 3.1 STATIC CIRCUIT TECHNIQUES 3.1.1. C o n v e n t i o n a l CVS C i r c u i t s i n NMOS and CMOS For s i n g l e - e n d e d c i r c u i t s , t h e g e n e r a l c o n c e p t [2] i s shown i n F i g . 3 . l ( a ) . A complex f u n c t i o n r e a l i z e d by the SCVS t r e e p r oduces a weak s i g n a l on node Q, which can be s t r e n g t h e n e d by a d e d i c a t e d sense a m p l i f i e r / b u f f e r . The c u r r e n t s o u r c e can be a d e p l e t i o n N - d e v i c e , and the sense amp./buffer can be a cas c a d e d NMOS i n v e r t e r p a i r w i t h s u i t a b l e p u l l - u p / p u l l - d o w n r a t i o ( F i g . 3 . 1 ( b ) ) . Because of the l a r g e c a p a c i t a n c e s u s u a l l y a s s o c i a t e d w i t h t h e SCVS t r e e network, performance improvement and power s a v i n g s can r e s u l t i f t h e l o g i c swing a t node Q i s d e c r e a s e d . T h i s can be a c c o m p l i s h e d , f o r example, by r e d u c i n g Vcc t o 3V w h i l e k e e p i n g Vdd a t 5V, so t h a t l e s s charge i s m a n i p u l a t e d on the c a p a c i t a n c e s of the t r e e network. A s l i g h t l y d i f f e r e n t c i r c u i t c o n f i g u r a t i o n [13] i s shown i n F i g . 3 . 2 . When, t h e t r e e network i s an open c i r c u i t , node Q i s p u l l e d h i g h t h r o u g h t r a n s i s t o r T1, w i t h t h e d r i v e on t r a n s i s t o r T1 i n c r e a s i n g t h r o u g h i t s c o n n e c t i o n t o out p u t f . Feedback from o u t p u t f t o the d e p l e t i o n - t y p e t r a n s i s t o r T1 m a i n t a i n s node Q a t l o g i c h i g h . When the t r e e network c o n d u c t s , node Q i s p u l l e d t o a low v o l t a g e l e v e l , t u r n i n g o f f t r a n s i s t o r T2. Thus, the 5 0 Vcc Q CURRENT SENSE AMP. SOURCE (1) AND BUFFER NODE Q \ BUFFER •» f SCVS TREE X7 F i g . 3 . l ( a ) The g e n e r a l s t r u c t u r e of SCVS c i r c u i t s Vcc=3V Vdd=5V i c \ HI -» f K 7 iSCVS TREE F i g . 3 . 1 ( b ) A s t a t i c NMOS SCVS c i r c u i t w i t h r e d u c e d l o g i c swing 51 Tl T2 \ ^S3 SCVS TREE F i g . 3 . 2 Another SCVS c i r c u i t c o n f i g u r a t i o n i n NMOS H u 1 T 2 > n 12 \ SCVS TREE F i g . 3 . 3 A s t a t i c SCVS c i r c u i t i n CMOS 52 v o l t a g e on node f r i s e s v i a i n v e r t e r 11, t u r n i n g on t r a n s i s t o r T3 which causes the v o l t a g e on out p u t f t o de c r e a s e t o a l o g i c low. The a c t i o n i s r e g e n e r a t i v e t h r o u g h the feedback from output f t o t r a n s i s t o r T1. The g e n e r a l scheme i n F i g . 3 . 1 ( a ) can a l s o be implemented i n CMOS t e c h n o l o g y (see F i g . 3 . 3 ) . The c u r r e n t s o u r c e i s a P-device whose g a t e i s a t ground. I n v e r t e r 11 a c t s as a CMOS b u f f e r whose t r a n s f e r c h a r a c t e r i s t i c s may be a d j u s t e d t o p r o v i d e e a r l y s e n s i n g of node Q. T2 a c t s as a c u r r e n t b o o s t e r r a i s i n g the d r i v e on node Q and a s s i s t i n g i n the p u l l - u p . D u r i n g steady s t a t e , when Q i s low, T1 i s p r o v i d i n g a DC c u r r e n t i n o r d e r t o s t a r t t h e p u l l - u p a c t i o n . T2 i s o f f s i n c e node f i s h i g h . Node Q r i s e s (SCVS t r e e open), s l o w l y a t f i r s t , u n t i l t h e ou t p u t of 11 goes low and t u r n s on T2. In d e s i g n i n g SCVS t r e e s , i t i s advantageous t o l o o k a t bo t h the t r u e and the complement form of the f u n c t i o n ; g e n e r a l l y , one form w i l l be e a s i e r t o implement. The form t h a t c o n t a i n s fewer l e v e l s of s t a c k i n g can be powered w i t h a h i g h e r c u r r e n t s o u r c e f o r t h e same l o g i c low l e v e l and w i l l r e s u l t i n a f a s t e r c i r c u i t . The d e s i r e d o u t p u t can be tak e n s i m p l y from the o t h e r b u f f e r . Note t h a t a l l t h e s t a t i c SCVS c i r c u i t d e s i g n s have a d i r e c t c u r r e n t t o ground, a l t h o u g h t h i s would not be v e r y i m p o r t a n t f o r h i g h f r e q u e n c y o p e r a t i o n . I f c i r c u i t s consuming no s t a t i c power a r e r e q u i r e d , CMOS DCVS d e s i g n i s t h e s o l u t i o n . 53 S t a t i c DCVS c i r c u i t s a r e commonly implemented i n e i t h e r NMOS or CMOS t e c h n o l o g y as shown i n F i g . 3 . 4 ( a ) and (b) r e s p e c t i v e l y . L e t us c o n s i d e r o n l y the d i f f e r e n t i a l CMOS l o g i c f a m i l y ( F i g . 3 . 4 ( b ) ) . Depending on the d i f f e r e n t i a l i n p u t s , e i t h e r node Q or Q' i s p u l l e d down by t h e DCVS t r e e network. R e g e n e r a t i v e a c t i o n s e t s t h e PMOS l a t c h t o s t a t i c o u t p u t s Q, Q1 of Vdd and ground. The l o g i c t r e e s a r e f r e e of d i r e c t c u r r e n t a f t e r t h e l a t c h s e t s . T h i s form of c i r c u i t has t h r e e advantages over c o n v e n t i o n a l s t a t i c CMOS c i r c u i t s w i t h s t a c k e d N-MOS and P-MOS d e v i c e s . F i r s t , t h e use of u n s t a c k e d P - t r a n s i s t o r s as p u l l - u p d e v i c e s i n l o a d and b u f f e r c i r c u i t r y r e s u l t s i n s h o r t e r r i s e t i m e s . Second, the a r e a r e q u i r e d can be two or t h r e e t i m e s s m a l l e r t h a n t h a t of the f u l l CMOS c i r c u i t . T h i r d , i n p u t gate c a p a c i t a n c e l o a d i n g i s t y p i c a l l y a f a c t o r of two or t h r e e t i m e s s m a l l e r than CMOS c i r c u i t s t h a t r e q u i r e complementary N-channel and P-channel d e v i c e s t o be d r i v e n , s i n c e t h e i n p u t s d r i v e o n l y the NMOS t r e e d e v i c e s . 3.1.2 D i f f e r e n t i a l S p l i t - L e v e l CMOS L o g i c Because of t h e h i g h s t a c k of N - d e v i c e s and l a r g e p a r a s i t i c c a p a c i t a n c e of the t r e e network, a few t e c h n i q u e s have been pr o p o s e d t o reduce the o u t p u t d e l a y t ime [ 1 4 ] , [ 1 5 ] . However, none of t h e s e has b e t t e r performance t h a n the D i f f e r e n t i a l S p l i t - L e v e l (DSL) CMOS L o g i c c i r c u i t t e c h n i q u e [ 1 6 ] . The DSL F i g . 3 . 4 ( b ) A s t a t i c DCVS c i r c u i t i n CMOS 55 c i r c u i t i s shown i n F i g . 3 . 5 . In t h i s t e c h n i q u e t h e l o g i c t r e e i s t h e same as i n DCVS, but t h e l o a d i s d i f f e r e n t . Two N - t r a n s i s t o r s T3 and T4 w i t h t h e i r g a t e s c o n n e c t e d t o a r e f e r e n c e v o l t a g e (VREF) a r e added t o reduce th e l o g i c swing a t nodes Q and Q', see F i g . 3 . 5 . I f VREF i s s e t t o Vdd/2 + V t h , where V t h i s the t h r e s h o l d v o l t a g e of the N - d e v i c e , then the nodes Q and Q' a r e clamped a t Vdd/2. Speed improvement has been a c h i e v e d by a s m a l l e r l o g i c swing on the i n t e r c o n n e c t i o n l i n e between the t r e e and the l o a d c i r c u i t r y , and the i n t e r n a l nodes of t h e t r e e i t s e l f . Suppose node Q i s p u l l e d down from 2.5V t o a low l e v e l , T1 s w i t c h e s from i t s low c u r r e n t t o i t s h i g h c u r r e n t d r i v e s t a t e v e r y f a s t , because T4 i s i n i t i a l l y o f f . The v o l t a g e on node f goes up t o 5V because T1 i s f u l l y on. Node Q' i s r a i s e d up t o 2.5V u n t i l T3 i s i n c u t o f f mode. Two problems can be seen w i t h t h i s t e c h n i q u e . For example, i f node Q' i s a t 2.5V, then T2 i s p a r t i a l l y on and i t i s p o s s i b l e t o d e s t r o y the low l o g i c l e v e l t h a t would have appeared on node f . A l t h o u g h r e d u c t i o n of t h e s i z e of t h e P - d e v i c e a l l e v i a t e s t h i s problem, i t w i l l d e c r e a s e t h e o u t p u t d r i v e c a p a b i l i t y and r e s u l t i n l o n g e r d e l a y . Thus, a t r a d e o f f s h o u l d be c o n s i d e r e d when the s i z e s of T1 and T2 a r e chosen. Another p r o b l e m i s due t o t h e body e f f e c t e x i s t i n g i n T3 and T4. A l t h o u g h V t h i s e q u a l t o 0.8V i n t h e N o r t h e r n Telecom 3jim CMOS p r o c e s s , s i m u l a t i o n s show t h a t i t i s n e c e s s a r y t o s e t VREF e q u a l 56 F i g . 3 . 5 A g e n e r a l s t r u c t u r e of DSL c i r c u i t s 57 t o 4.2V i n o r d e r t o clamp e i t h e r of t h e nodes Q or Q1 t o 2.5V. A l s o the clamped l o g i c swing i s s e n s i t i v e t o the s t a c k l e v e l of the DCVS t r e e f o r a f i x e d VREF. DSL c i r c u i t s would be e x p e c t e d t o be about two t i m e s f a s t e r t han s t a n d a r d DCVS c i r c u i t s due t o t h e h a l f r a i l - t o - r a i l l o g i c s w i n g , which r e s u l t s i n a r e d u c t i o n by two times of t h e charges needed t o be m a n i p u l a t e d i n the c i r c u i t . S i m u l a t i o n s of a f u l l adder c i r c u i t , d i s c u s s e d i n S e c t i o n 3.3, i n d i c a t e t h a t the DSL v e r s i o n i s about t w i c e as f a s t as a DCVS v e r s i o n . I n o r d e r t o t a k e advantage of t h e reduced l o g i c swing a t node Q and Q' i n DSL c i r c u i t s , t he l o a d c i r c u i t r y of t h e p r e v i o u s s t a g e i s kept c l o s e t o the t r e e network of i t s f o l l o w i n g s t a g e , and l o n g i n t e r c o n n e c t l i n e s a r e drawn between t h e open d r a i n o u t p u t s and t h e i r a s s o c i a t e d l o a d c i r c u i t r y . F i g . 3 . 6 ( a ) and (b) compare the i n t e r c o n n e c t i o n method of DSL w i t h t h a t of s t a n d a r d DCVS c i r c u i t s . DSL c i r c u i t s may be found t o be u s e f u l i f a t w o - l e v e l m e t a l l i z a t i o n scheme i s a v a i l a b l e . 3.2 DYNAMIC CVS CIRCUIT TECHNIQUES 3.2.1 Domino CMOS L o g i c The b a s i c dynamic CVS c i r c u i t scheme ( F i g . 3 . 7 ) i n v o l v e s p r e c h a r g i n g t h e dynamic o u t p u t node ( o r nodes i n t h e case of 58 OPEN DRAIN OUTPUTS Vdtj/2 SWING IN THESE LONG INTERCONNECT LINES n \ \ i DSL ! UUO . J F i l l Vdd SMIN6 HERE F i g . 3 . 6 ( a ) The i n t e r c o n n e c t i o n method of DSL c i r c u i t s F i g . 3 . 6 ( b ) The i n t e r c o n n e c t i o n method of DCVS c i r c u i t s 59 CLOCK \ I SCVS TREE i F i g . 3 . 7 ( a ) A dynamic SCVS gate CLOCK F i g . 3 . 7 ( b ) A dynamic DCVS gate 60 DCVS) t o a h i g h l o g i c l e v e l , w h i l e the c u r r e n t p a t h t o the ground l e v e l i s t u r n e d o f f . Changing of i n p u t s t o the dynamic gate must o c c u r d u r i n g t h i s p r e c h a r g e phase. At the c o m p l e t i o n of p r e c h a r g e , the p a t h t o Vdd i s t u r n e d o f f by a c l o c k and the p a t h t o ground i s t u r n e d on. Then, depending on the s t a t e of the i n p u t s , the o u t p u t w i l l e i t h e r f l o a t a t the h i g h l e v e l or w i l l be p u l l e d down. There a r e s e r i o u s problems because u s e f u l c i r c u i t s g e n e r a l l y have s e v e r a l l o g i c g a t e s i n s e r i e s and, i n t h e dynamic ap p r o a c h , no g a t e can be a c t i v a t e d u n t i l i t s i n p u t s have s t a b i l i z e d . T h i s problem can be s o l v e d by a d d i n g more c l o c k phases t o s y n c h r o n i z e the g a t e s . However, a more p r a c t i c a l a p p roach i s t o use the domino c i r c u i t t e c h n i q u e . The i m p o r t a n t p r o p e r t y of a domino c i r c u i t i s t h a t t h e t r a n s i t i o n from p r e c h a r g e to. e v a l u a t i o n i s a c c o m p l i s h e d by means of a s i n g l e c l o c k edge a p p l i e d s i m u l t a n e o u s l y t o a l l g a t e s i n t h e c i r c u i t . T h i s g r e a t l y s i m p l i f i e s c l o c k i n g and p e r m i t s u t i l i z a t i o n of the f u l l i n h e r e n t speed of t h e g a t e s . An example of a SCVS domino gat e i s shown i n F i g . 3 . 8 . The dynamic o u t p u t Q goes t o t h e s t a t i c b u f f e r 11, and o n l y the b u f f e r ouput f i s f e d t o o t h e r g a t e s of the c i r c u i t . T2 i s a h i g h impedance P - t r a n s i s t o r which s e r v e s as the feedback d e v i c e t o r e s t o r e the h i g h l o g i c l e v e l a t node Q, where c h a r g e s may be l o s t due t o c h a r g e s h a r i n g [ 1 7 ] . An example of t h i s phenomenon f o l l o w s . 61 F i g . 3 . 8 A SCVS domino gat e w i t h a feedback d e v i c e T2 F i g . 3 . 9 A SCVS domino g a t e w i t h p r e c h a r g e d i n t e r n a l nodes 62 D u r i n g t h e p r e c h a r g e phase, node Q i s c h a r g e d v i a T1 and o u t p u t node f i s f o r c e d down. Whether i n t e r n a l nodes N1 and N2 a r e c h a r g e d or not depends on the i n p u t p a t t e r n of the p r e v i o u s e v a l u a t i o n phase. I f , f o r example, i n p u t A was z e r o , and one of the i n p u t s B t o D and E t o F was h i g h , no i n t e r n a l nodes, except node Q, would be c h a r g e d . T h i s c o n d i t i o n may l e a d t o a charge s h a r i n g problem i n t h e next c y c l e . I f d u r i n g t h e e v a l u a t i o n phase i n t h a t c y c l e , i n p u t A and any one of the i n p u t s B t o D goes h i g h , and i n p u t s E and F remain a t t h e low l e v e l , the c h a r ge a t node Q i s s h a r e d w i t h t h e uncharged nodes N1 and N2, t h u s c a u s i n g a v o l t a g e drop a t node Q. The l o s s i s r e c o v e r e d v i a a feedback d e v i c e T2, but d u r i n g t h a t time a g l i t c h o c c u r s a t t h e o u t p u t . T h i s g l i t c h can l e a d t o l o g i c f a i l u r e , i f i t s magnitude exceeds a c r i t i c a l v a l u e , namely, t h a t of the t h r e s h o l d v o l t a g e o f an N d e v i c e . T h e r e f o r e , the magnitude of t h e g l i t c h has t o be c o n t r o l l e d . T h i s can be done by l i m i t i n g t h e maximum number of d e v i c e s i n each t r e e , w h i c h , i n t u r n , can be d e t e r m i n e d by t h e w o r s t c a s e r a t i o of t h e sum of a l l i n t e r n a l node c a p a c i t a n c e s t o t h e c a p a c i t a n c e a t t h e b u f f e r g a t e . F o r l a r g e t r e e n e t w o r k s , a c i r c u i t change as shown i n F i g . 3 . 9 e l i m i n a t e s g l i t c h e s a l t o g e t h e r . Each i n t e r n a l node of a t r e e has t o be c o n n e c t e d t o Vdd t h r o u g h a N - d e v i c e which i s o n l y t u r n e d on d u r i n g t h e p r e c h a r g e phase. The o n l y e x c e p t i o n s a r e node Q w h i c h i s s t i l l p r e c h a r g e d t h r o u g h T l and t h e d r a i n node N3 of the c l o c k e d N - d e v i c e w h i c h i s d i s c h a r g e d t o ground i n each 6 3 c y c l e . T h i s c o n f i g u r a t i o n g u a r a n t e e s t h a t a l l i n t e r n a l nodes a r e p r e c h a r g e d t o Vdd-Vth, so t h a t t h e r e i s no charge s h a r i n g . The feedback d e v i c e T2 i n F i g . 3 . 8 i s thus no l o n g e r n e c e s s a r y . A l t h o u g h the two s t a b i l i z i n g methods have been demonstrated u s i n g SCVS domino c i r c u i t r y , t h ey a r e a l s o a p p l i c a b l e t o DCVS c i r c u i t r y . We f i n d t h a t g e n e r a l l y , f o r s m a l l CVS c i r c u i t s w i t h l e s s than 15 N - d e v i c e s , t h e f i r s t method wh i c h r e q u i r e s a s i n g l e feedback d e v i c e i s s u f f i c i e n t . The l i m i t a t i o n of SCVS domino g a t e s i s t h a t o n l y t h e t r u e o u t p u t i s a v a i l a b l e , and i t s complement cannot be o b t a i n e d because of the n o n - i n v e r s i o n p r o p e r t y of t h e domino l o g i c . The DCVS domino gate has been proposed as a way t o a l l e v i a t e the problem by p r o v i d i n g complementary o u t p u t s [ 1 4 ] . In some c a s e s , a DCVS t r e e network has s l i g h t l y l a r g e r d e v i c e count t h a n i t s SCVS c o u n t e r p a r t , e.g. o n l y two more N - d e v i c e s i n the case of a n-way e x c l u s i v e - o r g a t e (see S e c t i o n 2.1.2.1). However, i n the worst c a s e , t h e DCVS t r e e network of a l o g i c f u n c t i o n can be t w i c e as l a r g e as would r e s u l t i f t h e f u n c t i o n was implemented i n SCVS l o g i c t r e e s . One o b v i o u s example i s t h e NAND gate shown i n F i g . 3 . 1 0 . An a l t e r n a t i v e method of g e n e r a t i n g d i f f e r e n t i a l o u t p u t s u s i n g s i n g l e - e n d e d l o g i c t r e e s has been proposed i n a t e c h n i q u e c a l l e d l a t c h e d domino ( l d o m i n o ) l o g i c [ 1 8 ] . An ldomino g a t e i s shown i n F i g 3.11. The c r o s s - c o u p l e d d e v i c e s T1 and T2 form an Fig.3.10(b) A DCVS domino NAND gate 65 Fig.3.11 An l a t c h e d domino c i r c u i t 66 u n b a l a n c e d l a t c h / s e n s e a m p l i f i e r t o g e t h e r w i t h feedback d e v i c e s T3 and T4, which a l s o a c t as l o a d d e v i c e s . D u r i n g the e v a l u a t i o n phase (0 i s h i g h ) , i f node N2 i s not d i s c h a r g e d by the l o g i c t r e e , the l a t c h i s d e s i g n e d such t h a t node N1 i s always d i s c h a r g e d . However, i f t h e l o g i c t r e e d i s c h a r g e s node N2, i t overpowers the unbalanced l a t c h and node N1 s t i l l s t a y s a t the h i g h l e v e l . Note t h a t the i n p u t g a t e s of t h e SCVS t r e e s h o u l d s t a b i l i s e d u r i n g the p r e c h a r g e phase (0= 0), o t h e r w i s e a g l i t c h w i l l appear a t output Q', or even complete f a i l u r e may oc c u r due t o t h e a c c i d e n t a l d i s c h a r g e of node N1. Ldomino g a t e s can t h e r e f o r e d r i v e domino g a t e s , but cannot be d r i v e n d i r e c t l y by domino g a t e s . T h i s t e c h n i q u e can o n l y be a p p l i e d t o the f i r s t s t a g e of l o g i c i n a s e r i e s of domino g a t e s , i f t h e g l i t c h - f r e e p r o p e r t y of domino l o g i c i s t o be p r e s e r v e d . The l a t c h e d , SCVS and DCVS forms of domino l o g i c can be used t o g e t h e r i n a c i r c u i t t o enhance the l o g i c f l e x i b i l i t y and reduce t h e c i r c u i t a r e a w i t h r e s p e c t t o a c i r c u i t implemented u s i n g o n l y one of the approaches a l o n e , w h i l e r e t a i n i n g t h e speed advantage. A l s o , o p t i m i z a t i o n methods [19] of e l i m i n a t i n g domino l o g i c .redundancy a r e found t o be h e l p f u l f o r i n c o r p o r a t i n g the t h r e e t y p e s of domino c i r c u i t s i n t o a random l o g i c d e s i g n . An example c o n s t r u c t i o n f o r a g l i t c h - f r e e domino l o g i c b l o c k i s shown i n F i g . 3 . 1 2 . N o t i c e t h a t t h e l a t c h e d domino g a t e w i t h s i n g l e - e n d e d i n p u t s can o n l y be a t the f i r s t s t a g e of the l o g i c b l o c k . DCVS domino g a t e s a c c e p t d i f f e r e n t i a l i n p u t s 67 LATCH PBEOWSE EVALUATE U I f GLITCH-FREE DOMINO L06IC BLOCK 6 LATCH 1_F i H t LATCHED Oi REHSTER j i LATCHED 6' H' ^ DCVS "T^joCVS SCVS n SCVS SCVS K K' REIISTER; F i g . 3 . 1 2 An example c o n s t r u c t i o n f o r a g l i t c h - f r e e domino l o g i c b l o c k 68 o n l y , w h i l e SCVS g a t e s can have d i f f e r e n t i a l or s i n g l e - e n d e d i n p u t s or b o t h . 3.2.2 NORA CMOS L o g i c NORA (NO RAce) CMOS t e c h n i q u e s [20] a r e s u i t a b l e f o r impl e m e n t i n g p i p e l i n e d l o g i c s t r u c t u r e s . In i t s o r i g i n a l form the s t r u c t u r e c o n s i s t s of n- and p - l o g i c g a t e s t o enhance l o g i c f l e x i b i l i t y . The p - l o g i c g a t e s u s u a l l y cause l o n g d e l a y t i m e s and consume l a r g e a r e a s . U s i n g CVS c i r c u i t s i n t h e NORA t e c h n i q u e w i l l e l i m i n a t e p - l o g i c g a t e s because of the a v a i l i a b i l i t y of i n v e r s i o n s i g n a l s . A CVS p i p e l i n e d s e c t i o n i s al m o s t t h e same as t h e domino CVS l o g i c b l o c k d e s c r i b e d i n F i g . 3 . 1 2 , but w i t h o u t p u t b u f f e r s i n the dynamic g a t e s of t h e l a s t s t a g e r e p l a c e d by C l o c k e d CMOS (CCMOS) r e g i s t e r s ( F i g . 3 . 1 3 ) . The r a c e - f r e e p r o p e r t i e s of NORA p i p e l i n e d s e c t i o n s r e q u i r e t h a t t h e l a t c h e d i n f o r m a t i o n s h o u l d not be a l t e r e d by the p r e c h a r g e s i g n a l s or by i n p u t v a r i a t i o n s . Futhermore, i t can be shown t h a t , a f t e r t he e v a l u a t i o n phase, a p r o p e r l y - d e s i g n e d NORA p i p e l i n e d - s e c t i o n keeps i t s o u t p u t r e s u l t s i n s p i t e of h i g h - h i g h o r low-low c l o c k o v e r l a p s ( c l o c k skew) [ 2 0 ] , T h i s p r o p e r t y i s d e s i r a b l e because the c o n t r o l of c l o c k skew i s e x t r e m e l y d i f f i c u l t , e s p e c i a l l y f o r h i g h speed c i r c u i t s w i t h unmatched 69 ^ FEEDBACK TRANSISTOR FROM OOMINO GATES CCMOS RE6ISTER F i g . 3 . 1 3 ( b ) The l a s t s t a g e of a CVS p i p e l i n e d s e c t i o n 70 c l o c k l o a d s o r a d i s t r i b u t e d c l o c k . Depending on t h e t y p e s of c i r c u i t t h a t precede t h e CCMOS r e g i s t e r , t h e f o u r - t r a n s i s t o r CCMOS c i r c u i t may be reduced t o a t h r e e - t r a n s i s t o r c i r c u i t . When th e r e g i s t e r i s preceded by N-type dynamic l o g i c (such as a CVS l o g i c b l o c k ) , the v e r s i o n shown i n F i g . 3 . 1 4 ( a ) i s used. The v e r s i o n shown i n F i g . 3 . 1 4 ( b ) i s used when preceded by P-type dynamic l o g i c . The advantage of the Reduced C l o c k e d CMOS (RCCMOS) over CCMOS r e g i s t e r s i s t h e s i g n i f i c a n t i n c r e a s e i n conductance of the c r i t i c a l d e l a y p a t h . The two t r a n s i s t o r s i n s e r i e s t h a t t u r n on when t h e p r e c h a r g e d s t a t e changes t o a n o t h e r s t a t e a r e reduced t o one t r a n s i s t o r . The d i s a d v a n t a g e of RCCMOS i s t h a t now t h e r e i s an a d d i t i o n a l c o n s t r a i n t on the c l o c k skew, as i s d i s c u s s e d l a t e r . F o r a h e a v i l y p i p e l i n e d s t r u c t u r e , speed c o n s i d e r a t i o n s may a l l o w o n l y one dynamic g a t e t o be p r e s e n t i n a p i p e l i n e d s e c t i o n . I n o r d e r t o e v a l u a t e a complex f u n c t i o n w i t h i n one dynamic g a t e d e l a y , t h e l o g i c power of CVS c i r c u i t s s h o u l d be e x p l o i t e d . 0 - s e c t i o n s c o n t a i n i n g a SCVS and a DCVS gate a r e shown i n F i g s . 3 . 1 5 ( a ) and (b) r e s p e c t i v e l y . By i n t e r c h a n g i n g t h e c l o c k p h a s e s , i . e . , c h a n g i n g 0 t o 0' i n p u t s , a 0' - s e c t i o n i s o b t a i n e d . I n t h e f o l l o w i n g d i s c u s s i o n , o n l y t h e SCVS p i p e l i n e d s t a g e shown i n F i g . 3 . 1 5 ( a ) i s c o n s i d e r e d . The arguments s t i l l a p p l y t o t h e DCVS s t a g e . D u r i n g t h e e v a l u a t i o n phase (0=1), node N1 i s e i t h e r f l o a t i n g o r d i s c h a r g e d depending on t h e i n p u t s . The 71 Fig.3.15(a) A NORA 0 - s e c t i o n Fig.3.15(b) A NORA 0-section w i t h a SCVS t r e e w i t h a DCVS t r e e 72 RCCMOS r e g i s t e r i s a c t i n g as a c l o c k e d i n v e r t e r , and the output can be e i t h e r h i g h or low. D u r i n g the pr e c h a r g e phase (0=0), the ground p a t h of the r e g i s t e r i s b l o c k e d . I f the o u t p u t r e s u l t i n g from the p r e v i o u s e v a l u a t i o n i s h i g h , then the o u t p u t c o n t i n u e s t o be h i g h . I f the o u t p u t i s low ( i . e . , node N1 has never been d i s c h a r g e d ) and T1 i s on, then the ou t p u t c o n t i n u e s t o be low because no ch a r g e s can be added t h r o u g h T2. Thus f o r a 0 - s e c t i o n , the output changes f r e e l y when 0 i s h i g h and i s l a t c h e d a t t h e f a l l i n g edge of 0. Now we examine t h e c o n s t r a i n t on the c l o c k skew. F i g . 3 . 1 6 shows a 0' - s e c t i o n c a s c a d e d t o a 0 - s e c t i o n , w i t h the r e l e v a n t c l o c k i n g d i a g r a m . The o v e r l a p c o n s t r a i n t a r i s e s from the case when 0 i s h i g h and t h e ou t p u t of the f i r s t s t a g e changes from low t o h i g h but 0' i s not y e t low. The i n p u t t r a n s i s t o r of the second s t a g e t u r n s on t o o e a r l y , and the dynamic o u t p u t might a c c i d e n t a l l y d i s c h a r g e because 0' i s h i g h . Thus, the o v e r l a p between h i g h 0 and h i g h 0' must be l e s s than the time e q u i v a l e n t t o a dynamic gate d e l a y ( t y p i c a l l y a few nanoseconds). N o t i c e t h a t t h i s c o n s t r a i n t i s independent of the c l o c k f r e q u e n c y . I n some s i t u a t i o n s , a p i p e l i n e d s t a g e t h a t p r o v i d e s a d i f f e r e n t i a l o u t p u t but r e q u i r e s s i n g l e - e n d e d i n p u t s may be needed. Such a c i r c u i t ( 0 - s e c t i o n ) i s shown i n F i g . 3 . 1 7 . I f the SCVS t r e e i s open d u r i n g t h e e v a l u a t i o n phase (0=1), then nodes N1 and Q a r e h i g h and nodes N2 and Q' a r e low. O t h e r w i s e i f node 73 i i , ! EVALUATION ! \ ™ i Vi STAGE #i f EVALUATION | OVERLAP ° FOR i TINE STAGE #i+l ' CONTRAINT F i g . 3 . 1 6 The t i m i n g d i a g r a m f o r a 0 ' - s e c t i o n c a s c a d e d t o a 0 - s e c t i o n 74 F i g . 3 . 1 7 A p i p e l i n e d s t a g e which p r o v i d e s d i f f e r e n t i a l o u t p u t from s i n g l e - e n d e d i n p u t s 75 N1 i s d i s c h a r g e d , then nodes N2 and Q' change t o h i g h and node Q changes t o low. D u r i n g the p r e c h a r g e phase (0=0, 0'=1), the d i s c h a r g i n g p a t h of the N-type RCCMOS r e g i s t e r i s b l o c k e d . I f node N1 i s d i s c h a r g e d a t the p r e c e d i n g e v a l u a t i o n phase, then nodes Q' and Q remain a t h i g h and low l e v e l s r e s p e c t i v e l y . However i f node N1 i s not d i s c h a r g e d a t the p r e v i o u s e v a l u a t i o n phase, t r a n s i s t o r s T1 and T2 w i l l remain o f f . Thus, we have shown t h a t o u t p u t i n f o r m a t i o n i s c o r r e c t l y l a t c h e d d u r i n g the p r e c h a r g e phase. Now we t u r n our a t t e n t i o n a t t h e c l o c k skew c o n s t r a i n t of t h i s c i r c u i t . The case when ou t p u t Q' i s c o n n e c t e d t o the next 0' - s e c t i o n i s s i m i l a r t o t h e p r e v i o u s a n a l y s i s f o r the SCVS c i r c u i t shown i n F i g . 3 . 1 6 . The c o n s t r a i n t t h a t the c l o c k o v e r l a p s h o u l d be l e s s than a dynamic ga t e d e l a y s t i l l h o l d s . However, we s h o u l d f u r t h e r a n a l y s e t h e c l o c k c o n s t r a i n t on the o t h e r o u t p u t p a t h t h r o u g h node Q ( F i g . 3 . 1 8 ) . The danger a r i s e s when 0 changes from h i g h t o low and 0' i s not h i g h y e t . Nodes N1 and N2 a r e p r e c h a r g e d t o h i g h and low r e s p e c t i v e l y . The c h a r g i n g p a t h of the o u t p u t r e g i s t e r of the f i r s t s t a g e b e i n g m o m e n t a r i l y t u r n e d on may cause e r r o n e o u s c h a r g i n g of o u t p u t node Q, i f the o v e r l a p time between low 0 and low 0 ' i s more than an i n v e r t e r ( I I ) d e l a y . T h i s c o n s t r a i n t i s a l s o independent of the c l o c k f r e q u e n c y . To remove t h i s c o n s t r a i n t , we s u p p l y 0' u s i n g the 0 - c l o c k t h r o u g h an i n v e r t e r w i t h i n a 0 - s e c t i o n . 76 ' o / L 1 • t 0 I I I OVERLAP I TIME CONTRAINT F i g . 3 . 1 8 A t i m i n g c o n s t r a i n t a d d i t i o n a l t o F i g . 3 . 1 6 i f t h e p i p e l i n e d s t a g e i n F i g . 3 . 1 7 i s used 77 3.3 PERFORMANCE COMPARISONS OF CMOS FULL ADDERS Having d i s c u s s e d g e n e r a l i s s u e s i n the i m p l e m e n t a t i o n of v a r i o u s CVS c i r c u i t t e c h n i q u e s , i t i s i m p o r t a n t t o compare the performance of t h e s e c i r c u i t s w i t h t h e more c o n v e n t i o n a l c i r c u i t s . The e v a l u a t i o n p r e s e n t e d here i s based on SPICE s i m u l a t i o n s w i t h the para m e t e r s of t h e N o r t h e r n Telecom 3nm CMOS p r o c e s s ( d e s c r i b e d i n S e c t i o n s 4.3 and 4.4). S i n c e the f u l l adder i s t h e most common b u i l d i n g b l o c k i n d i g i t a l hardware, we use i t as a v e h i c l e f o r our comparison purpose. The f u l l a d ders s i m u l a t e d i n c l u d e t h o s e implemented by s t a t i c c i r c u i t t e c h n i q u e s , namely, f u l l CMOS, DCVS and DSL, and dynamic c i r c u i t t e c h n i q u e s , namely, NORA, m o d i f i e d NORA and DCVS NORA. The r e s u l t s a r e summarized i n T a b l e 3.1. Some of t h e SPICE i n p u t l i s t i n g s and o u t p u t s a r e g i v e n i n Appendix A. A c i r c u i t f o r t h e s t a t i c f u l l CMOS adder i s shown i n F i g . 3 . 1 9 . Two s u b c i r c u i t s a r e i d e n t i f i e d , one t o g e n e r a t e the sum s i g n a l and one t o g e n e r a t e t h e c a r r y out s i g n a l . The 3-way e x c l u s i v e - o r gate i n t h e SUM c i r c u i t has the h i g h e s t s t a c k l e v e l and l a r g e s t p a r a s i t i c c a p a c i t a n c e , and th u s d e t e r m i n e s the worst case d e l a y time of t h e ad d e r . T h i s c i r c u i t i s r e l a t i v e l y f a s t compared w i t h o t h e r p o s s i b l e s t a t i c f u l l CMOS i m p l e m e n t a t i o n s because t h e complemented o u t p u t s a r e o b t a i n e d t h r o u g h o n l y one ga t e d e l a y from the complementary i n p u t s . The f u l l CMOS adder i s X ^ P R O P E R T Y C I R C U 1 T X T E C H N I O U E \ I N P U T G R T E C R P R C 1 T R N C E ( F F ) O U T P U T L O R D C R P R C I T R N C E ( F F ) ft OF P- y DEV1CE5 / / 1 OF N-/ DEVICES U D R 5 T C R S E D E L A Y T I M E ( n s > S T A T I C F U L L C M O S 155 50 15/15 19 S T A T I C D C V S 85 50 4/15 20 S T A T I C D S L 85 60 4/19 13 N O R A 110 150 12/10 15 M O D I F I E D N O R A 45 150 8/20 12 D C V S N O R A 85 150 12/26 9 D C V S D O M I N O 85 150 12/22 8 T a b l e 3.1 Comparison o f s i m u l a t i o n r e s u l t s f o r d i f f e r e n t t y p e s of f u l l a d ders 79 Fig.3.19 A s t a t i c CMOS f u l l adder 80 found t o have the same d e l a y as the s t a t i c DCVS ( F i g . 3 . 4 ( b ) ) adder, but t o have a l a r g e r (*2 t i m e s ) i n p u t gate c a p a c i t a n c e and t o need more d e v i c e s . The DSL ( F i g . 3 . 5 ) adder which has almo s t the same i n p u t g a t e c a p a c i t a n c e and c i r c u i t a r e a as the DCVS adder o f f e r s a 35% i n c r e a s e i n performance. A p p a r e n t l y , the f u l l adder implemented i n DSL i s t h e f a s t e s t amongst t h e v a r i o u s k i n d s of CMOS s t a t i c a d d e r s . The c o n v e n t i o n a l NORA adder w i t h s e r i a l n- and p - l o g i c b l o c k s i s shown i n F i g . 3 . 2 0 . T h i s c i r c u i t i s c h a r a c t e r i z e d by a l a r g e i n p u t g a t e c a p a c i t a n c e because of the wide t r a n s i s t o r s i n the p - l o g i c b l o c k , and a slow speed due t o the use of two l e v e l s of g a t e d e l a y and because h a l f of the l o g i c i s performed by p - t r a n s i s t o r s . A m o d i f i e d NORA adder [22] shown i n Fig.3.21 c o n t a i n s a v e r y s p e c i a l 3-way XOR gate t o g e n e r a t e the sum s i g n a l . T h i s c i r c u i t has two t i m e s s m a l l e r i n p u t gate c a p a c i t a n c e and i s 20% f a s t e r t h a n the s e r i a l NORA ad d e r . The d i s a d v a n t a g e i s t h a t a c c i d e n t i a l d i s c h a r g e due t o r a c e s i s p o s s i b l e under c e r t a i n c o n d i t i o n s . F o r example, i f A=0, B=1 and C=1, t h e gate of T14 (or s o u r c e of T15) and t h e gate of T15 ( o r sour c e of T14) a r e p u l l e d down. I f the d r a i n nodes of T7 and T10 do not p u l l down a t s i m i l a r r a t e s so t h a t a v o l t a g e d i f f e r e n c e of more than a t h r e s h o l d i s d e v e l o p e d a c r o s s the g a t e nodes of T14 and T15, the d r a i n node of T13 d i s c h a r g e s a c c i d e n t a l l y . T h i s r e q u i r e s a Fig.3.20 A c o n v e n t i o n a l NORA f u l l adder M L * Fig.3.21 A m o d i f i e d NORA f u l l adder 83 c a r e f u l s i z i n g of the t r a n s i s t o r s a l o n g the d i s c h a r g i n g paths so t h a t t h e conductance t o ground and the c a p a c i t i v e l o a d a s s o c i a t e d w i t h each of the p u l l , down pa t h s i s e q u a l . A t i g h t p r o c e s s c o n t r o l and d e t a i l e d s i m u l a t i o n t h r o u g h c i r c u i t e x t r a c t i o n a r e needed i f t h i s c i r c u i t i s t o be s u c c e s s f u l l y implemented. The DCVS NORA ( F i g . 3 . 1 5 ( b ) ) adder has s m a l l e r i n p u t gate c a p a c i t a n c e and d e l a y time than t h e c o n v e n t i o n a l NORA adder, a l t h o u g h the a r e a consumed i s l a r g e r . T h i s c i r c u i t i s a l s o b e t t e r , compared t o the m o d i f i e d NORA, i n terms of c i r c u i t f l e x i b i l i t y due t o the complementary o u t p u t s , and r e l i a b i l i t y as a c c i d e n t a l d i s c h a r g e cannot o c c u r . The DCVS domino ( F i g . 3 . 1 0 ( b ) ) adder i s s i m i l a r t o the DCVS NORA adder i n eve r y a s p e c t . I t i s the o n l y k i n d of f u l l adder c i r c u i t which can be i n c l u d e d i n a domino c h a i n w i t h o u t c a u s i n g r a c e p roblems. 84 CHAPTER 4 : A HIGH SPEED CVS PIPELINED MULTIPLIER DESIGN 4.1 ALGORITHM AND ARCHITECTURE Both GaAs MESFET and S i b i p o l a r t e c h n o l o g i e s a r e b e i n g used c u r r e n t l y t o r e a l i z e e x t r e m e l y f a s t l o g i c c i r c u i t s such as m u l t i p l i e r s [ 2 3 ] , [ 2 4 ] . However, the f e a s i b i l i t y of CMOS c i r c u i t d e s i g n i n hi g h - p e r f o r m a n c e I Cs s t i l l has t o be demonstrated. In some a p p l i c a t i o n s , f o r example r e a l - t i m e d i g i t a l s i g n a l p r o c e s s i n g or image p r o c e s s i n g , where l a t e n c y i s not c r i t i c a l but a h i g h throughput r a t e i s r e q u i r e d , p i p e l i n e d l o g i c s t r u c t u r e s i n CMOS a r e v e r y u s e f u l . The CMOS t e c h n o l o g y i s a t t r a c t i v e because of i t s lower power d i s s i p a t i o n and h i g h e r l e v e l of i n t e g r a t i o n compared w i t h o t h e r t e c h n o l o g i e s . Bandwidth and l a t e n c y a r e two f i g u r e s of m e r i t f r e q u e n t l y used t o d e t e r m i n e the computing power of a machine. Bandwidth ( o r , t h r o u g h p u t r a t e ) i s t h e number of t a s k s t h a t can be exe c u t e d i n a u n i t time i n t e r v a l . L a t e n c y i s t he l e n g t h of time r e q u i r e d t o p e r f o r m a s i n g l e t a s k . A p i p e l i n e d a r i t h m e t i c u n i t i s b r o a d l y d e f i n e d as a c o l l e c t i o n of hardware r e s o u r c e s c a l l e d segments o r s e c t i o n s , which a r e o r g a n i z e d as a l i n e a r assembly l i n e o r p i p e l i n e w i t h s y n c h r o n i z e d t i m i n g c o n t r o l , such t h a t a f l o w of s u b d i v i d e d t a s k s can be s i m u l t a n e o u s l y e x e c u t e d by the s u c c e s s i v e s e c t i o n s of the p i p e l i n e . 85 To d e s i g n an 8 - b i t p i p e l i n e d m u l t i p l i e r , t he b a s i c NORA b u i l d i n g b l o c k s shown i n F i g . 3 . 1 5 and 3.17 were used. We s u b d i v i d e the m u l t i p l i e r i n t o k s e c t i o n s , and each s e c t i o n has the maximum l a t e n c y e q u a l t o T . I t i s c o n s t r u c t e d by a l t e r n a t i n g 0 and 0' - s e c t i o n s as i l l u s t r a t e d i n F i g . 4 . 1 . F o r phase 0=1 0'=O, the 0 - s e c t i o n s a r e i n the e v a l u a t i o n phase w h i l e the 0 ' - s e c t i o n s a r e p r e c h a r g e d . The 0 ' - s e c t i o n o u t p u t s a r e h e l d c o n s t a n t by the RCCMOS r e g i s t e r s . Then, f o r phase 0=0 0'=1, the 0 ' - s e c t i o n s a r e i n t h e e v a l u a t i o n phase and t h e 0 - s e c t i o n s a r e p r e c h a r g e d . Now t h e 0 ' - s e c t i o n o u t p u t s , e v a l u a t e d i n the p r e v i o u s phase, a r e h e l d c o n s t a n t i n such a way t h a t the 0 ' - s e c t i o n s can use t h e i n f o r m a t i o n t o compute the c o r r e s p o n d i n g r e s u l t s . I n t h i s way, t h e r e i s a complete f l o w of i n f o r m a t i o n s t t h from t h e 1 s t a g e t o t h e k s t a g e a f t e r a d u r a t i o n of k * r . The thr o u g h p u t r a t e of t h e p i p e l i n e i s t h e i n v e r s e of the maximum l a t e n c y T per s e c t i o n , not of the l a t e n c y o r d u r a t i o n k*r of the e n t i r e p i p e l i n e . T h e r e f o r e , the i n c r e a s e i n the p i p e l i n e l e n g t h (number of s e c t i o n s ) does not a f f e c t t h e throughput r a t e . A number of a l g o r i t h m s have been d e v e l o p e d f o r p a r a l l e l m u l t i p l i e r s . C e l l u l a r a r r a y m u l t i p l i e r s [25] such as P e z a r i s ' , T r i - s e c t i o n , B i - s e c t i o n and the Baugh-Wooley scheme a r e advantageous because they use o n l y a few t y p e s of f u l l adder c e l l s and p o s s e s s r e g u l a r i t y i n s t r u c t u r e . However, they g e n e r a l l y r e q u i r e l a r g e amounts of hardware and become p r o h i b i t i v e when t h e operands a r e more than 16 b i t s . The Dadda STAGE #1 STAGE #2 STAGE IK INPUTS AL f -SECTION I*'-SECTION r -SECTION o o f -SECTION fcV*UMTIO* ^-SECTION PRECHMK) jf-SECTION mEVOK) • • 1 / j -SECTION FOR QOO K] o OUTPUTS 1 j -SECTION PRECHMK) •'-SECTION C V M J M T I M TINE F i g . 4 . 1 The NORA p i p e l i n e scheme and i t s t i m i n g 87 scheme and the W a l l a c e t r e e [26] can a t t a i n a t h e o r e t i c a l 0 ( l o g N) d e l a y (N i s the number of b i t s ) ; however, t h e s e t r e e schemes a r e r a r e l y used i n m o n o l i t h i c m u l t i p l i e r s , because the speedup they can g i v e f o r s m a l l N i s not c o n s i d e r e d t o be s i g n i f i c a n t enough t o j u s t i f y t h e more d i f f i c u l t i n t e r c o n n e c t i o n s and t h e i r r e g u l a r i t y of the s t r u c t u r e . Other newly proposed s t r u c t u r e s i n c l u d e Luk's m u l t i p l i e r [27] and a p i p e l i n e d Dadda m u l t i p l i e r [ 2 8 ] . The a l g o r i t h m t h a t has been chosen f o r our 8 - b i t p i p e l i n e d m u l t i p l i e r i s the M o d i f i e d (or Q u a t e r n a r y ) Booth's a l g o r i t h m [ 2 9 ] . T r a d i t i o n a l l y , m u l t i p l i c a t i o n of two n - b i t b i n a r y numbers c o n s i s t s of g e n e r a t i n g n p a r t i a l p r o d u c t s and a d d i n g p a r t i a l p r o d u c t s t o t h e s h i f t e d sum of a l l p r e v i o u s r e s u l t s . T h i s t e c h n i q u e i n c r e a s e s speed by r e d u c i n g the number of p a r t i a l p r o d u c t s by a f a c t o r of two; t h i s reduces the number of c a r r y save a r r a y (CSA) s t a g e s , and of c o u r s e , the hardware r e q u i r e d and t h e m u l t i p l i c a t i o n t i m e . A b r i e f summary of t h e q u a t e r n a r y Booth's a l g o r i t h m [29] i s g i v e n below, w i t h o u t t h e d e t a i l e d p r o o f [ 3 0 ] . L e t the n - b i t 2's complement m u l t i p l i c a n d and m u l t i p l i e r be e q u a l t o A = a a ... a a , n-1 n-2 1 0 and B= b b ... b b n-1 n-2 1 0 r e s p e c t i v e l y . From the b i t s of m u l t i p l i e r B, we o b t a i n the 88 Booth's recoded d i g i t w . = b . + . -2* b„. , 3 2 3-1 2 D 2:+1 where j=0,1,2... (n-2)/2 and b =0. Note t h a t the v a l u e of w. i s e i t h e r 0, ±1 or ±2. Each p a r t i a l p r o d u c t i s formed from w_. t i m e s the m u l t i p l i c a n d A s h i f t e d l e f t 2*j b i t s . More f o r m a l l y , the p r o d u c t i s g i v e n by p - z ( . n : 2 , / V *A* 2 2 j . 3 = 0 3 T h i s a l g o r i t h m s h o u l d e f f i c i e n t l y p r o c e s s operands w i t h up t o 16 b i t s . When operands w i t h more than 16 b i t s a r e c o n c e r n e d , an o c t a l or even h i g h e r o r d e r v e r s i o n of Booth's a l g o r i t h m may be used. An o c t a l Booth's a l g o r i t h m r e q u i r e s p a r t i a l p r o d u c t s t h a t a r e 0, ±1, ±2, ±3, ±4, t i m e s the m u l t i p l i c a n d . The m u l t i p l i c a t i o n t i m e s t h r e e poses problems. A l t h o u g h e x t r a hardware and time a r e needed t o p r e c a l c u l a t e t h i s m u l t i p l i c a t i o n t i m e s t h r e e , t h e o v e r a l l speed advantage and a r e a s a v i n g a r e s i g n i f i c a n t [ 3 1 ] . F o r t h e q u a t e r n a r y Booth's a l g o r i t h m , the m u l t i p l i c a t i o n t i m e s ±1, ±2 can be r e s o l v e d i n t o two b a s i c o p e r a t i o n s complementing and s h i f t i n g the m u l t i p l i c a n d b i t s . A l l the p a r t i a l p r o d u c t s can be g e n e r a t e d by a s t r u c t u r e where o n l y m u l t i p l e x i n g e l e m e n t s and an add o p e r a t i o n a t t h e l e a s t s i g n i f i c a n t b i t a r e r e q u i r e d . For an 8 - b i t m u l t i p l i e r . T a b l e 4.1 shows the r e l a t i o n s h i p between t h e m u l t i p l i c a n d A= a^ a^ ... a^ and a p a r t i a l p r o d u c t PP^ = pp;? pp^ ... pp;? . A p p a r e n t l y , we 8 7 0 s h o u l d p e r f o r m an e x t r a a d d i t i o n t o t a k e i n t o a c c o u n t the adder RE COOED SIGNED TO. REPRESENTATION OF wj PARTIAL PRODUCT PPJ addj DIGIT M J PPe PPJ? PPe ppi PPJ2 PPJ 0 000 0 0 0 0 0 0 0 0 0 0 + 1 001 Q7 9 7 9 6 9 5 94 9 3 9 2 9 0 0 -1 101 i 9 7 r 8 ? 1 9 6 i 9 5 94 i 9 5 8 2 9 i 1 9 0 1 +2 010 e ? 9 6 9 5 9 4 9 3 9 2 8 1 9 8 0 0 -2 110 i Q ? 9 6 > 8 5 > 9 4 > 8 3 j 8 i 8 B 1 1 T a b l e 4.1 A t r u t h t a b l e of the m u l t i p l e x e r a r r a y 90 o p e r a t i o n on the LSB b i t . However, i t i s p o s s i b l e t o d e l a y t h i s o p e r a t i o n by s i m p l y u s i n g a common c a r r y save t e c h n i q u e and a c a r r y l o o k - a h e a d (CLA) a t t h e bottom of the a r r a y . I n o r d e r t o g e n e r a t e the c o r r e c t 2's complement p r o d u c t , the n i n t h b i t of each p a r t i a l p r o d u c t , i . e . , t h e s i g n b i t pp^ , 8 ought t o e x t e n d a l l t h e way t o t h e l e f t . There a r e two p o s s i b l e a pproaches t o s o l v e t h e problem of s i g n e x t e n s i o n . The f i r s t a p p roach i s c a l l e d the " s i g n p r o p a g a t e " method, which r e q u i r e s some complex decoding l o g i c t o implement. We choose the second approach c a l l e d the " s i g n g e n e r a t e " method [ 3 2 ] . The s i g n b i t of the r e s u l t can be w r i t t e n as 0 * 5 „i 1 15 i S = p p o * I . _ 2 + p p o * £. m n 2 8 i=8 8 1=10 2 ^ 15 i 3 ^ 15 i y V 8 1=12 P P 8 i=14 I t can be p r o v e d t h a t 0 ^ 8 1 10 2 , 12 3 ^ 14 S = - P P 8 * 2 + - p p 8 * 2 + - p p 8 * 2 + - p p 8 * 2 9 11 13 ^15 ^8 + 2 + 2 + 2 + 2 + 2 where - PPg =1" PPg The above e q u a t i o n can be i n t e r p r e t e d a s : 1. Complement the n i n t h b i t ( pp^ ) of each p a r t i a l p r o d u c t . 8 2. Add 1 t o the l e f t of t h e s i g n b i t of each p a r t i a l p r o d u c t . 3. Add 1 t o the n i n t h b i t of t h e f i n a l p r o d u c t . 91 The a r c h i t e c t u r a l scheme of an 8 - b i t m u l t i p l i e r i s shown i n F i g . 4 . 2 . The r e c o d e r b l o c k examines each t h r e e - b i t group of B's and g e n e r a t e s the a p p r o p r i a t e w_. 's s i m u l t a n e o u s l y . The recoded d i g i t W j i s r e p r e s e n t e d as a s i g n e d magnitude s t r i n g ( sub^ , 2X. , 1X. ), which c o n s t i t u t e s the a c t u a l c o n t r o l s i g n a l s of the m u l t i p l e x e r s . The m u l t i p l e x e r s p e r f o r m the m u l t i p l i c a t i o n t i m e s 0,±1,±2 o p e r a t i o n s and the f o u r p a r t i a l p r o d u c t s formed a r e reduced t o two operands t h r o u g h t h e c a r r y save a r r a y (CSA). The l a s t s t a g e i s a two-operand p a r a l l e l a dder, such as a c a r r y l o o k - a h e a d a d d e r, which g i v e s t h e f i n a l p r o d u c t . The c e l l l e v e l schemes f o r t h e r e c o d e r s , m u l t i p l e x e r s and c a r r y save a r r a y b l o c k s a r e i l l u s t r a t e d i n F i g s . 4 . 3 , 4.4 and 4.5 r e s p e c t i v e l y . The c a r r y save a r r a y r e q u i r e s t h r e e c e l l l e v e l s which c o n s i s t of h a l f adders and f u l l a d d e r s . We can reduce t h e a r r a y t o o n l y two l e v e l s , i f two ( 5 , 3 ) - c o u n t e r s a r e used i n the f i r s t l e v e l . A ( 5 , 3 ) - c o u n t e r i s a s p e c i a l k i n d of adder which reduces f i v e i n p u t b i t s of t h e same o r d e r t o two o u t p u t b i t s of d i f f e r e n t o r d e r . I t may be advantageous t o use the 2 - l e v e l scheme because a ( 5 , 3 ) - c o u n t e r i s p r o b a b l y f a s t e r than two cas c a d e d f u l l a d ders i f implemented i n CVS l o g i c . However, the 3 - l e v e l scheme i s more e f f i c i e n t i n t h e a s p e c t of p a r t i t i o n i n g t h e t o t a l d e l a y i n t o e q u a l amounts of d e l a y a t each l e v e l . T h i s i s a l w a y s i m p o r t a n t i n a p i p e l i n e d d e s i g n . 92 RECOOERS 7 6 0 A a 3 7 8 6 - a O 3 MULTIPLEXERS ( W j ) j=0.1.2.3 1* (PP^.addj) j-0.1.2.3 CARRY SAVE ARRAY ^ > n l 5 n l 4 - " n Q 16-BIT ADDER O p p p v r 1 5 r 1 4 " r 0 F i g . 4 . 2 T h e a r c h i t e c t u r a l s cheme o f a n 8x8 m u l t i p l i e r CI CI w CI CI F i g . 4 . 3 The c e l l l e v e l scheme of a r e c o d e r a r r a y 8 7 8 6 a 5 8 4 3 3 a 2 a i 3 0 SUb. C3 4 T C3 H C3 H LruriJriJrLrUri C3 HC3 C3 HC3 C3J-C3J (C2) HC3 PP .j PP* PP* PP* PP* PP* PP* PPj PP* addj SAME STRUCTURE FOR j-0.1.2. 3 F i g . 4 . 4 The c e l l l e v e l scheme of a m u l t i p l e x e r a r r a y 94 95 Three t y p e s of s t r u c t u r e a r e commonly used i n h i g h p erformance p a r a l l e l adder d e s i g n . They a r e 2 - b i t l o o k - a h e a d (or PARADD scheme) [ 3 3 ] , 4 - b i t l o o k - a h e a d [ 3 4 ] , and the r e c u r r e n c e s o l v e r [35] s t r u c t u r e . The number of c e l l l e v e l s r e q u i r e d by t h e s e p a r a l l e l adders a r e 9, 5 and 6 r e s p e c t i v e l y , f o r the case of 1 6 - b i t operands (N=16). The 4 - b i t l o o k - a h e a d s t r u c t u r e i s alw a y s f a s t e r and r e q u i r e s l e s s a r e a than the 2 - b i t l o o k - a h e a d s t r u c t u r e . T h i s i s p r i m a r i l y due t o the 4 - b i t s t r u c t u r e o n l y r e q u i r i n g h a l f the l e v e l s of the 2 - b i t s t r u c t u r e w i t h l e s s than t w i c e t h e d e l a y time per l e v e l . The number of l e v e l s r e q u i r e d by the r e c u r r e n c e s o l v e r s i s about t h e same as t h e 4 - b i t l o o k - a h e a d a p p r o a c h . A problem of t h e r e c u r r e n c e s o l v e r s i s the worst case f a n o u t N/2 as w e l l as t h e l o n g w i r e s ( t h e l o n g e s t w i r e has t o t r a v e l N/2 b i t s ) t o be d r i v e n by a s i n g l e d e v i c e . T h i s causes l a r g e v a r i a t i o n s of d e l a y time i n d i f f e r e n t p a t h s . T h i s w i l l i n t r o d u c e a d i f f i c u l t y i n p a r t i t i o n i n g the t o t a l d e l a y i n t o an e q u a l amount ' of d e l a y f o r each l e v e l i n our p i p e l i n e d i m p l e m e n t a t i o n . T h e r e f o r e , t h e 4 - b i t l o o k - a h e a d adder i s chosen, w i t h i t s c e l l l e v e l scheme shown i n F i g . 4 . 6 . N o t i c e t h a t the low e r o r d e r b i t s a r e computed t h r o u g h the r i p p l e c a r r y . T h i s does not i n t r o d u c e a d d i t i o n a l d e l a y s t a g e s s i n c e t h e lower o r d e r operand b i t s a r e a v a i l a b l e a t an e a r l i e r t ime (see F i g . 4 . 5 a l s o ) . T h i s c o m b i n a t i o n r e q u i r e s l e s s hardware, as compared t o a f u l l c a r r y l o o k - a h e a d i m p l e m e n t a t i o n . "l5 "15 N " " » "13 V ^ " l ! *U "ll"llV* T» N 8 "V M ? ^ 6 " 5 »5 "< N* "3 N, V , 11,1., ^ HR HR HB HR HR HR HR HR HR HR HR I T T T T T T T T T T T T T T T T T T~l T _ r 15 P , 5 \< 1* 9.3 1, 9,2 1, '„ % 1l % P 9 A 8 P 8 *? 4 6 P G 9 5 " 5 If) % Pg "8 r 8 '? r? *f> "G 3 5 " 5 99 9P„ 99, CP C8 C5 .15 13 .13 9P. C5 "\2 91P?B \ % 1 c? CO C5 . 1 C l l C1B c 9 PI2 1 P r P r Ffl Ffl J fi D 5, 5 I? 09 C5 C8 I I CP F T T T T T T T I T FR FR I HR *v *v *v 4* P P P P F * 5 ? I » -BIT CRRRY RIPPLE RDOER CR P. r P. P.. P. 15 14 13 1? II IB 9 8 ? t. — 11-BIT OWJT inrXHFHD HTfCR F i g . 4 . 6 The c e l l l e v e l scheme of an 1 6 - b i t adder 9 7 4.2 CELL TYPES AND THEIR CIRCUITS W i t h the f u n c t i o n s and c o n n e c t i o n s between i n d i v i d u a l c e l l s d e f i n e d i n S e c t i o n 4.1 and F i g . 4 . 3 - 4 . 6 , our t a s k i s t o d e s i g n a CVS t r a n s i s t o r - l e v e l i m p l e m e n t a t i o n f o r each c e l l . The p r o c e d u r e s d e s c r i b e d i n Chapter Two a r e e x t r e m e l y u s e f u l i n d e s i g n i n g the CVS l o g i c a l t r e e n e t w o r k s . The c l o c k e d l o a d f o r the DCVS t r e e , shown i n F i g . 3 . 1 5 ( b ) , i s used i n most p a r t s of our m u l t i p l i e r d e s i g n . The e x c e p t i o n s a r e when o n l y a s i n g l e - e n d e d output i s r e q u i r e d , or when d i f f e r e n t i a l o u t p u t s a r e needed from a SCVS t r e e s t r u c t u r e . I n t h e s e c a s e s , the c l o c k e d l o a d s i l l u s t r a t e d i n F i g s . 3 . 1 5 ( a ) and 3.17 a r e used. A s i m p l e method of o b t a i n i n g a SCVS t r e e i s by ' p r u n i n g ' a DCVS t r e e . Suppose we need t o p r e s e r v e o n l y the open d r a i n o u t p u t Q of a DCVS t r e e . S t a r t i n g from node Q, e v e r y time we t r a v e r s e each p o s s i b l e p a t h t o ground, we mark the t r a n s i s t o r s w hich a r e c o n t a i n e d i n t h i s p a t h . A f t e r a l l t h e p a t h s have been t r a v e r s e d , t h e unmarked t r a n s i s t o r s a r e d e l e t e d from the t r e e . S i m i l a r l y , f o r p r e s e r v i n g the o u t p u t Q', p a t h s e a r c h i n g s t a r t s from node Q'. Now, we w i l l d i s c u s s the DCVS t r e e d e s i g n s f o r each c e l l of our m u l t i p l i e r . The r e c o d e r c e l l CI has b,.. , b . and b . (the 2 3 - 1 2 ] 2 ] + 1 m u l t i p l i e r B a r r a n g e d i n 3 - b i t g r o u p s , see F i g . 4 . 3 ) as i n p u t s 98 and w. = ( sub. , 2 X . , 1 X . ) as o u t p u t s . The b l o c k diagram of 3 3 3 D the c e l l and i t s t r u t h t a b l e a r e shown i n F i g . 4 . 7 . Because t h e r e a r e t h r e e l o g i c a l f u n c t i o n s t o be e v a l u a t e d , t h e c e l l c o n s i s t s of t h r e e d i f f e r e n t CVS t r e e s . The r e l a t i o n 1 X . = b . + b . can 3 2 ] - 1 2 } e a s i l y be r e c o g n i z e d , and implemented u s i n g the DCVS e x c l u s i v e - o r t r e e s t r u c t u r e shown i n F i g . 2 . 4 ( a ) . The K-map pro c e d u r e i n S e c t i o n 2 . 1 . 2 . 2 i s used t o implement the sub_. and 2 X . f u n c t i o n s , and t h e i r CVS t r e e s a r e shown i n F i g . 4 . 8 . 3 Now we c o n s i d e r the d e s i g n of the m u l t i p l e x e r c e l l s . From T a b l e 4 . 1 , we observe t h a t the f o l l o w i n g B o o l e a n r e l a t i o n s h o l d : f o r j = 1 t o 4 , i = 0 t o 8 : add . = sub . pp. =[( IX. • a. ) + ( 2 X . • a. t ) ] © sub. i D i 3 1-1 3 where a = sub. and a„ = " 0 " - 1 3 8 The f i r s t B o o l e a n f u n c t i o n add. i s e v a l u a t e d by the c e l l C 2 . 3 T h i s c e l l i s v e r y s i m p l e and i s i d e n t i c a l t o the p i p e l i n e d r e g i s t e r ( o r d e l a y element) t h a t w i l l be d i s c u s s e d l a t e r . The c e l l C3 e v a l u a t e s t h e second Boolean f u n c t i o n p p 3 . A l t h o u g h t h i s c i r c u i t can be d e s i g n e d u s i n g a f i v e - v a r i a b l e K-map, a s i m p l e i n t u i t i v e approach i s p r e f e r r e d . L e t P= 1 X . • a. + 2 X . • a. , 3 1 3 1 - I and P' = ( IX'. + a'. )• ( 2 X ' . + a'. ). 3 1 3 1 - 1 CI 2Xj lXj Ban B«-» so, 2Xi lXj 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 1 0 1 1 0 1 0 1 0 0 1 1 0 1 0 1 1 0 1 1 1 0 1 0 1 1 1 1 0 0 0 F i g . 4 . 7 A r e c o d e r c e l l C1 and i t s t r u t h t a b l e F i g . 4 . 8 The DCVS c i r c u i t s f o r the f u n c t i o n s 2 X J and sub 100 The s e r i e s / p a r a l l e l networks c o r r e s p o n d i n g t o f u n c t i o n P and P' a r e shown i n F i g . 4 . 9 . In o r d e r t o c o n s t r u c t the DCVS network f o r pp? , we employ the 2-way e x c l u s i v e - o r c o n f i g u r a t i o n of F i g . 2 . 4 , and r e p l a c e i n p u t x ( x' ) by sub. ( sub'. ) and t r a n s i s t o r x„ 1 1 3 3 2 ( x'^ ) by network P (P') r e s p e c t i v e l y , as shown i n F i g . 4 . 9 . The c a r r y save a r r a y c o n s i s t s of h a l f adder (HA) and f u l l adder (FA) c e l l s . T h e i r b l o c k diagrams and l o g i c a l f u n c t i o n s a r e shown i n F i g . 4 . 1 0 . The DCVS networks c o r r e s p o n d i n g t o t h e s e l o g i c a l f u n c t i o n s have a l r e a d y been d i s c u s s e d i n Chapter Two ( F i g . 2 . 4 , 2.6(a) and 2 . 7 ( b ) ) . For t h e c a r r y l o o k - a h e a d a d d e r , the " g e n e r a t e " s i g n a l s (G's) and "propagate" s i g n a l s (P's) a r e o b t a i n e d t h r o u g h t h e h a l f a d d e r s . The c e l l C4 (see F i g . 4 . 6 ) e v a l u a t e s t h e b l o c k c a r r y g e n e r a t e GG and the b l o c k c a r r y p r o p a g a t e GP. The c e l l s C5, C6 and C7 compute the c a r r y out C's from t h e s e g e n e r a t e and pr o p a g a t e s i g n a l s . The l a s t s t a g e i s a row of C8 c e l l s w hich a r e a c t u a l l y e x c l u s i v e - o r g a t e s . The b l o c k diagrams and l o g i c a l f u n c t i o n s o f the c e l l s C4, C5, C6 and C7 a r e i l l u s t r a t e d i n F i g . 4 . 1 1 . Note t h a t the l o g i c f u n c t i o n i s r e c u r s i v e and i s i n the form o f c = g + p c , where n £ 1. A DCVS s t r u c t u r e n n n n-1 whic h implements t h i s f u n c t i o n i s shown i n F i g . 2 . 5 . However, the d i s a d v a n t a g e of t h i s t r e e network i s t h e h i g h s t a c k h e i g h t 2n+1 (eg . 9 s t a c k l e v e l s f o r n=4), and t h i s a f f e c t s t h e performance s i g n i f i c a n t l y . By a p p l y i n g t h e s e r i e s / p a r a l l e l d e c o m p o s i t i o n as 101 NETWORK P NETWORK_P' ixHI H i IF- 8 i - i i g . 4 . 9 A DCVS c i r c u i t t o g e n e r a t e t h e m u l t i p l e x e d o u t p u t s A B C S= A 0 B C o u t= AB Cout S s= AeBec Cout= AB+BC+CA F i g . 4 . 1 0 The h a l f adder and f u l l adder b l o c k s and t h e i r l o g i c a l f u n c t i o n s *P4 «A *A H 11 11 11 C4 1 1 G6, GPj 1AJJL - C o C6 T c 2 l i -es "-Co *A *2h 1111 11 - C o C7 C3 V WiVi'.V.'i1'! F i g . 4 . 1 1 The b l o c k diagrams and l o g i c a l f u n c t i o n s o f c a r r y l o o k - a h e a d c e l l s 103 shown i n F i g . 4 . 1 2 , t h e s t a c k h e i g h t of the DCVS t r e e reduces t o n+1, w i t h the same number of t r a n s i s t o r s r e q u i r e d . T h i s v e r s i o n of t h e c i r c u i t which has almost h a l f of the s t a c k h e i g h t of the former v e r s i o n , i s d e s i r a b l e i n our h i g h performance a p p l i c a t i o n . In o r d e r t o s y n c h r o n i z e the p r o p a g a t i n g s i g n a l s p r o p e r l y i n the p i p e l i n e , a d d i t i o n a l d e l a y s t a g e s a r e sometimes needed between l o g i c a l b l o c k s . The CCMOS r e g i s t e r shown i n F i g . 3 . 1 3 ( a ) can be used as a d e l a y element. However, t h e two P - t r a n s i s t o r s i n s e r i e s slow down t h e charge-up and c o n s e q u e n t l y l i m i t t h e c a p a b i l i t y of d r i v i n g a l a r g e o u t p u t l o a d . Dynamic d e l a y s t a g e s as shown i n F i g . 4 . 1 3 ( a ) and (b) can d r i v e l a r g e l o a d s w i t h a few t i m e s s m a l l e r i n p u t g a t e c a p a c i t a n c e compared t o t h e CCMOS r e g i s t e r . F o r example, a 200fF l o a d can be d r i v e n t o a l o g i c h i g h i n 5ns by the c i r c u i t of F i g . 4 . 1 3 ( a ) w i t h an i n p u t c a p a c i t a n c e of 15fF. A 60fF l o a d d r i v e n by a CCMOS r e g i s t e r , f o r which t h e i n p u t gate c a p a c i t a n c e i s f o u r t i m e s t h a t of t h e dynamic d e l a y s t a g e , r e q u i r e s a l s o 5ns t o r e a c h a l o g i c h i g h . c , c , 9 9 I«;HC BLOCK (1) . I F ] ] K c J C * » c c t° \ BLOCK (N) i BLOCK (N-l)j L4i]---u4J ^ ^ 7 F i g . 4 . 1 2 An a l t e r n a t i v e c o n s t r u c t i o n of c i r c u i t s i n F i g . 2 . 5 ( a ) and (b) i q . 4 . 1 3 ( b ) A d e l a y s t a g e w i t h complementary o u t p u t s 106 4.3 PROCESS AND SPEED CRITERIA The p r o c e s s chosen f o r our m u l t i p l i e r d e s i g n i s the 3*im CMOS p r o c e s s [36] of N o r t h e r n Telecom E l e c t r o n i c s (NTE) of Ottawa, Canada. T h i s p r o c e s s i s the scaled-down v e r s i o n of the Sum p r o c e s s which has been commonly used by the u n i v e r s i t y d e s i g n community. Some of the d e s i g n r u l e s a r e i d e n t i c a l t o the 5nm p r o c e s s , w h i l e o t h e r s a r e s i m p l i f i e d . The p r o c e s s f e a t u r e s 16 —3 p-type w e l l s ( N «5x 10 cm ) on the n-type s u b s t r a t e 1 5 -3 a x ( N »5x 10 cm ), a p o l y s i l i c o n l a y e r w i t h g a t e o x i d e d t h i c k n e s s of .05Mm, and a s i n g l e l a y e r of m e t a l l i z a t i o n . The p r o c e s s i s q u i t e c o n v e n t i o n a l and by no means the most advanced p r o c e s s of t h e t i m e . Some advanced p r o c e s s e s s h r i n k the minimum f e a t u r e s i z e down t o below 1.5MH. A l s o , s i l i c i d e d p o l y s i l i c o n ( p o l y s i l i c o n c l a d w i t h m e t a l ) w i t h much s m a l l e r sheet r e s i s t a n c e may be used t o reduce the p o l y i n t e r c o n n e c t i o n l i n e d e l a y . F u r t h e r m o r e , i t i s o f t e n advantageous t o have two s e p a r a b l e n- and p - w e l l s , so t h a t d o p i n g i n one w e l l can be a d j u s t e d i n d e p e n d e n t l y of the o t h e r , p o s s i b l y l o w e r i n g the do p i n g l e v e l i n the p - w e l l . The lower d o p i n g i n t h e p - w e l l r e d u c e s the j u n c t i o n c a p a c i t a n c e of the so u r c e and t h e d r a i n of the n-channel t r a n s i s t o r . T h i s would be v e r y d e s i r a b l e f o r h i g h performance CVS l o g i c because of the l a r g e s h a r e d d r a i n and so u r c e c a p a c i t a n c e s a s s o c i a t e d w i t h t h e t r e e n e t w o r k s . 107 C i r c u i t performance depends on both the p r o c e s s t e c h n o l o g y and the c i r c u i t t e c h n i q u e s used. I t i s n e c e s s a r y t o s e p a r a t e the m e r i t of t h e c i r c u i t t e c h n i q u e from t h a t of the p r o c e s s f o r comparison p u r p o s e s . A c o n v e n i e n t f i g u r e of m e r i t f o r the speed of a p r o c e s s i s the i n v e r t e r d e l a y as d e t e r m i n e d by a r i n g o s c i l l a t o r . We have s i m u l a t e d a s e v e n - s t a g e r i n g o s c i l l a t o r by u s i n g the SPICE program [37] w i t h l e v e l 2 t r a n s i s t o r model p a r a m e t e r s . The w i d t h of t h e p u l l - u p and p u l l - d o w n t r a n s i s t o r s a r e 5.4um and 3/xm r e s p e c t i v e l y , and mininum l e n g t h c h a n n e l s of 3um a r e used f o r b o t h . The p e r i o d of o s c i l l a t i o n i s found t o be 31ns, and t h e d e l a y per i n v e r t e r s t a g e i s about 2.2ns ( = 3 l n s / ( 2 * 7 ) ) a t 27°C. I d e a l l y a c i r c u i t d e s i g n s h o u l d be such t h a t a major r e d e s i g n i s not r e q u i r e d when a d i f f e r e n t CMOS p r o c e s s i s used. In our d e s i g n , l o a d m a t c h i n g would p r o b a b l y have t o be redone by a d j u s t i n g t h e w i d t h of t h e b u f f e r t r a n s i s t o r s i n each c e l l . A f u r t h e r i d e a l s i t u a t i o n would be t h a t t h e performance of the c i r c u i t improve i n t h e same r a t i o as t h e d i m e n s i o n s i n t h e p r o c e s s a r e scaled-down. T h i s c o n d i t i o n i s h a r d t o f u l f i l l and i t o f t e n depends on t h e p r o c e s s . C o n s i d e r the dynamic CVS c i r c u i t as an example. A lumped model f o r speed c o n s i d e r a t i o n s i s shown i n F i g . 4 . 1 4 ( a ) . Suppose i n i t i a l l y t h e v o l t a g e of node N1 i s h i g h ( 5 V ) , w h i l e b o t h of nodes N2 and N3 a r e low (0V). Node N1 i s a l l o w e d t o d i s c h a r g e t h r o u g h t h e CVS t r e e and thus t r a n s i s t o r T1 i s t u r n e d on. F i n a l l y node N3 i s c h a r g e d t o Vdd LUMPED RC MOOEL OF CVS TREE F i g . 4 . 1 4 ( a ) A lumped model of a CVS c i r c u i t c l n t * c o .4.14(b) A s i m p l i f i e d RC model of a CVS c i r c u i t 109 t h r o u g h t h e i n t e r c o n n e c t l i n e . The t o t a l gate p r o p a g a t i o n d e l a y i s d e t e r m i n e d by t h e RC time c o n s t a n t of the CVS t r e e , p l u s the RC time c o n s t a n t of t h e t o t a l o u t p u t l o a d . A s i m p l i f i e d RC model as shown i n F i g . 4 . 1 4 ( b ) i s more c o n v e n i e n t f o r c a l c u l a t i o n p u r p o s e s . R and C a r e the c v s c v s e q u i v a l e n t r e s i s t a n c e and t o t a l c a p a c i t a n c e of the CVS t r e e . R. and C. a r e the r e s i s t a n c e and c a p a c i t a n c e of the i n t i n t i n t e r c o n n e c t l i n e . R i s the o n - r e s i s t a n c e of the d r i v i n g o t r a n s i s t o r and C i s t h e ou t p u t c a p a c i t i v e l o a d (eg. i n p u t gate o of next s t a g e ) . A c c o r d i n g t o MOS s c a l i n g laws [ 3 8 ] , the o n - r e s i s t a n c e of t r a n s i s t o r s ( R and R ) cannot be s c a l e d . o c v s However, C i s s c a l e d l i n e a r l y , and t h u s the d e l a y t h r o u g h t h e C V s t r e e ( t h e p r o d u c t R C ) can be s c a l e d down. The d e l a y c v s c v s t h r o u g h the i n t e r c o n n e c t p a t h , e s p e c i a l l y the p o l y l i n e , i s dominated by t h e time c o n s t a n t R. C. which does not s c a l e . i n t i n t T h i s l e a d s t o t h e c o n c l u s i o n t h a t c i r c u i t performance may not n e c e s s a r i l y improve i n t h e same r a t i o as t h a t by wh i c h t h e d i m e n s i o n s i n the p r o c e s s a r e s c a l e d down. The d e l a y t h r o u g h the CVS t r e e i s t y p i c a l l y o n e - h a l f t o t w o - t h i r d s t h a t of t h e t o t a l g a t e d e l a y . T h i s i s the g e n e r a l c o n c l u s i o n which can be drawn from s i m u l a t i o n s of d i f f e r e n t c e l l s i n our d e s i g n . T h i s can a l s o be shown by t h e f o l l o w i n g n u m e r i c a l example. C o n s i d e r a f u l l adder c e l l whose ou t p u t i s c o n n e c t e d t o a 60fF l o a d t h r o u g h a 500Mm minimum w i d t h p o l y 110 l i n e . The c a p a c i t a n c e of each d i f f u s i o n r e g i o n ( d r a i n or source) of a t r a n s i s t o r i s e s t i m a t e d t o be 4 0 f F , and t h e r e a r e 20 such r e g i o n s i n the DCVS t r e e . The conductance of the t r e e i s d e s i g n e d t o be e q u i v a l e n t t o the conductance of a minimum-size n - d e v i c e . Suppose the conductance of the d r i v i n g p - d e v i c e i s a l s o e q u a l t o t h a t of a minimum-size N - d e v i c e . The r e s i s t a n c e and c a p a c i t a n c e of t h e p o l y l i n e a r e ap p r o x i m a t e d as I0fi/um and .22fF/mn r e s p e c t i v e l y [ 3 6 ] . We c a r r y out t h e f o l l o w i n g c a l c u l a t i o n : R = R = L / [ W M C (Vdd-Vth)] ~ 3 . 5 k f i c v s o ox C = 40fF*20 =800fF c v s R. =l0£i/nm * 500um = 5kfi i n t C. =.22fF/Mm * 500Mm = 1 l 0 f F i n t C = 60fF o Hence, we get R C = 3.5kn*800fF = 2.8ns c v s c v s ( R + R. )*( C. + C ) = 8.5kO*9l0fF ~1.4ns o i n t i n t o We see t h a t the time c o n s t a n t of t h e CVS t r e e i s about t w o - t h i r d s t h a t of t h e t o t a l t i m e c o n s t a n t . T h i s r a t i o i s p r e d i c t e d by d e t a i l e d SPICE s i m u l a t i o n s , a l t h o u g h t h e i n d i v i d u a l d e l a y t i m e s a r e found t o be about d o u b l e t h o s e c a l c u l a t e d by the s i m p l e RC t i m e c o n s t a n t s . 111 4 . 4 SIMULATIONS OF THE CELLS T h i s s e c t i o n d i s c u s s e s t h e t e c h n i q u e s of s i z i n g the t r a n s i s t o r s w i t h i n a c e l l t o meet a c e r t a i n speed r e q u i r e m e n t . The m u l t i p l i e r i s i n t e n d e d t o o p e r a t e a t a t h r o u g h p u t r a t e of 50MHz. T h i s i m p l i e s t h a t each NORA CVS g a t e must have a p r e c h a r g i n g t i m e and e v a l u a t i o n t i m e of 10ns. B e f o r e g o i n g i n t o t h e d e t a i l s of s i z i n g the t r a n s i s t o r s i n a c e l l d e s i g n , we f i r s t d i s c u s s the m o d e l l i n g of the o u t p u t l o a d i n g of a c e l l . Suppose a t r a n s i s t o r ( o n - r e s i s t a n c e = R^ ) i s d r i v i n g a c a p a c i t i v e l o a d C t h r o u g h a d i s p e r s i v e l i n e of l e n g t h -1, w i t h o c h a r a c t e r i s t i c r e s i s t a n c e r and c a p a c i t a n c e c per u n i t l e n g t h . o o There a r e t h r e e models of p r o p a g a t i o n time a l o n g a w i r e t o be c o n s i d e r e d : 1. Synchronous model - the p r o p a g a t i o n time i s c o n s t a n t . 2. C a p a c i t i v e model - the p r o p a g a t i o n r e q u i r e s 0(1) t i m e . 2 3. D i f f u s i o n model - the p r o p a g a t i o n r e q u i r e 0( 1 ) t i m e . D e f i n e p a r a m e t e r s 7 = c l / C and p = r l / R . A c r i t e r i o n which has o o been d e s c r i b e d i n Ref. [29] may be used t o choose a s u i t a b l e model f o r s i m u l a t i o n p u r p o s e s . T h i s c r i t e r i o n i s d e r i v e d from s o l v i n g the c l a s s i c a l t r a n s m i s s i o n l i n e e q u a t i o n w i t h a s e t of p r o p e r l y chosen boundary c o n d i t i o n s . The r e s u l t i s summarized i n F i g . 4 . 1 5 . The v a r i a b l e c ( p , 7 ) i s t h e r e l a t i v e d e v i a t i o n of a c t u a l d e l a y from the d e l a y R* C (1+7+p) i n an i d e a l i z e d 112 F i g . 4 . 1 5 Contour l i n e s of r e l a t i v e d e v i a t i o n e(p,i) i n R e f . [ 3 9 ] HI HI HI i 5 r i in i Co F i g . 4 . 1 6 ( a ) A c a p a c i t i v e model f o r t h e o u t p u t l o a d F i g . 4 . 1 6 ( b ) A lumped RC model f o r the o u t p u t l o a d 113 c a p a c i t i v e model. I f (pty) l i e s i n the synchronous or c a p a c i t i v e r e a l m , the c a p a c i t i v e o u t p u t model ( F i g . 4 . 1 6 ( a ) ) may be used. Note t h a t a c o r r e c t i o n term r l C /R i s added t o t h e c a p a c i t i v e o o model t o t a k e account of the i n t e r c o n n e c t l i n e r e s i s t a n c e . I f (p,7) l i e s i n " the d i f f u s i o n r e a l m , the lumped RC model ( F i g . 4 . 1 6 ( b ) ) i s more a p p r o p r i a t e . Here i s an example t o show how the e q u i v a l e n t output c a p a c i t a n c e i s d e t e r m i n e d . The f o l l o w i n g d a t a i s g i v e n : l=500Mm, r=lOfi/Mm, c=.22fF/um ( p o l y l i n e ) C =60fF, R =3.5kO o o p = r l / R = 10*500/3500 » 1.43 o 7 = c l / C = .22*500/60 ^ 1.83 o Because (P,T) l i e s i n t h e c a p a c i t i v e r e g i o n (see F i g . 4 . 1 5 ) , the c a p a c i t i v e model can be used. C = C d+p+7) out o = C + (c + r * C / R )*1 o 0 0 = C + c ' * l o - 60fF + ,39tF/w * 500Mm = 255fF Two u s e f u l parameters w h i c h h e l p t o choose th e p r o p e r output l o a d model f o r SPICE s i m u l a t i o n s a r e c' and 1 . The max e q u i v a l e n t c a p a c i t a n c e c' per u n i t l e n g t h of i n t e r c o n n e c t l i n e i s e q u a l t o c + r * C / R q . T h i s i s the p r o p o r t i o n a l c o n s t a n t w h i c h d e t e r m i n e s t h e dependence of e q u i v a l e n t c a p a c i t a n c e c o u t on 1 i n t h e c a p a c i t i v e model. To d e t e r m i n e t h e maximum l e n g t h 1 14 1 of i n t e r c o n n e c t l i n e under which the c a p a c i t i v e model max h o l d s , we draw a s t r a i g h t l i n e p/y i n F i g . 4 . 1 5 and mark the p o i n t which i n t e r s e c t s w i t h the boundary of the d i f f u s i o n r e a l m . L i s e q u a l t o the s m a l l e r of the two v a l u e s y C /c and max o p R / r a t t h i s p o i n t , o I n the s i m u l a t i o n s of i n d i v i d u a l c e l l s of the m u l t i p l i e r , the c a p a c i t i v e output model i s g e n e r a l l y v a l i d . Only i n the case of e x c e e d i n g l y l o n g w i r e s (eg. c l o c k l i n e , power s u p p l y l i n e ) w i t h h e a v i l y d i s t r i b u t e d c a p a c i t i v e l o a d i s the lumped RC model used. Now we t u r n t o the problem of s i z i n g t r a n s i s t o r s i n a CVS g a t e . As mentioned i n S e c t i o n 4.3, t h e t o t a l gate d e l a y i s due t o t h e d i s c h a r g i n g d e l a y of the CVS t r e e p l u s the d e l a y of t h e o u t p u t b u f f e r . We a l l o t 6ns t o t h e CVS t r e e d e l a y and 4ns t o the b u f f e r d e l a y . An i n i t i a l guess would be t o s i z e the t r a n s i s t o r s i n the CVS t r e e s uch t h a t t h e e q u i v a l e n t conductance of any s i n g l e d i s c h a r g i n g p a t h i s t h e same as t h e conductance of a minimum-size N - t r a n s i s t o r . For example, a p a t h w i t h f o u r s e r i a l l y c o n n e c t e d t r a n s i s t o r s r e q u i r e s each t r a n s i s t o r c o n t a i n e d i n t h a t p a t h t o be I2^tm ( = 4*3MITI) wide. The advantage of t h i s a p p r o a c h i s t o keep R (see F i g . 4 . 1 4 ( b ) ) c o n s t a n t CVS i r r e s p e c t i v e of t h e t r e e h e i g h t H. I f C i n c r e a s e s l i n e a r i l y CVS w i t h H, and i s not s t r o n g l y dependent on the t r a n s i s t o r w i d t h , 115 then the t r e e d e l a y has a l i n e a r dependence on H. O t h e r w i s e i f we keep the i n d i v i d u a l t r a n s i s t o r w i d t h c o n s t a n t , R a l s o c v s i n c r e a s e s l i n e a r i l y w i t h H and t h e t r e e d e l a y has a q u a d r a t i c dependence on H [ 4 0 ] , Sometimes i n a CVS t r e e not eve r y c o n d u c t i n g p a t h has t h e same l e v e l of s t a c k s . I n such c a s e s , the p a t h w i t h a s m a l l e r s t a c k l e v e l can c o n t a i n s m a l l e r t r a n s i s t o r s w i t h o u t a f f e c t i n g the performance. A f t e r t h e t r a n s i s t o r s i z e s have been a s s i g n e d , we s h o u l d v e r i f y t h r o u g h SPICE s i m u l a t i o n s t h a t the t r e e d e l a y indeed meets the re q u i r e m e n t of 6ns. In o r d e r t o f i n d out the worst time d e l a y of the CVS t r e e , we may t r y a l l the p o s s i b l e c o m b i n a t i o n s of i n p u t s and f i n d out t h e i r c o r r e s p o n d i n g d i s c h a r g e t i m e s . T h i s t a s k i s q u i t e f o r m i d a b l e because u s u a l l y t h e r e a r e many p o s s i b l e i n p u t c o m b i n a t i o n s . A b e t t e r method and the p r o p e r method i s t o f i n d out t h e c r i t i c a l d i s c h a r g i n g p a t h s by i n s p e c t i n g the CVS t r e e s t r u c t u r e . The c i r c u i t i s s i m u l a t e d u s i n g t h e i n p u t c o m b i n a t i o n s w h i c h t u r n on t h e s e c r i t i c a l d i s c h a r g i n g p a t h s . The c r i t i c a l d i s c h a r g i n g p a t h s a r e t h o s e t r e e c o n d u c t i n g p a t h s a s s o c i a t e d w i t h t h e l a r g e s t p a r a s i t i c c a p a c i t a n c e s . To make t h e e s t i m a t i o n e a s i e r , we assume t h a t t h e s o u r c e and d r a i n of a t r a n s i s t o r have e q u a l j u n c t i o n c a p a c i t a n c e and we c a l l b o th a d i f f u s i o n node. For example, g i v e n a c a r r y l o o k - a h e a d c i r c u i t as shown i n F i g . 4 . 1 7 , i t s c r i t i c a l d i s c h a r g i n g p a t h i s sought. 1 16 TO CLOCKED LOAD GND NODE (DRAIN OF A CLOCKED N-OEVICE) Fi g . 4 . 1 7 A c i r c u i t example f o r f i n d i n g the c r i t i c a l d i s c h a r g i n g p a t h \wjfl8ER OF \0IFFUSIW  \W0ES PATH n. 1 STflCK LEVEL 2 3 4 TOTAL 1 OF DIFFUSION NODES III A PATH flBCD 2 3 3 2 10 ABE 3 3 2 8 RF 3 2 5 G 2 2 T a b l e 4.2 The d i s t r i b u t i o n of d i f f u s i o n nodes f o r t h e CVS t r e e i n F i g . 4 . 1 7 1 1 7 We a s s i g n the s t a c k l e v e l numbers t o the s h a r e d nodes of the p a t h s t a r t i n g from the d r a i n of the bottom t r a n s i s t o r . The s h a r e d c a p a c i t a n c e a t s t a c k l e v e l i (£1) i n a p a r t i c u l a r p a t h has t o d i s c h a r g e t h r o u g h a s e r i e s of i t r a n s i s t o r s t o the ground node. T a b l e 4.2 summarizes the d i s t r i b u t i o n of d i f f u s i o n nodes i n t h e d i f f e r e n t c o n d u c t i n g p a t h s . The c r i t i c a l p a t h i s ABCD because i t has t h e h i g h e s t s t a c k l e v e l number and the l a r g e s t t o t a l number of d i f f u s i o n nodes. I n o r d e r t o c a r r y out the worst case s i m u l a t i o n , we s h o u l d s e t i n p u t s A t o D h i g h and E t o G low. By o b s e r v i n g t h e open d r a i n o u t p u t • of the t r e e i n the e v a l u a t i o n phase, we can f i n d the worst case t r e e d e l a y . In some c a s e s i t i s h a r d t o d e t e r m i n e which p a t h i s more c r i t i c a l i f one p a t h has a s m a l l e r t o t a l number of d i f f u s i o n nodes ( l e s s h e a v i l y branched) but h i g h e r s t a c k h e i g h t ( t a l l e r t r e e ) t h a n the o t h e r p a t h . I t i s l e f t f o r the s i m u l a t i o n t o de t e r m i n e t h e worst c a s e p a t h . Some g e n e r a l r u l e s may be a p p l i e d t o e l i m i n a t e t h e n o n - c r i t i c a l p a t h s . Suppose t h e r e a r e two d i s c h a r g i n g p a t h s and . P a t h i s l e s s c r i t i c a l ( t h u s s i m u l a t i o n i s not needed) i f : 1. P and P have about the same t o t a l number of d i f f u s i o n 1 2 nodes but the s t a c k h e i g h t of P i s l a r g e r than t h a t of P 2 ' 2. o r , P and P 'have about t h e same s t a c k h e i g h t but has a l a r g e r t o t a l number of d i f f u s i o n nodes, 118 3. o r , P and P„ have about the same s t a c k h e i g h t and t o t a l 1 2 number of d i f f u s i o n nodes but P^ has a l a r g e r p r o p o r t i o n of d i f f u s i o n nodes l o c a t e d a t a h i g h e r s t a c k l e v e l than t h a t of P„ . 2 A f t e r s i m u l a t i n g each c e l l of t h e m u l t i p l i e r , we f i n d t h a t the l o n g e s t t r e e d e l a y o c c u r s i n c e l l s C4 and FA. They b a r e l y meet t h e 6ns r e q u i r e m e n t , even i f the e q u i v a l e n t r e s i s t a n c e R c v s of the t r e e i s s e t t o t h a t of a minimum-size N - d e v i c e . Some examples of c e l l s i m u l a t i o n s a r e g i v e n i n Appendix B. The next t a s k i s t o s i z e the l o a d d e v i c e s such t h a t they can d r i v e t h e r e q u i r e d c a p a c i t i v e l o a d i n g t o a l o g i c h i g h w i t h i n the 4ns time s l o t . C o n s i d e r the l o a d c i r c u i t r y . shown i n F i g . 4 . 1 8 ( a ) . T r a n s i s t o r T6 i s the d i s c h a r g i n g d e v i c e and s h o u l d be a t l e a s t as b i g as t h e w i d e s t t r a n s i s t o r i n t h e t r e e . The p r e c h a r g i n g P - d e v i c e T l i s d e s i g n e d such t h a t i t can charge up N1 and i n t e r n a l nodes of the t r e e t o 5V w i t h i n 10ns d u r i n g the p r e c h a r g e phase. From s i m u l a t i o n r e s u l t s , T l i s i n the range of 12-18MII» wide f o r t h e v a r i o u s c e l l s i n o r d e r t o g i v e s u f f i c i e n t p r e c h a r g e c u r r e n t . I f T1 i s t o o s m a l l , node N1 may not r i s e up t o 5V a f t e r 10ns. T h i s w i l l d e c r e a s e t h e a l l o w a n c e f o r v o l t a g e d r o p a t N1 due t o charge s h a r i n g , and a l s o slow down the d i s c h a r g i n g of C t h r o u g h T4 and T5 d u r i n g t h e f o l l o w i n g out e v a l u a t i o n phase. 119 F i g . 4 . 1 8 ( a ) A NORA s t a g e w i t h s i n g l e - e n d e d o u t p u t F i g . 4 . 1 8 ( b ) A NORA s t a g e w i t h complementary o u t p u t s 120 A s u i t a b l e s i z e f o r the feedback t r a n s i s t o r T2 i s 3*im f o r most of the c e l l s . I f T2 i s t o o s m a l l , then N1 may drop below 4.2V due t o charge s h a r i n g even though the t r e e i s n o n - c o n d u c t i n g . S i n c e V t h f o r T3 i s e q u a l t o 0.8V, i t may cause a c c i d e n t i a l c h a r g i n g of C t h r o u g h T3. I f T2 i s t o o l a r g e and out p r o v i d e s a s i g n i f i c a n t p u l l - u p c u r r e n t , i t may slow down t h e d i s c h a r g e of N1 d u r i n g e v a l u a t i o n when the t r e e i s c o n d u c t i n g . The s i z e s of T4 and T5 a r e e q u a l and a r e chosen such t h a t they can d i s c h a r g e C from 5V t o below 0.3V i n 10ns i f N1 out s t a y s h i g h d u r i n g the e v a l u a t i o n phase. However, e x c e s s i v e l y wide T4 and T5 w i l l have a n e g a t i v e e f f e c t on t h e charge-up. speed of C i f N1 changes t o low d u r i n g e v a l u a t i o n . F o r a out t y p i c a l C Q u t e q u a l t o l 5 0 f F , a s u i t a b l e w i d t h f o r T4 and T5 i s about 6um. The s i z e of T3 i s chosen such t h a t when N1 changes t o low, T3 w i l l p r o v i d e enough c u r r e n t t o charge up c o u f c t o above 4V w i t h i n 4ns. From s i m u l a t i o n r e s u l t s , the w i d t h of T3 s h o u l d be about t h r e e o r f o u r t i m e s t h a t of T4 or T5. Note t h a t even though C i s not ch a r g e d up t o a f u l l 5V ( s a y , 4V) d u r i n g the out e v a l u a t i o n phase, C w i l l u l t i m a t e l y r i s e up t o 5V i n the next out p r e c h a r g e phase because N1 i s not l i k e l y t o change from low t o h i g h i m m e d i a t e l y and t h u s some r e s i d u a l c u r r e n t w i l l f l o w t h r o u g h T3. 121 C o n s i d e r a n other t y p e of c l o c k e d l o a d as shown i n F i g . 4 . 1 8 ( b ) . The w i d t h s of t r a n s i s t o r s T7 and T13 a r e determined i n a s i m i l a r manner t o t h o s e of T1 and T6. The s i z e s of T10 and T11 a r e e q u a l and a r e chosen such t h a t they can charge c Q u t from OV t o 5V i n 10ns p r o v i d e d N4 s t a y s low d u r i n g the e v a l u a t i o n phase. A w i d t h of 18-21MIII i s needed f o r T10 and T11, i f C i s out about l 5 0 f F . The s i z e s of T8 and T12 d e t e r m i n e the d e l a y from N3 t o N5 when N3 i s d i s c h a r g e d . G e n e r a l l y we r e q u i r e t h e s i z e of T12 t o be t h r e e t i m e s s m a l l e r t h a n , and the s i z e of T8 t o be the same a s , the s i z e of T10 or T11. The w i d t h r a t i o of T8/T9 i s s e t t o f o u r i n o r d e r t o i n c r e a s e t h e b u f f e r ' s s e n s i t i v i t y t o the v o l t a g e d r o p i n N3. A s m a l l e r s i z e of T8 and T9 may be chosen t o reduce th e l o a d i n g a t node N3. 4.5 INPUT AND OUTPUT CONSIDERATIONS The p i p e l i n e d m u l t i p l i e r i s d i v i d e d i n t o 14 dynamic s t a g e s w i t h i n p u t pads a t one end and outpads a t t h e o t h e r end. The s t a g e s a r e numbered from one t o f o u r t e e n . The c l o c k l i n e 0 i s s u p p l i e d t o t h e odd s t a g e s , w h i l e the c l o c k l i n e 0' i s s u p p l i e d t o t h e even s t a g e s , as shown i n F i g . 4 . 1 9 . We d i s c u s s t h e i n p u t pad d e s i g n f i r s t . The i n p u t t e r m i n a l s of a d i g i t a l MOS i n t e g r a t e d c i r c u i t , w hich a r e c o n n e c t e d t o a g a t e e l e c t r o d e , have t o be p r o t e c t e d a g a i n s t t h e damage which input pads U's.B's) stags #1 •tagt f 2 stage # 3 stags #14 output pads P's dock pad f F i g . 4 . 1 9 The s t a g e s of the p i p e l i n e d m u l t i p l i e r 123 c o u l d be caused by e l e c t r o s t a t i c d i s c h a r g e s . Because of the v e r y h i g h i n p u t impedance of an MOS g a t e , e l e c t r i c c h a r g e s may be ac c u m u l a t e d on the i n p u t gate and g e n e r a t e a h i g h e l e c t r i c f i e l d i n t h e gate o x i d e ; t h i s gate o x i d e may thus break down and be per m a n e n t l y damaged. A t y p i c a l g a t e p r o t e c t i o n s t r u c t u r e ( F i g . 4 . 2 0 ( a ) ) c o n s i s t s b a s i c a l l y of a p a i r of d i o d e s (D1 arid D2) w h i c h can s i n k l a r g e c u r r e n t s i f t h e v o l t a g e of the o f f - c h i p i n p u t i s o u t s i d e the range of Vdd and Gnd, and a s e r i e s of d i s t r i b u t e d d i o d e s d e s i g n e d t o a t t e n u a t e the c u r r e n t and v o l t a g e s u p p l i e d t o t h e g a t e . The c r o s s - s e c t i o n of t h e p r o t e c t i o n s t r u c t u r e i s shown i n F i g . 4 . 2 0 ( b ) . Diode D1 i s c o n s t r u c t e d by h a v i n g a p+ d i f f u s i o n i n the n - s u b s t r a t e . Note t h a t a p+ d i f f u s i o n f i x e d a t Gnd i s p l a c e d near D1 t o c o l l e c t the l a r g e amount of h o l e s e m i t t e d by D1. S i m i l a r l y , D2 i s formed by h a v i n g a n+ d i f f u s i o n i n the p - w e l l . The a d j a c e n t n+ d i f f u s i o n s f i x e d a t Vdd a c t as e l e c t r o n c o l l e c t o r s . P i p e l i n e s t a g e #1 c o n s i s t s of i n p u t d r i v e r s which c o n v e r t s i n g l e i n p u t s i g n a l s t o d i f f e r e n t i a l s i g n a l s f o r t h e next DCVS l o g i c s t a g e . T r a n s m i s s i o n g a t e s a r e p l a c e d a t the i n p u t l i n e s i n o r d e r t o l a t c h t h e d a t a when i t i s v a l i d . The s c h e m a t i c of a b a s i c c e l l of s t a g e #1 i s shown i n F i g . 4 . 2 1 . The t r a n s m i s s i o n gate i s c l o s e d (0=0) when t h e stage i s p r e c h a r g e d , and the g a t e v o l t a g e of T1 i s a l l o w e d t o v a r y w i t h 124 A -7£ « OFF CMP DMT DISTRIBUTED oj ores BATE DMT F i g . 4 . 2 0 ( a ) A t y p i c a l gate p r o t e c t i o n s t r u c t u r e f o r input pads Fig.4 . 2 0(b) A cro s s s e c t i o n of the p r o t e c t i o n s t r u c t u r e i n Fig.4 . 2 0(a) F i g . 4 . 2 1 The schematic of a basic c e l l of stage #1 r — i r * i I «jf200 INPUT FfiON , r STAGE #13 M L 4 0 H STAGE #14 750 :0FF CHIP ^ OUTPUT (lOpF LOAD) 240 OUTPUT PAD F i g . 4 . 2 2 The output stage of the m u l t i p l i e r . The numbers i n d i c a t e the widths (um) of the t r a n s i s t o r s 126 the i n p u t v o l t a g e . The i n p u t v o l t a g e i s r e q u i r e d t o s t a b l i z e b e f o r e the t r a n s m i s s i o n g a t e opens (0=1), i . e . , a t the time the e v a l u a t i o n phase b e g i n s . The i n p u t s i g n a l i s s t o r e d i n the form of e l e c t r i c c h a r g e s a t the gate of T1. Note t h a t the i n p u t s e t - u p time i s e q u a l t o the d e l a y of a t r a n s m i s s i o n gate (=2ns). W i t h a s t a n d a r d CMOS i n t e r f a c e , the i n p u t l o g i c swing i s from 0 t o 5V. Suppose the d r i v e r , i . e . s t a g e #1, i s d e s i g n e d such t h a t a gate v o l t a g e of 5V on T1 p r o v i d e s enough d i s c h a r g i n g c u r r e n t such t h a t Q and Q1 can be e v a l u a t e d w i t h i n 10ns. I f the gat e v o l t a g e of T1 can o n l y go up t o 3V, as i n t h e case of TTL l o g i c l e v e l s , then v a l i d o u t p u t s Q and Q' may not be o b t a i n e d i n an e v a l u a t i o n time of 10ns. However, t h i s c o u l d be compensated f o r by i n c r e a s i n g t h e w i d t h of T1. A c c o r d i n g t o s i m u l a t i o n r e s u l t s , a w i d t h i n c r e a s e of 60% i s needed i f t h e gate v o l t a g e of t h e h i g h l o g i c l e v e l i s 3V i n s t e a d of 5V. Thus, st a g e #1 per f o r m s the a d d i t i o n a l f u n c t i o n of l e v e l s h i f t i n g , and can c o n v e r t a TTL i n p u t s i g n a l t o a CMOS s i g n a l f o r t h e i n t e r n a l c i r c u i t , or r e s t o r e a bad CMOS i n p u t s i g n a l ( w i t h v o l t a g e lower than normal) t o a good one. Now we t u r n our a t t e n t i o n t o the o u t p u t pad d e s i g n . The t r a d i t i o n a l o u t p u t pad u s u a l l y c o n t a i n s t h r e e i n v e r t e r d r i v e r s w i t h an i n c r e a s i n g s i z e r a t i o of 3 t o 4. The d e l a y time f o r such an o u t p u t pad i s g e n e r a l l y about 15-25ns. F o r our p i p e l i n e d m u l t i p l i e r , t h i s o u t p u t pad d e l a y w i l l be l o n g e r than the d e l a y 127 of each i n t e r n a l s t a g e . A new arrangement i s t h e r e f o r e n e c e s s a r y . Our d e s i g n has o n l y one l a r g e i n v e r t e r i n the output pad, and s a c r i f i c e s an e x t r a p i p e l i n e s tage ( s t a g e #14) t o d r i v e t h e gate l o a d of the ou t p u t pad ( F i g . 4 . 2 2 ) . The t r a n s i s t o r s a r e s i z e d such t h a t the d e l a y s of s t a g e #14 and the ou t p u t pad are e q u a l t o 10ns. Large t r a n s i s t o r s w i t h l a r g e v a l u e s -of w i d t h / l e n g t h r a t i o a r e r e q u i r e d i n the ou t p u t d r i v e r and pad d e s i g n . Gates of the s e t r a n s i s t o r s a r e u s u a l l y a r r a n g e d i n the form of a meander w i t h d r a i n and s o u r c e c o n t a c t s p l a c e d i n one of t h r e e d i f f e r e n t ways, as i l l u s t r a t e d i n F i g . 4 . 2 3 . The t r a n s i s t o r i n F i g . 4 . 2 3 ( a ) o c c u p i e s t h e l a r g e s t a r e a of t h e t h r e e , a l t h o u g h t h e s o u r c e and d r a i n r e s i s t a n c e s a r e m i n i m i z e d . To reduce t h e a r e a o c c u p i e d , t h e l a y o u t of F i g . 4 . 2 3 ( b ) may be used. U n f o r t u n a t e l y , t h i s s i m p l e placement of c o n t a c t s c a u s e s a d e g r a d a t i o n of t h e W/L r a t i o of t h e meander-type t r a n s i s t o r , i . e . , the a c t u a l W/L r a t i o i s much lower than the W/L v a l u e e s t i m a t e d from t h e t r a n s i s t o r ' s l a y o u t [ 4 1 ] . The W/L r a t i o d e g r a d a t i o n of the t r a n s i s t o r of F i g . 4 . 2 3 ( b ) i s due t o t h e d i s t r i b u t e d r e s i s t a n c e of t h e s o u r c e and d r a i n r e g i o n s . The v o l t a g e d r o p a l o n g t h e sou r c e and d r a i n r e g i o n s c a u s e s p o s i t i o n - d e p e n d e n t b i a s s i n g of the d r a i n - s o u r c e and g a t e - s o u r c e r e g i o n s of t h e t r a n s i s t o r . The most imp o r t a n t problem a p p e a r s t o be t h e d i f f e r e n c e s i n g a t e / s o u r c e v o l t a g e and [ DRAIN CONTACTS ////////////////////////A '4 SOURCE CONTACTS 6ATE ORAIN CONTACTS ^GATE >///////////< SOURCE CONTACTS ORAIN CONTACTS I I ^GATE SOURCE CONTACTS 2 (a) (b) (c) F i g . 4 . 2 3 The t h r e e t y p e s of c o n t a c t placement i n ou t p u t pad d e s i g n to CO 129 t h e l o c a l v a l u e s of s o u r c e / s u b s t r a t e v o l t a g e which a f f e c t l o c a l v a l u e s of t h r e s h o l d v o l t a g e . The p a r t of the t r a n s i s t o r which i s remote from the s o u r c e c o n t a c t , and t h e r e f o r e has a h i g h e r v a l u e of the t h r e s h o l d v o l t a g e and lower v a l u e of the g a t e - t o - s o u r c e v o l t a g e , b e g i n s t o s a t u r a t e , whereas the o t h e r p a r t of the t r a n s i s t o r s t i l l o p e r a t e s i n the t r i o d e r e g i o n . Even though a l l p a r t s of t h e t r a n s i s t o r approach s a t u r a t i o n , the l o c a l t h r e s h o l d v o l t a g e s and g a t e / s o u r c e v o l t a g e s s t i l l remain d i s t r i b u t e d n o n u n i f o r m l y a l o n g the t r a n s i s t o r g a t e , c a u s i n g a d e c r e a s e of t h e c u r r e n t i n those p a r t s of t h e c h a n n e l t h a t a r e remote from the s o u r c e c o n t a c t . The l a y o u t as i l l u s t r a t e d i n F i g . 4 . 2 3 ( c ) was chosen f o r o u t p u t pad d e s i g n i n t h i s work, and a l l e v i a t e s t h e W/L r a t i o d e g r a d a t i o n p r o blem w i t h o n l y a s m a l l p e n a l t y i n a r e a . The s o u r c e c o n t a c t s a r e p l a c e d as c l o s e as p o s s i b l e t o t h e t r a n s i s t o r , w h i l e l e a v i n g the d r a i n c o n t a c t s as b e f o r e . The c o n t r i b u t i o n of t h e d r a i n d i s t r i b u t e d r e s i s t a n c e t o t h e d e g r a d a t i o n i s f a r l e s s i m p o r t a n t t h a n the c o n t r i b u t i o n of t h e s o u r c e d i s t r i b u t e d r e s i s t a n c e . T h i s i s because v o l t a g e d r o p a l o n g t h e s o u r c e d i s t r i b u t e d r e s i s t a n c e i s " a m p l i f i e d " by i t s e f f e c t on the t h r e s h o l d and g a t e / s o u r c e v o l t a g e s . A n o t h e r problem i s the l a t c h - u p which may o c c u r i n the o u t p u t d r i v e r s . I n a b u l k CMOS p r o c e s s the p-n-p-n (or SCR) p a t h s a r e formed by p a r a s i t i c l a t e r a l pnp t r a n s i s t o r s and 130 v e r t i c a l npn t r a n s i s t o r s , as shown i n the c r o s s - s e c t i o n of a CMOS i n v e r t e r i n F i g . 4 . 2 4 . The i n v e r t e r can l a t c h up i n t h r e e d i f f e r e n t modes: ( a ) f r o m Vdd t o Gnd, ( b ) f r o m Vdd t o the out p u t node and ( c ) f r o m the o u t p u t node t o Gnd ( F i g . 4 . 2 5 ) . L a t c h - u p w i l l be t r i g g e r e d when j u n c t i o n s and j a r e f o r w a r d b i a s e d , and j i s r e v e r s e d b i a s e d . The l a r g e amount of h o l e s e m i t t e d from r e g i o n p^ sweeps a c r o s s j and p r o v i d e s s u f f i c i e n t base d r i v e f o r t h e npn t r a n s i s t o r o p e r a t i n g i n the a c t i v e mode. The e l e c t r o n s e m i t t e d from r e g i o n n^ w i l l , i n t u r n , p r o v i d e base c u r r e n t f o r t he pnp t r a n s i s t o r . T h i s a c t i o n i s r e g e n e r a t i v e i n n a t u r e and causes f a i l u r e of the i n v e r t e r . To h e l p p r e v e n t t he problem, we can e i t h e r i n c r e a s e the l a t e r a l pnp base w i d t h ( d e c r e a s e t he PNP t r a n s i s t o r g a i n ) or reduce t h e r e s i s t a n c e s R and R . In t h e case of t h e out p u t pad s w d e s i g n , t h e P - t r a n s i s t o r i s p l a c e d about l50Mm away from the p - w e l l and t h e a r e a i n between i s used t o accommodate t h e me t a l pad. I f t h e P - t r a n s i s t o r cannot be p l a c e d f a r enough away from the N - t r a n s i s t o r , f o r example, due t o a r e a c o n s t r a i n t s , then one must e n s u r e t h a t no p a r t of an e m i t t i n g j u n c t i o n i s p h y s i c a l l y d i s t a n t from a s u b s t r a t e o r p - w e l l c o n t a c t i n o r d e r t o reduce R s and R . A l a y o u t shown i n F i g . 4 . 2 6 may h e l p t o pr e v e n t w l a t c h - u p . A n o t h e r p o t e n t i a l cause of l a t c h - u p i n p - w e l l CMOS d e v i c e s i s due t o an improper power-up sequence [ 4 2 ] , Suppose a CMOS 131 F i g . 4 . 2 4 The c r o s s s e c t i o n of a CMOS i n v e r t e r w i t h p a r a s i t i c t r a n s i s t o r s shown vdd Vdd 1 OUTPUT Vdd 9 9 PI M Nl M Nl J J3 - J m — 1 OUTPUT M F i g . 4 . 2 5 The l a t c h - u p modes of a CMOS d r i v e r SUBSTRATE CONTACTS SOURCE CONTACTS SATE INPUT DRAIN CONTACTS SUBSTRATE CONTACTS ADDITIONAL RONS Of CONTACTS P-MEU CONTACTS M L SOURCE CONTACTS P-NELL CONTACTS P-MEU. OUTPUT F i g . 4 . 2 6 A l a y o u t of output pad which h e l p t o p r e v e n t l a t c h - u p to to 133 i n v e r t e r d r i v e r i s f e d by an abnormal power-up sequence, where V i s r a i s e d b e f o r e Vdd (see F i g . 4 . 2 7 ) . At t h e b e g i n n i n g of out power-up, when V i s f i r s t r a i s e d , base d r i v e i s s u p p l i e d t o out the l a t e r a l pnp, t u r n i n g i t on (see the model i n F i g . 4 . 2 5 ( c ) ) . T h i s t e n d s t o t u r n on the v e r t i c a l npn a l s o , which w i l l h e l p s u p p l y base d r i v e t o t h e l a t e r a l pnp. At the p o i n t when Vdd i s r a i s e d , i t may t e n d t o s u s t a i n the l a t c h - u p (see F i g . 4 . 2 5 ( a ) ) The remedy i s t o add a d i o d e , as shown i n F i g . 4 . 2 8 , so t h a t c u r r e n t cannot f l o w back from r e g i o n n^ t o t h e Vdd l i n e which i s m o m e n t a r i l y low a t the b e g i n n i n g , thus r e d u c i n g the p o t e n t i a l f o r l a t c h - u p b e i n g . t r i g g e r e d . T h i s t e c h n i q u e i s e s p e c i a l l y u s e f u l where TC boards c o n t a i n i n g CMOS c h i p s have t o be "hot p l u g g a b l e " , i . e . , i n s e r t e d and removed w h i l e power i s on. 4.6 FLOOR PLAN AND CELL LAYOUTS The f l o o r p l a n of the m u l t i p l i e r i s shown i n F i g . 4 . 2 9 . The i n p u t pads a r e l o c a t e d a t one edge w h i l e the o u t p u t pads a r e p l a c e d a t t h e o p p o s i t e edge. Two i n p u t pads a r e used f o r each of the c l o c k s i g n a l s 0 and 0 ', so t h a t t h e c u r r e n t f l o w t h r o u g h the c l o c k b u sses i s h a l v e d and t h e v o l t a g e d r o p a c r o s s the busses i s r e d u c e d . Two s e t s of Vdd and Gnd pads a r e used f o r a s i m i l a r r e a s o n , t h u s r e d u c i n g t h e n o i s e c o u p l i n g t h r o u g h the power b u s s e s . The l a y o u t s of some of the major c e l l s a r e shown i n g.4.27 An abnormal power-up sequence f o r a CMOS i n v e r t e r F i g . 4 . 2 8 The a d d i t i o n of an d i o d e t o p r e v e n t l a t c h - u p 135 3D 8-BIT A's 8-BIT B's I INPUT PADS AND ORIVERS GnJ Gnj RECOOERS AND MULTIPLEXER RON DRIVERS MULTIPLEXER ROW MULTIPLEXER ROW MULTIPLEXER ROW ii-BIT CARRY LOOK-AHEAD ADDER 5-81T_ RIPFLE CARFY ADDER" VdJ OUTPUT PADS AND DRIVERS to VdJ 16-BIT P's t F i g . 4 . 2 9 The f l o o r p l a n o f t h e m u l t i p l i e r 136 Appendix C. The whole c h i p w i t h pads measures 4mm by 4mm and w i l l be mounted i n a 4 0 - p i n package. The d e s i g n was s u b m i t t e d t o th e Canadian M i c r o e l e c t r o n i c s Corp, the s i l i c o n b r o k e r f o r N o r t h e r n Telecom, i n J a n u a r y 1986. 137 CHAPTER 5 : CONCLUSION The new CMOS c i r c u i t t e c h n i q u e of cascode v o l t a g e s w i t c h l o g i c has been examined i n t h i s t h e s i s . The f e a t u r e s of c i r c u i t d e s i g n , c i r c u i t w i r a b i l i t y and c i r c u i t l a y o u t have been d i s c u s s e d i n the c o n t e x t of b o t h ' s t a t i c and dynamic o p e r a t i o n . A comparison of the v a r i o u s forms of CVS l o g i c w i t h more c o n v e n t i o n a l CMOS t e c h n i q u e s , i . e . f u l l CMOS and NORA, has been made v i a SPICE s i m u l a t i o n s of a f u l l adder c i r c u i t . I t i s shown t h a t t h e d i f f e r e n t i a l s p l i t l e v e l form of CVS i s the f a s t e s t s t a t i c i m p l e m e n t a t i o n . F o r dynamic c i r c u i t r y the DCVS c i r c u i t i s f a s t e s t . The major c o n t r i b u t i o n of t h e work i s the p o s t u l a t i o n and development of two n o v e l p r o c e d u r e s f o r the d e s i g n of CVS t r e e s [ 4 3 ] . One method i s based on Karnaugh mapping t e c h n i q u e s and i s s u i t a b l e f o r c i r c u i t s whose Boolean f u n c t i o n s of s i x or l e s s v a r i a b l e s need t o be e v a l u a t e d . The o t h e r method, based on the Quine-McCluskey t a b u l a r method, i s more t e d i o u s t o a p p l y but i s s u i t a b l e f o r any number of v a r i a b l e s . Both t h e s e methods a r e s i m p l e r and more i n s i g h t f u l than CVS d e s i g n methods p r e v i o u s l y p u b l i s h e d . The n o v e l d e s i g n methods have been used i n t h i s t h e s i s t o l a y o u t an 8x8 p i p e l i n e d m u l t i p l i e r . SPICE s i m u l a t i o n s i n d i c a t e t h a t t h e m u l t i p l i e r w i l l r un a t 50MHz. The m u l t i p l i e r c h i p i s 138 b e i n g f a b r i c a t e d a t N o r t h e r n Telecom, Ottawa. The cascode v o l t a g e s w i t c h l o g i c f a m i l y c e r t a i n l y has advantages over a l l o t h e r c o n v e n t i o n a l MOS l o g i c f a m i l i e s i n term of performance. However, w i r i n g up the c i r c u i t s may be d i f f i c u l t because of the l a r g e number of d u a l s i g n a l l i n e s and the i r r e g u l a r t r e e s t r u c t u r e s . I t i s recommended t h a t , i f both a r e a e f f i c i e n t and f a s t c i r c u i t have t o be implemented, a r e g u l a r a r c h i t e c t u r e w i t h r e p e a t e d c e l l s s h o u l d be sought. 139 REFERENCES 1. L . G . H e l l e r and W.R.Gr i f f i n , "Cascode V o l t a g e S w i t c h L o g i c : A D i f f e r e n t i a l CMOS L o g i c F a m i l y " , P r o c . IEEE ISSCC, pp.16-17, 1984. 2. C . K . 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K.Hwang, Computer A r i t h m e t i c : P r i n c i p l e s , A r c h i t e c t u r e , and D e s i g n , W i l e y : New Yo r k , pp.161-84, 1979. 26. C.S.Wallace, "A S u g g e s t i o n f o r a F a s t M u l t i p l i e r " , IEEE T r a n s , on E l e c t r o n i c Computers, 14-17, 1964. 27. W.K.Luk, "A R e g u l a r Layout f o r P a r a l l e l M u l t i p l i e r of 142 0( l o g N) Time", CMU Confer e n c e on VLSI Systems and Comp u t a t i o n s , P i t t s b u r g , Penn., pp.317-26, 1981. 28. P . R . C a p p e l l o and K . S t e i g l i t z , "A VLSI Layout f o r a P i p e l i n e d Dadda M u l t i p l i e r " , ACM T r a n s , on Computer Systems, v o l . 1 , pp.157-174, 1983. 29. O.L.MacSorley, "High-Speed A r i t h m a t i c i n B i n a r y Computers", P r o c . IRE, v o l . 4 9 , pp.67-91, 1961. 30. L . P . R u b i n f i e l d , "A P r o o f of the M o d i f i e d Booth's A l g o r i t h m f o r M u l t i p l i c a t i o n " , IEEE T r a n s , of Computers, v o l . 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P u u k i l a , "CMC Guide f o r D e s i g n e r s U s i n g the N o r t h e r n 143 Telecom CMOS3 P r o c e s s " , Report No. IC85-6, Canadian M i c r o e l e c t r o n i c s C o r p o r a t i o n , 1985. 37. A . V l a d i m i r e s c u and S . L i u , "The S i m u l a t i o n of MOS I n t e g r a t e d C i r c u i t s U s i n g SPICE2," E l e c t o n i c s R e s e a r c h L a b o r a t o r y , UC B e r k e l e y , 1980. 38. H.E.Oldham and S . L . P a r t r i d g e , "Comparison of MOS P r o c e s s e s f o r V L S I " , I EE P r o c , v o l . 130, 94-104, 1983. 39. G . B i l a r d i , M . P r a c c h i and F . P . P r e p a r a t a , "A C r i t i q u e of Network Speed i n VLSI Models of C omputation", IEEE J o u r n a l of S o l i d - S t a t e C i r c u i t s , v o l . S C - 1 7 , 696-702, 1982. 40. C.Mead and L.Conway, I n t r o d u c t i o n t o VLSI Systems, Addison-Wesley, pp.22-3, 1980. 41. M.Maly and M . S y r z y c k i , "Layout R e l a t e d D e f o r m a t i o n s of Meander-type MOS T r a n s i s t o r I/V C h a r a c t e r i s t i c s " , IEE P r o c , v o l . 132, 13-6, 1985. 42. A.H.Taber, " C i r c u i t Technique t o H e l p P r e v e n t CMOS L a t c h - u p " , IBM T e c h n i c a l D i s c l o s u r e B u l l e t i n , v o l . 2 6 , 5296-8, 1984. 43. K.M.Chu and D . L . P u l f r e y , "Design P r o c e d u r e s f o r D i f f e r e n t i a l Cascode V o l t a g e S w i t c h C i r c u i t s " , IEEE J o u r n a l o f S o l i d - S t a t e C i r c u i t s , a c c e p t e d f o r p u b l i c a t i o n , 1986. 144 Appendix A : SPICE l i s t i n g s f o r t h e s i m u l a t i o n of f u l l a d ders In t h i s a p p e n d i x , the SPICE i n p u t and o u t p u t l i s t i n g s of t h r e e d i f f e r e n t f u l l a d d e r s a r e shown. The l e v e l 2 MOSFET parameters of the N o r t h e r n Telecom 3um CMOS p r o c e s s a r e used i n the s i m u l a t i o n s . The programs a r e run on the MTS system of the UBC computing f a c i l i t y . Listing of -0SL1 at 22:03:44 on APR 9, 1986 for CCId'KCHU Page 1 2 3 4 S 6 7 8 9 10 11 12 13 14 13 16 17 18 19 20 21 22 23 24 29 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 4S 46 47 48 49 50 51 52 S3 54 55 56 57 58 1»»««*«»04-09-86 ******** SPICE 20.1 (150CT80) ••••••••22:03:23***** "DIFFERENTIAL SPLIT LEVEL FULL ADDER (SUM CIRCUIT) 0*« INPUT LISTING TEMPERATURE • 27.000 DEO C .OPTIONS ITL4«1000 ITL5-0 LIMPTS-300 • ML1 14 2 1 1 PDEV2 L«3U W*12U A0-71.3P AS-66.2P + P0-38.4U PS-37.2U NRS"0.61 NRD-0.55 ML2 15 3 1 1 PDEV2 L-3U W-12U AD-71.3P AS-66.2P + PD-38.4U PS-37.2U NRS-0.61 NRD-0.55 MLS 14 16 3 O NDEV2 L"3U W-12U AD-71.3P AS-71.3P • PD-38.4U PS-38.4U NRS*0.55 NRO-0.55 ML4 15 16 2 0 NDEV2 L-3U W-12U A0-71.3P AS-71.3P • P0-38.4U PS-38.4U NRS-0.5S NRD-0.55 CL1 14 0 35F CL2 15 0 35F * M1 3 4 10 0 NDEV2 L-3U W-12U AO-121.7P AS-S4.0P • P0-3O.4U PS"21U NRS-.38 NRD-1.14 M2 2 5 10 0 NDEV2 L-3U W-12U AD-71.3P AS-54.0P + PD-38.4U PS"21U NRS-.38 NRD-0.43 M3 3 5 11 O NDEV2 L-3U W-12U AD-71.3P AS-54.0P • PD-3B.4U PS*21U NRS-.3B NRO-0.43 M4 2 4 11 O N0EV2 L-3U W-12U AD-71.3P AS-54.0P • P0-38.4U PS-21U NRS-.38 NRO-0.43 MS 10 7 12 0 NDEV2 L-3U W-12U A0-S4.0P AS-121.7P • PD-21U PS-50.4U NRS-1.14 NRD-.38 M6 10 6 13 0 NDEV2 L-3U W-12U AD»54.0P AS-71.3P + PD-21U PS-38.4U NRS-0.43 NRD-.38 M7 11 6 12 O NDEV2 L-3U H-12U A0-54.OP AS-54.0P • P0-21U PS-21U NRS-.38 NRD*.38 M8 11 7 13 0 NDEV2 L"3U W-12U AD-54.0P AS"54.0P + P0-21U PS"21U NRS-.38 NRD-.38 M9 12 9 O O NDEV2 L-3U W>12U A0-54.OP AS-71.3P • P0-21U PS-38.4U NRS-0.43 NR0-.38 M10 13 8 O 0 NDEV2 L-3U W-12U A0-S4.OP AS-71.3P • P0-21U PS-38.4U NRS-0.43 NRD-0.38 CI 2 0 10F C2 3 O 10F • VDD 1 0 OC S VREF 16 O DC 4.3 VA 8 0 PWL(0 S 25NS 5 29NS 0 45NS 0 VAN 9 O PWL(0 5 ENS S 10NS O 25NS O VB 6 0 PWHO 5 6NS 5 10NS O) VBN 7 O DC 5 VC 4 0 DC 5 VCN 5 0 PWL(0 5 6NS 5 10NS 0) * .MODEL PDEV2 PM0S(LEVEL-2 VT0--O.8 KP-5E-6 GAMMA-O.6 PHI-0.6 • LAMBDA-0.03 PB-0.6 CGS0-2.5E-10 CGDO-2.5E-10 CGB0-5.E-10 • RSH-80 CJ"1.5E-4 MJ-0.6 COSW-4.E-10 MJSW-0.6 JS-1.0E-5 01 9 C O 3 ro O v> 0> a a » 49NS S) 29NS 5 45NS 5 49NS O) •b Listing of 99 60 61 62 63 64 69 66 67 6B 69 70 71 72 73 74 79 76 77 78 79 60 81 82 83 84 89 86 B7 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 1 10 1 1 1 112 1 13 1 14 1 15 1 16 -DSL 1 at 12.-39.-9S on APR 7, 1986 for CCId-KCHU Page 2 • T0X-9.E-8 NSUB-3.E15 XJ«5.E-7 LD-2.SE-7 U0-250 • VMAX-0.7E9) .MODEL N0EV2 NM0S(LEVEL-2 VT0-0.7 KP-16E-6 SAMMA-1.1 PH1-0.6 • LAM8DA-0.01 PB-0.7 CGS0-3.E-10 CGD0-3.E-10 CGB0-9.E-10 • RSH-2S CJ-4.4E-4 MJ-0.5 CJSW-4.E-10 MJSW-0.3 JS-1.E-9 • T0X-9.E-8 NSUB-1.7E16 XJ-6.E-7 LD-3.5E-7 UO-775 • VMAX-1.E5) .MODEL P0EV3 PM0S(LEVEL-3 VTO--O.B KP-5E-6 GAMMA«0.6 PHt-0.6 • PB"0.6 CGS0-2.5E-1O CGD0-2.5E-1O CGB0"5.E-1O • RSH-BO CJ-1.5E-4 MvJ-0.6 CJSW-4.E-10 MJSH-0.6 JS-1.0E-9 • T0X-5.E-8 NSUB-S.E19 XJ-5.E-7 LD-2.5E-7 U0-25O • VMAX-0.7E5 THETA-0.13 KAPPA-1.0 ETA-0.3) .MODEL NDEV3 NMOSUEVEL-3 VTO-0.7 KP-16E-6 OAMMA-1.1 PHI-0.6 • PB-0.7 CGS0-3.E-10 CGDD-3.E-10 CGBO-5.E-10 • RSH-25 CJ-4.4E-4 MJ'0.5 CJSW-4.E-10 MdSW-0.3 JS-1.E-9 • T0X-9.E-B NSUB-1.7E16 XJ-6.E-7 LD-3.5E-7 UO-775 • VMAX-1.E5 THETA-0.11 KAPPA-1.0 ETA-0.05) • .WIDTH OUT-80 .IC V(2)-.3 V(3)-0.3 V(10)-2 V O O - . 2 V<12)-.1 V(13)-.1 . TRAN . 5NS 60NS UK .PLOT TRAN V(2) V(3) V(I4) V(1S) (0,5) .END ........04-07-86 ••*••••• SPICE 20.1 (1S0CT80) ••••••••11:44:13****« OOSL 3-XDR TREE WIDTH-12U 0«**« MOSFET MODEL PARAMETERS TEMPERATURE - 27.000 DEG C 0....................................................................... PDEV2 NDEV2 PDEV3 NDEV3 OTVPE PMOS NMOS PMOS NMOS OLEVEL 2.000 2.000 3.000 3.000 OVTO -0.800 0.700 -0.800 0.700 OKP 9 .OOE-06 1 60E-05 S 00E-O6 1 60E-05 OGAMMA 0.600 1 . 100 0.600 1 . 100 OPHI 0.600 0.600 O.60O 0.600 OLAMBOA 3 .OOE-02 1 OOE-02 0 0 0 0 OPB 0.600 0.700 0.600 0.700 OCGSO 2 .90E-10 3 OOE-10 2 50E-10 3 OOE-10 OCGDO 2 .50E-10 3.00E-10 2 50E-10 3 OOE-IO OCGBO 9 .OOE-10 5 OOE-10 5 OOE-10 5 OOE-10 ORSH BO. 000 25.0O0 80.000 25.000 OCd 4 . 50E-04 4 40E-04 1 50E-04 4 40E-04 OMd 0.600 0.500 0.600 0.500 OCOSW 4 .OOE-10 4 OOE-10 4 OOE-10 4 OOE-10 OMJSW 0.600 0.300 0.600 0.300 OOS 1 .OOE-05 1 OOE-05 1 OOE-05 1 00E-05 OTOX 9 .OOE-08 5 OOE-08 S.00E-08 5 OOE-08 ONSUB 5 .00E*15 1 TOE*16 5 00E*15 1 70E+16 OX J 5 -OOE-07 6 OOE-07 5 OOE-07 6 OOE-07 OLD 2 .50E-07 3 50E-07 2 50E-07 3 50E -07 OUO 250.000 775.000 250.OOO 775.000 OVMAX 7 .00E*04 1 00E*05 7 O0E*04 1 00E+05 Listing of -0SL1 at 12:35:53 on APR 7. 19B6 for CC1d«KCHU Page 3 117 OTHETA 0.0 0.0 0.130 0.110 IIS OETA 0.0 0.0 0.300 0.050 119 OKAPPA 0.200 0.200 1.000 1.000 120 121 122 ODSL 3-XOR TREE WIDTH* 12U 123 124 0*«*» TRANSIENT ANALYSIS TEMPERATURE • 123 126 127 128 129 OLEQEND: 130 131 • ; V(2) 132 •; V(3) 133 • ; V(14) 134 $: V(1S) 133 X 136 TIME V(2) 137 138 x(.*.$) — 0.0 1.250E*00 2.3O0E+0O 139 140 0 0 2 203E+00 X X 141 3 OOOE-10 1 453E*00 . X •» 142 1 O00E-09 1.258E+00 X X 143 1 3O0E-09 1 . 136E*00 X. X 144 2 OOOE-09 1 .060E*00 X . -» 14S 2 500E-09 9 990E-01 X X 146 3 OOOE-09 9 621E-01 X •» 147 3 500E-09 9 292E-01 X X 148 4 OOOE-09 9 O68E-01 X . $-149 4 500E-09 8 850E-01 X X 150 5 OOOE-09 8 719E-01 X X 151 3 500E-09 8 588E-01 X X 152 6 OOOE-09 8 486E-01 X X 153 6 5O0E-09 8 004E-01 X X 154 7 000E-09 7 716E-01 X X 155 7 SOOE-09 7 644E-01 X . $• 156 8 OOOE-09 7 614E-01 X X 157 8 300E-09 7 767E-01 X X 158 9 OOOE-09 8 023E-01 X . J " 159 9 5O0E-09 8 434E-01 . $• 160 f O00E-08 8 697E-01 *+ %m 161 1 050E-08 9 O33E-01 * • . $ « 162 1 100E-08 9 25BE-01 • +. $ " 163 1 150E-08 9 3B2E-01 * + $ • 164 1 200E-0B 9 410E-01 • .• $ -165 1 250E-08 9 433E-01 * . +$ 166 1 30OE-08 9 307E-01 ' . * * 167 1 350E-0B 9 180E-01 • . $ • -168 1 400E-08 9 018E-01 • .» + 169 1 450E-08 8 835E-01 * .* • 170 1 500E-08 B 636E-01 • $ + 171 1 550E-08 8 3B3E-01 • * • 172 1 60OE-0B 8 .131E-01 • $. + . 173 1 650E-08 7 .873E-01 • t. * 174 1 700E-08 7 .615E-01 • * . * 11:44:13* 3.7S0E+00 5.0O0E*OO Listing of -05L1 at 12:39:55 on APR 7. 1986 fop CCId-KCHU Page 179 1 790E-08 7.356E-01 . * $ . • 176 1 8O0E-O8 7.094E-01 . • « . + • 177 1 850E-08 6.834E-01 . * $ . * 178 1 90OE-08 6 600E-01 . * * + • 179 1 950E-08 6 366E-01 . • * + • 180 2 OOOE-08 6 149E-01 . * $ • • 181 2 O50E-08 5 941E-01 . • $ • m 182 2 100E-08 9 741E-01 . • * + m 183 2 150E-O8 9 S64E-01 . • $ + • 184 2 2OOE-08 9 388E-01 . * f + • 185 2 250E-O8 9 231E-01 . • $ • 186 2 3O0E-O8 9 O79E-01 . • $ • 187 2 350E-08 4 937E-01 . • $ • 188 3 400E-08 4 808E-01 . • $ » 189 2 450E-08 4 679E-01 . • 190 2 5O0E-O8 4 563E-01 . • » • 191 2 550E-08 4 427E-01 . • * • 192 2 600E-08 4 297E-01 . • $ + . 193 2 650E-08 4 225E-01 . • $ 194 2 700E-08 4 196E-01 . • $ 195 2 750E-O8 4 229E-01 . • $ 196 2 800E-08 4 348E-01 . * $ 197 2 B50E-08 4 471E-01 . * $ • • 198 2 900E-08 4 780E-01 . • t + » 199 2 950E-08 5 248E-01 . • $ 4 200 3 OOOE-08 9 B59E-01 . * $ 4 • 201 3 0S0E-08 6 601E-01 . • $ . * • 202 3 10OE-08 7 366E-01 . • $ . • • 203 3 150E-08 8 203E-01 . • *.• • 204 3 200E-08 9 085E-O1 . • .X 205 3 250E-08 9 977E-01 . • • $ 206 3 3OOE-08 1 090E+00 . • 4 * • 207 3 350E-08 1 183E+00 . • 4 S • 208 3 4O0E-0B 1 277E*00 . X • 209 3 450E-08 1 371E+00 . t • 210 3 5O0E-O8 1 464E+O0 . • « • 211 3 550E-08 1 554E+O0 . 4 • t " 212 3 600E-0B 1 644E400 . 4 • 213 3 650E-08 1 728E+00 . • • t 214 3 7O0E-O8 1 811E+00 . • • % 215 3.750E-08 1 868E+00 . • • $ 216 3 BOOE-08 1 909E*0O . * * $ . 217 3 B50E-08 1 950E+00 . 4 . « • 218 3 9OOE-08 1 991E*00 . ft 219 3 950E-08 2 033E+00 . • f 220 4 OOOE-08 2 067E*00 . 4 m * $ 221 4 050E-08 2 099E400 . 4 m * f 222 4 10OE-08 2 130E+00 . 4 m . ft t 223 4 150E-08 2 157E+00 . • • . ft % 224 4 2O0E-O8 2 184E+00 . 4 m . • * % 225 4 250E-08 2 207E*O0 . 4 • • % 226 4 300E-08 2 230E+00 . 4- • * % 227 4 350E-08 2 25OE+0O . 4 • ft % 228 4 400E-OB 2 269E+0O . • • ft % 229 4 450E-08 2 288E*00 . 4 • ft $ 230 4 500E-08 2 305E*00 . 4 • ft $ 231 4 550E-0B 2 322E*00 . 4- • • * 232 4 600E-08 2 337E*0O . 4 • ft Listing of -0SL1 at 12:39:59 on APR T. 1986 for CCId-KCHU Page 233 4 690E-08 2 33BE*00 . • 234 4 700E-08 2 335E*00 . + • • 239 4 750E-08 2 273E«00 . • • * 236 4 800E-08 2 195E*00 . • • * 237 4 850E-0B 2 055E+0O . • • • 238 4 900E-08 1 B85E«00 . • • • 239 4 950E-O8 1 692E*00 . • • * 240 3 O00E-O8 1 543E*00 . • • . • 241 S 050E-08 1 433E*00 . + » . • 242 5 100E-08 1 368E+00 . • ». • 243 5 130E-08 1 317E*00 . 244 5 2O0E-O8 1 289E*00 . 245 5 250E-08 1 269E+00 . * • • 246 5.300E-08 1 254E*00 . 247 5 350E-08 1 246E*00 . X 248 3 400E-08 1 238E*00 . 249 3 450E-08 1 234E*O0 . 290 9 5O0E-O8 1 230E*OO . • • • 251 3 550E-O8 1 218E*00 . • + X. 252 3 600E-08 1 203E+00 . •. + $ . 253 5 650E-08 1 182E*00 . • * 254 3 700E-08 1 I45E*00 . ** 235 3 750E-08 1 109E+00 . • . $• 256 9 8O0E-O8 1 064E*00 . • . * * 257 5 850E-O8 1 017E*00 . • . $ • 258 9 9O0E-08 9 714E-01 . • . $ • 259 5.950E-08 9 272E-01 . • .t + 260 6 000E-08 8 830E-01 . * t • 261 262 263 264 Y 265 0 266 JOB CONCLUDED 267 0 TOTAL JOB TIME 0.0 Listing of -CV4 at 22:05:31 on APR 9. 1986 for CC1d«KCHU Page 1 1 1"««««»04-09-86 •••••»•* SPICE 2G.1 (150CT80) ••••••••22 :05: 19«"*« 2 3 OSTATIC OCVS FULL ADDER (SUM CIRCUIT) 4 5 <>••*• INPUT LISTING TEMPERATURE • 27.000 DEG C 6 7 Q . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 9 10 11 .OPTIONS ITL4-1000 ITL5«0 LIMPTS-300 12 • 13 ML 1 7 8 1 1 P0EV2 L-3U W«9U AD-49.7P AS-46.4P 14 * PD-32.4U PS-31.2U NRS«0.67 NRO'0.61 15 ML2 8 7 11 PDEV2 L-3U V"9U AD>49.7P AS-46.4P 16 • PD-32.4U PS-31.2U NRS-0.67 NRD'0.61 1 0 17 • g 18 Ml 8 13 10 O NDEV2 L-3U W-12U AD-58.7P AS-58.7P c 19 • PD"38.4U PS-38.4U NRS«0.52 NRD'0.52 M 20 M2 7 13 9 0 N0EV2 L"3U W-12U AD-S8.7P AS-S8.7P J> 21 • PD-38.4U PS"38.4U NRS»0.52 NRD«0.S2 |J. 22 M3 8 14 9 0 NDEV2 L-3U W>12U AD'58.7P AS-58.7P Q 23 * PD-38.4U PS-38.4U NRS'0.52 NRD-0.52 3 24 M4 7 14 10 O N0EV2 L"3U W-12U AD-58.7P AS-58.7P 23 + PD-38.4U PS-38.4U NRS".52 NRD-0.52 ° 26 MS 10 15 12 O NDEV2 L-3U W«12U AD-58.7P AS-58.7P 27 + P0-3B.4U PS'38.4U NRS"0 52 NRD..52 rt 28 M6 9 15 11 O NDEV2 L-3U W-12U AD-58.7P AS"5B.7P 3" 29 • PD-38.4U PS-38.4U NRS'0.52 NR0..52 * 30 M7 10 16 11 O NDEV2 L-3U W-12U AD«58.7P AS"58.7P m 31 • P0-38.4U PS-38.4U NRS-.52 NRD-.52 rr 32 MS 9 16 12 0 NDEV2 L'3U W-12U AD'58.7P AS-58.7P 01 33 • PD-38.4U PS-38.4U NRS-.52 NRD',52 "* 34 M9 11 17 O O N0EV2 L-3U W-12U A0-58.7P AS-9S.4P 33 + PD-38.4U PS*37.2U NRS>0.52 NR0-.58 36 M10 12 18 0 O NDEV2 L-3U W-12U AD-S8.7P AS-55.4P O 37 • PD-3B.4U PS-37.2U NRS>0.52 NRD'0.58 2 38 CL1 7 O 60F S 39 CL2 8 O 60F 40 • M I 41 VDD 1 0 DC 3 C 42 VA 13 O DC 3 £ 43 VAN 14 O PWL(0 3 9NS 3 11NS 0) 44 VB 13 0 DC 3 01 45 VBN 16 O PHL(0 3 9NS 5 11NS 0) Q. 46 VC 17 O PWL(0 3 34NS 5 36NS O) g* 47 VCN 18 0 PWL(0 5 9NS 5 11NS O 34NS 0 36NS 3) ™ 48 • 49 .MODEL P0EV2 PM0S(LEVEL-2 VTO'-O.B KP-5E-6 QAMMA-0.6 PHI-0.6 50 • LAMBDA-0.03 PB-0.6 CGS0-2.5E-1O CG00"2.5E-10 CGBO'S.E-10 51 + RSH-80 CU-1.5E-4 Md-0.6 CJSW-4.E-10 MJSW-0.6 JS«1.0E-5 52 + T0X-5.E-8 NSUB-5.E15 XJ-5.E-7 LD-2.5E-7 UO-250 53 + VMAX-0.7E5) 54 .MOOEL NDEV2 NM0S(LEVEL-2 VT0-0.7 KP-16E-6 GAMMA"1.1 PHI-0.6 55 + LAM8DA=0.01 PB-0.7 CGS0"3.E-10 CGD0-3.E-1O CGB0«5.E-10 56 + RSH=25 CJ»4.4E-4 MJ-O.S CJSV-4.E-10 MdSW'0.3 JS"1.E-5 — 57 + T0X-5.E-8 NSUB-1.7E16 X0"6.E-7 LD-3.5E-7 UO-775 Ol 58 + VMAX'I.ES) ° Listing of -CV4 at 12:33:33 on APR 7, 1986 for CCId-KCHU Page 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 73 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 1 10 111 112 113 1 14 115 116 .MODEL PDEV3 PMDSUEVEL-3 VTO—0.8 KP-5E-6 GAMMA"0.6 PHI-0.6 • PB-0.6 CGS0«2.5E-I0 CGO0-2.3E-1O CGBO-S.E-IO • RSH-80 Cd-I.SE-4 Md-0.6 C0SW-4.E-1O MdSW-0.6 JS-1.0E-5 • T0X-5.E-8 NSUB-5.E1S Xd-S.E-7 LD-2.SE-7 UO-250 • VMAX-0.7E3 THETA-0.13 KAPPA-1.0 ETA-0.3) .MODEL NDEV3 NM0S(LEVEL-3 VTO-0.7 KP-16E-6 GAMMA"1.1 PHI-0.6 • PB-0.7 CGS0-3.E-10 CGOO-3.E-10 CGB0-3.E-10 • RSH-2S CJ-4.4E-4 MJ-0.5 C.JSW-4.E-10 MJSW-0.3 JS-1.E-5 • T0X-5.E-B NSUB-1.7E16 XJ-6.E-7 LD-3.5E-7 UO-775 • VMAX-1.E5 THETA-0.11 KAPPA-1.0 ETA-0.05) « .WIDTH OUT"80 .IC V(7)-.4 V(8)-.4 • V(9)-.3 V(10)-.3 V(11)-.2 V(12)-.2 • V(1)-3 .TRAN .5N5 TONS UIC .PLOT TRAN V(7) V(8) (0,3) . END 1>..«*».04-07-86 •••••••* SPICE 2G.1 (130CT80) •••••••»12:27:19-OCVSL 3-WAY EXCLUSIVE-OR WIDTH-12U <)•••• 0»»««« MOSFET MODEL PARAMETERS TEMPERATURE • 27.000 DEG C OTYPE OLEVEL OVTO OKP OGAMMA OPHI OLAMBDA OPB OCGSO OCGOO OCGBO ORSH OCJ OMJ OCJSW OMJSW OJS OTOX ONSUB OX J OLD OUO OVMAX OTHETA OETA OKAPPA ....... PDEV2 PMOS 2.000 -0.800 3.COE-06 0.600 0.600 3.OOE-02 0.600 2.S0E-10 2.50E-10 5.OOE-10 80.000 1.50E-04 0.600 4.OOE-10 0.600 1.OOE-05 3.OOE-08 5.00E+15 5. OOE-07 2.50E-07 250. OOO 7.00E+04 0.0 0.0 0.200 "04-07-86 *•• NDEV2 NMOS 2.000 0.700 1.60E-05 1 . 1O0 0.600 1.OOE-02 0.700 3.OOE-10 3.OOE-10 5.OOE-10 25.OOO 4.40E-04 0.500 4.OOE-10 0.300 1.OOE-05 5. OOE-08 1.70E*16 6.O0E-07 3.50E-07 775.000 1 .OOE+05 0.0 0.0 0.200 SPI PDEV3 PMOS 3.000 -0.800 S.OOE-06 0.600 0.600 0.0 0.600 2.50E-10 2.30E-10 3.OOE-10 80.000 1.50E-04 0.600 4.OOE-10 0.600 1.OOE-05 3.OOE-08 5.00E+15 5.OOE-07 2.50E-07 250.000 7.00E+04 O. 130 0.300 1 .000 CE 2G.1 ( NDEV3 NMOS 3.000 0. 700 1.60E-05 1. 100 0.600 0.0 0.700 3.OOE-10 3.OOE-10 5.OOE-10 25.OOO 4.40E-04 O.SOO 4.OOE-10 0.300 1.OOE-05 5. OOE-08 1.70E*16 6. OOE-07 3.50E-07 775.000 1,O0E*O5 O. 1 10 0.050 1 .000 150CTB0) * Listing of -CV4 at 12:35:32 on APR 7. 1986 for CCId-KCHU Page 3 11? OCVSL 3-MY EXCLUSIVE-OR WIDTH-12U 118 119 0**»» TRANSIENT ANALYSIS TEMPERATURE • 120 121 122 123 124 OLEQEND: 125 126 • . V(7) 127 •: V(8) 128 X 129 TIME V(7) 130 131 xc*) 0.0 1. 250E+00 2 .500E+00 132 133 0 0 7.118E-01 . X 134 5 OOOE-IO 1.278E+O0 . X 135 1 OOOE-09 1 . 165E*00 . X. 136 1 5O0E-09 1.044E+00 . X . 137 2 OOOE-09 9.539E-01 . X 138 3 500E-09 8.792E-01 . X . • 139 3 OOOE-09 8.293E-01 . X 140 3 500E-09 7.910E-01 . X 141 4 OOOE-09 7.526E-01 . X 142 4 500E-09 7.336E-01 . X 143 5 000E-09 7.173E-01 . X 144 5 500E-09 7.017E-01 . X 145 6 OOOE-09 6.947E-01 . X 146 6 500E-09 6.878E-01 . X 147 7 OOOE-09 6.819E-01 . X 148 7 S00E-O9 6.789E-01 . X 149 8 OOOE-09 6.759E-01 . X 150 8 500E-09 6.737E-01 . X 151 9 OOOE-09 6.724E-01 . X 152 9 SOOE-09 5.795E-01 . X 153 1 OOOE-08 5.192E-01 . X 154 1 050E-08 3.040E-01 . X 155 1 1O0E-O8 5.480E-01 . X 156 1 150E-O8 6.177E-01 . X 157 1 200E-08 6.760E-01 . X 158 1 250E-08 7.161E-01 . * + 159 1 3O0E-O8 7.390E-01 . 160 1 3S0E-O8 7.619E-01 . • • . 161 1 400E-08 7.549E-01 . • + 162 1 450E-08 7.442E-01 . 163 1 500E-08 7.317E-01 . • . + 164 1 550E-08 7.002E-01 . 165 1 600E-08 6.687E-01 . » . + 166 1 650E-O8 6.340E-01 . • + 167 1 700E-08 5.915E-01 . * + 168 1 7S0E-08 5.490E-01 . 169 1 800E-08 5.057E-01 . * +. 170 1 850E-08 4.6I4E-01 . 171 1 900E-0B 4.172E-01 . * + 172 1 9S0E-08 3.7S9E-01 . 173 2 OOOE-08 3.359E-01 . 174 2 .050E-08 2.95BE-01 . * 3.7SOE+00 S.OOOE+OO K) Listing of -CV4 at 12:38:32 on APR 7. 1986 for CCId'KCHU Page 4 179 2 100E-08 2 623E-01 * + 176 2 150E-08 2 296E-01 • + . 177 2 200E-08 1 976E-01 * 178 2 250E-08 1 726E-01 * . + 179 2.300E-08 1 475E-01 • + 180 2. 350E-08 1 2S0E-01 . * 181 2 400E-08 1 086E-01 . * + 182 2 450E-O8 9 228E-02 . * • 183 2.500E-08 7 8E9E-02 • 184 2 550E-08 6 798E-02 185 2 600E-08 5 T2TE-02 . * 186 2. 650E-08 4 917E-02 . * • 187 2 700E-08 4 224E-02 188 2.750E-08 3 531E-02 189 2 800E-08 3.056E-02 190 2 B50E-08 2 608E-02 + 191 2 900E-08 2 174E-02 + . 192 2 950E-08 1 889E-02 • . 193 3 OOOE-08 1 603E-02 194 3 050E-08 1 390E-O2 195 3 100E-08 1 177E-02 196 3 150E-0B 1 005E-02 197 3 200E-08 8 663E-03 198 3 250E-08 7 628E-03 * . 199 3 300E-08 6 992E-03 200 3 350E-08 5 735E-03 201 3 400E-08 4 958E-03 202 3 450E-O8 8 55IE-03 203 3 SOOE-08 -2 011E-03 204 3 550E-08 -1 968E-02 205 3 600E-08 -4 117E-02 206 3 65OE-08 -6 266E-02 207 3 700E-08 -7 B57E-02 • 208 3 750E-OB -B 874E-02 • 209 3 800E-08 -9 356E-02 210 3 850E-08 -9 256E-02 + 211 3 900E-08 -8 339E-02 + 212 3 950E-08 -6 724E-02 • 213 4 OOOE-08 -4 877E-02 214 4 050E-08 -1 990E-02 215 4 100E-08 8 978E-03 * •. 216 4 150E-0B 4 284E-02 * • , 217 4 2O0E-08 8 046E-02 .« + . 218 4 250E-08 1 184E-OI . * + 219 4 3OOE-08 1 652E-01 . * • 220 4 350E-08 2 121E-01 * + 221 4 400E-08 2 638E-01 * * 222 4 450E-08 3 205E-01 * + 223 4 500E-08 3 771E-01 * + 224 4 5S0E-08 4 414E-01 * + 225 4 60OE-O8 5 090E-01 * + 226 4 650E-08 5 767E-01 * + 227 4 700E-0B 6 551E-01 * . + 228 4 750E-08 7 349E-01 • . • 229 4 800E-08 8 159E-01 230 4 B50E-O8 9 091E-01 • + 231 4 .900E-08 1 .002E*00 * + , 232 4 950E-08 1 .1OOE*0O *+ . <J1 L'lstlng of -CV4 at 12:35:32 on APR T, 1986 for CC1d-KCHU Page 233 B OOOE-08 1 208E+00 234 5 050E-08 1 317E+00 235 3 tOOE-08 1 434E*O0 236 3 150E-08 1 S59E+00 * • 237 3 200E-08 1 685E+00 238 3 250E-08 1 825E+00 + * 239 3 300E-08 1 972E+O0 • • 240 3 350E-08 2 118E+00 241 3 400E-08 2 282E+00 + • 242 3 450E-08 2 449E*0O + 243 3 500E-08 2 616E+00 + 244 3 550E-08 2 795E+00 • • 245 5 600E-08 2 974E+00 • • 246 3 650E-08 3 152E+00 • 247 3 7O0E-O8 3 327E+00 • • 248 5 750E-08 3 502E+00 • • 249 5 80OE-08 3 676E+00 250 3 850E-0B 3 847E+00 . • 231 3 900E-08 4 018E+00 252 3 950E-08 4 155E+00 . • • 233 6 OOOE-08 4 276E+00 .+ • 254 6 050E-08 4 397E+00 .* • 255 6 1O0E-08 4 4B0E+00 .+ * 256 6 150E-08 4 559E+00 . + • 257 6 200E-08 4 635E+00 .+ * 258 6 250E-08 4 682E+00 .• * 259 6 300E-OB 4 729E+00 • 260 6 350E-0B 4 770E+00 + * 261 6 4O0E-08 4 797E+00 + * 262 6 450E-08 4 B25E+00 + • 263 6 SOOE-08 4 B47E+00 + • 264 6 550E-0B 4 864E+00 * • 363 6 600E-08 4 881E+00 + 266 6 650E-08 4 893E+00 + 267 6 700E-08 4 9O3E+0O • 268 6 750E-08 4 913E+O0 + 269 6 BOOE-08 4 920E+00 • 270 6 B50E-08 4 927E+00 • 271 6 900E-08 4 934E+00 • 272 6 950E-08 4 939E+00 + 273 7 OOOE-08 4 944E+00 + 274 . 273 276 277 V 278 O 279 JOB CONCLUDED 280 0 TOTAL JOB TIME 0.0 281 JOB CONCLUDED 282 O TOTAL JOB TIME 0.0 155 0 1 o a. S i m u l a t i o n of the domino DCVS f u l l adder (c m n Oi u. 3 » ft o • * 8 o o a n D . n D . i f i o . v i • N O N O IP U> n tp < N I D I • o or D 3 O < Z < • O 3 3 p> a in *» to t „ 2 ^ .,- , • i O * * (P * • * i o • tt D Z < O • O _ _ . O n O a n a u a » or Z O Z O Z D Z • <p • ID fl 0 ) > -9 3 •» 3 to 3 w : 3 d * 9 • • o <M z • CM 3 • :_ n O n o n Z n z n z n z n z n z • « • • • • » • • » JWJifl JDJ3JDJDJ3J3 0 ) •> *» I • H O I o z < : CM I tP • V 16 * b • 3 « ) m pj in ) a i oc Z - J 2 : CM z CM > > o > c iono • o i CM CM CM - m > J CM U J > • O . to a in z in Z u>; - i 3 : N CM C CM - > "> U J i rs Q I H Z "•or) m 2 •* • O 3 • •» in •» |p - 4 o * - ") a. a ,=°= • » CM * » • in p-CD • • tn o oo m H in O D • < a o 2 < 3 CM CM 3 c »- m CM u * 6 • < • * i 3 tn i n o : ? ! • Z D . - J • 3 -I Pi •» > • CM ui CO > p n U J o a o 03 * 0> i in i i o o D • O O • < tr o or < o z < z a 3 3 Z CM I CM D D t a < c z ; i « 3 1 3 trt CO t n a i I i 2 - J R -J 3 - J 3 3 CM • » • » CM - 0 > • CM • > * U J CD > co U J a> a n u n o n z • a • 2 « ^ in z in tn o o. a O a O CM 3 3 O 3 -ro •» •» tn 3 or co 2 • CM CM * -cn • 6* • 3 tn co a « 2 - J « Q • < D < O or a 3 Z 3 Z CM CO CM i n m i n > in w • D O M < II O Q or 3 a Z CM Z CM CM II CM « **• CM it in > m I T i in x • * • O 3 O » a 3 II CO II m 3 tn P I tn n tn a n a » a - J a Z t Z J Z z T J CM ' • > CO U J I P ) Q C • Z i 1 CO U J CO o : co Q n z * 2 u > tn mo a O a cn o. co a u. u. - o o 3 3 m in • 9 CO 1 » - * " CD CM I- CM CM • » CM (P ( 0 ^ n i t i to i s a o o ••- a CM o. P I a •» • » P ) t P * » ( P C O C M P - C M C M f M CMOl^r • 9 CM CM PJ p> co <p m »- •» l e o R r - i n v n i t n * • • O O O O O O O Q O a . i n a . t p a r - a e o a o i a * - D . * - o . n c o n c o ^ e D * « e o ' - - c o i n t x i * - s ( P c o < - c o a> o o • ^ • C O ^ P J ^ C O ^ C O P J ^ P ) n ^ p i co CM P J I • • • O • • O • •. •»- n • CO »r O D N O » O N D * - 0 0 ) 0 - D O ) 0 ' - Q . O o, a a D . o. a. a a a. o o. *- n • ^ c M n - « t n i p t » - » m ' - - i - J Listing of -D0CVS4 at 12:36:17 on APR 7, 1986 for CCId-KCHU Page 2 99 VDO 1 0 DC 9 60 VCLK 2 0 PWL(0 0 14NS O 16NS 5 29NS 5 3INS 0 44NS 0 46N5 5) 61 VA 13 O DC 9 62 VAN 14 0 DC 0 63 VB 19 O DC 9 64 VBN 16 0 DC 0 65 VC 17 O PWL(0 9 42NS 9 44NS O) 66 VCN 18 O PWL(0 0 42NS O 44NS 5) 67 • 68 .MODEL PDEV2 PM0S(LEVEL-2 VT0»-0.8 KP-5E-6 GAMMA-0.6 PHI-0.6 69 • LAMBDA-0.03 PB-0.6 CGS0-2.5E-10 CGD0-2.5E-10 CGB0-5.E-1O 70 • RSH-80 CJ-1.5E-4 MJ-0.6 CJSW-4.E-10 MJSW-0.6 JS-1.0E-5 71 • T0X-9.E-8 NSUB-9.E19 XJ-9.E-7 LD"2.5E-7 U0-25O 72 • VMAX-0.7E3) 73 .MODEL NDEV2 NMOSUEVEL-2 VTO-0.7 KP>16E-6 GAMMA"1.1 PHI-0.6 74 • LAMBDA'0.01 PB-0.7 CGS0-3.E-1O CGD0-3.E-10 CGB0-5.E-10 75 • RSH-25 CJ-4.4E-4 MJ-0.5 CJSW-4.E-10 MJSW-0.3 JS-1.E-5 76 • T0X-5.E-B NSUB-1.7E16 XJ-6.E-7 LD-3.5E-7 U0-775 77 * VMAX-1.E5) 78 .MODEL PDEV3 PM0S(LEVEL-3 VT0--0.8 KP-5E-6 GAMMA"0.6 PHI-0.6 79 • PB-0.6 CGS0-2.5E-1O CG00-2.3E-1O CGB0-5.E-10 80 • RSH-80 Cd-1.SE-4 Md-0.6 CdSW-4.E-10 MJSW-0.6 JS-1.0E.-5 81 • T0X-5.E-8 NSUB-5.E13 XJ-5.E-7 LD-2.5E-7 U0-250 82 • VMAX-0.7E9 THETA-O.13 KAPPA-1.0 ETA-0.3) 83 .MODEL NDEV3 NM0S(LEVEL«3 VTO-0.7 KP-16E-6 GAMMA-1.1 PHI-0.6 84 + PB-0.7 CGS0-3.E-10 CGD0-3.E-10 CGB0-5.E-10 85 • RSH-25 CJ-4.4E-4 MJ-O.S CJSW-4.E-10 MJSW-0.3 JS-1.E-5 86 * T0X-5.E-B NSUB-1.7E16 XJ-6.E-7 L0-3.5E-7 U0-775 87 • VMAX-1.E5 THETA-O. 11 KAPPA-1.0 ETA-0.05) 88 • 89 .WIDTH OUT-80 90 .IC V(4)-.2 V(3)-4.9 V(6)-.1 V(9)-4.8 V(7)-.4 V(8)-.4 91 • V(9)«.3 V(10)-.3 V(11)-.2 V(12)-.2 92 * V(19)-.1 V(1)-9 V(2)-0 93 .TRAN .9NS 60NS UIC 94 .PLOT TRAN V(4) V(3) V(7) V(8) V(2) (0.9) 95 .END g G ........04.07-85 ........ SPICE 2G.1 (1S0CT80) ••••••••12:30:52***«« 97 98 ODOMINO CVSL 3-WAY EXCLUSIVE-OR WIDTH.12U 99 100 <»•••• MOSPET MODEL PARAMETERS TEMPERATURE • 27.000 DEO C 101 102 0»......«».»... 103 104 105 106 107 PDEV2 NDEV2 PDEV3 NDEV3 108 OTYPE PMOS NMOS PMOS NMOS 109 OLEVEL 2.000 2.000 3.000 3.000 110 OVTO -0.800 0.700 -0.800 0.700 1 1 1 OKP 5 :00E-06 1 .60E-05 5 00E-O6 1.60E-05 1 12 OGAMMA 0.600 1 . 1O0 0.6OO 1. 100 113 OPHI 0.600 0.600 0.60O 0.600 114 OLAMBDA 3 .OOE-02 1 .OOE-02 0. .0 0.0 1 15 OPB 0.600 0.700 0.600 0.700 116 OCGSO 2 .50E-10 3 .00E-10 2 .50E-10 3.00E-10 Listing of -D0CV54 at 12:36:17 on APR 7, 1966 for CCId-KCHU Page 3 117 OCGDO 2 50E-10 3 OOE-10 2.50E-10 3.OOE-10 118 OCGBO 3 OOE-IO 5 OOE-10 5.OOE-10 5.OOE-10 119 ORSH 80.000 25.000 80.000 25.000 120 OCJ 1 50E-04 4 40E-04 1.50E-04 4.40E-04 121 OMJ 0.600 0.500 0.600 0.500 122 OCJSW 4 OOE-IO 4 OOE-10 4.OOE-10 4.OOE-10 123 OMJSW 0.600 0.300 0.600 0.300 124 OJS 1 00E-05 1 00E-05 1.00E-05 1.00E-05 12S OTOX 5 OOE-08 3 OOE-08 5.OOE-08 5.OOE-08 126 ONSUB 5 00E+15 1 70E+16 5.00E+15 1.70E+16 127 OXJ 5 OOE-07 6 OOE-07 5.OOE-07 6.OOE-07 128 OLD 2 50E-07 3 SOE-07 2.50E-07 3.50E-07 129 OUO 250.000 775.OOO 250.OOO 775.000 130 OVMAX 7 OOE+04 1.OOE+05 7.00E+04 1.00E+05 131 OTHETA 0.0 0.0 0.130 0.110 132 OETA 0.0 0.0 0.300 0.050 133 OKAPPA 0.200 0.200 1.000 1.000 134 12:30:S2***** 135 136 OOONINO CVSL 3-WAY EXCLUSIVE-OR WIDTH*12U 137 138 0**>* TRANSIENT ANALYSIS TEMPERATURE • 27.000 DEG C 139 140 141 142 143 OLEGEND: 144 145 • : V(4) 146 +; V(3) 147 • ; V(7) 148 *: V(8) 149 0: V(2) 150 X 151 TIME V(4) 152 133 X(»*-$0) 1.250E+O0 2.300E*00 3.730E+00 5.OOOE+00 154 155 0 0 2.034E-01 0 • $ • 156 3 000E-10 7.532E-01 0 • . * - • 157 1 OOOE-09 1 .061E+0O 0 • . $ -158 1 50OE-O9 1.245E+00 0 • $ • 159 2 OOOE-09 1.336E+00 0 .$ • 160 2 300E-09 1.4O2E+0O 0 . • $ • 161 3 OOOE-09 1.442E+0O 0 * $ • '. 162 3 SO0E-O9 1.465E+O0 0 * t • 163 4 OOOE-09 1.480E+00 0 • .* • 164 4 S00E-09 1.492E+00 0 • $-165 S OOOE-09 1 .504E+00 0 * X 166 3 500E-09 1.515E+00 0 * X 167 6 OOOE-09 1 .525E+00 0 * X 168 6 500E-09 1.S35E+00 0 * X 169 7 OOOE-09 1 .540E+OO 0 * «$ 170 7 500E-09 1.545E+00 0 * X 171 8 OOOE-09 1.549E+00 0 • •* . 172 8 500E -09 1.552E+00 0 * -$ . 173 9 O0OE-O9 1.555E+00 0 • X . 174 9 5O0E-O9 1.5S7E+CO 0 * -$. Listing of -D0CVS4 at 12:36:17 on *PR 7, 1986 fop CC1d-KCHU Pags 4 173 1. OOOE-08 1 3S9E+00 0 • •t. 176 1.05OE-O8 1 561E+00 0 • •*. 177 1 1OOE-08 1 S62E+00 0 • •*. 178 1 150E-08 1 564E+0O 0 * X. 179 1 200E-08 1 965E+00 0 • X. 180 1 250E-08 1 566E+O0 0 • X. 181 1.300E-08 1 567E+00 0 * X. 182 1 350E-08 1 567E+00 0 * X. 183 1 40OE-O8 1 568E+00 0 * X. 184 1 450E-08 1 575E+00 0 * «$ 183 1 S00E-08 1 568E+00 * 0 186 1 350E-08 1 471E+O0 * 187 1 600E-08 1 271E*00 0 188 1 650E-08 9 98OE-01 • • "X 189 1 700E-08 7 606E-01 • • • $0 190 1 750E-08 9 701E-01 • • • 10 191 1.800E-08 4 259E-01 • • t o 192 1 850E-08 3 205E-01 * • « . $ 0 193 1 900E-08 2 777E-01 $ 0 194 1 950E-08 2 610E-01 * + $ 0 199 2 OOOE-08 3 311E-01 * . • * * 0 196 2 050E-O8 4 244E-01 * 0 197 2 100E-08 5 856E-01 • + . • t 0 198 2 150E-08 7 862E-01 X S 0 199 2 200E-08 1 071E+00 • * . » S 0 200 2 250E-08 1 413E+00 * 0 201 2 3O0E-O8 1 807E+00 + .• • . % 0 202 2 350E-08 2 260E+00 • -. * » 0 203 2 400E-08 2 711E+00 • . t o 204 2 450E-08 3 125E+00 • • • t o 209 2 5O0E-08 3 539E+00 • . t o 206 2 550E-0B 3 864E+00 .+ a .• t o 207 2 600E-08 4 143E+00 .+ • • t o 208 2 650E-08 4 383E+00 .+ • t o 209 2 7O0E-O8 4 510E+00 . + • t o 210 2 750E-08 4 636E+0O • • •t 0 211 2 BOOE-08 4 728E+O0 • X 0 212 2 850E-08 4 813E-KXJ • • t« 0 213 2 900E-08 4 B81E+00 • m t*0 214 2 950E-08 4 913E+O0 + a 0 t •. 213 3 OOOE-08 4 942E+00 • a r t * . 216 3.050E-08 4 973E+O0 + • 0 t • 217 3 100E-08 5 0O7E+O0 X a t * 218 3 150E-08 5 030E+00 X a t * 219 3 2O0E-O8 5 034E+00 X . a t • 220 3 250E-08 5 02BE+00 X a t* 221 3 300E-08 5 021E+00 X a t« 222 3 350E-08 5 012E+00 X a X 223 3 4O0E-08 5 001E+00 X X 224 3 450E-08 4 990E+00 X X 225 3 5O0E-08 4 980E+00 X X 226 3 550E-08 4 970E+00 X • X 227 3 600E-08 4 960E+00 X • . X 228 3 650E-08 4 949E+00 X •t 229 3 700E-0B 4 937E*00 X •t 230 3 750E-08 4 920E+00 X •t 231 3 SOOE -08 4 902E+O0 X •t 232 3 .850E-08 4 883E+O0 X •t listing of -D0CVS4 at 12:36:17 on APR 7. (966 for CCId-KCHU Paga 3 233 3 9 OOE-08 4 863E+00 X • • % 234 3 950E-08 4 B43E+0O X m • % 233 4 OOOE-08 4 829E+00 X • * $ 236 4 0S0E-08 4 815E+O0 X •+ t 237 4 1O0E-08 4 804E+O0 X 238 4 150E-08 4 794E+00 X • • • 239 4 2 OOE-08 4 785E+00 X X $ 240 4 250E-08 4 77BE+00 X X % 241 4 300E-08 4 772E+00 X 242 4 350E-08 4 766E+00 X 243 4 400E-08 4 761E+00 X 244 4 450E-08 4 761E+00 • 0 243 4 500E-08 4 747E+00 * 0 246 4 550E-08 4 662E+00 * ( ) * •. 247 4 600E-08 4 416E+00 . • • »0 248 4 650E-08 3 B95E+00 • . 0 249 4 7O0E-08 3 539E+0O • • 0 230 4 750E-08 3 089E+00 • • »0 251 4 8OOE-08 2 652E+00 X 0 232 4 850E-08 2 232E+00 * • o 253 4 900E-08 1 841E+O0 • * t • 0 254 4 950E-08 1 317E+00 • . • * 0 255 3 OOOE-08 1 223E+O0 • • t 0 256 3 O50E-O8 9 844E-01 .• • . $ 0 257 5 10OE-08 7 937E-01 . • • . *. 0 258 3 150E-08 6 341E-01 • • * 0 259 3 2 OOE-08 4 885E-01 0 260 3 250E-08 3 959E-01 • + . • • 0 261 3 300E-08 3 034E-01 • • . « • 0 262 3 350E-08 2 434E-01 • .X • 0 263 3 4O0E-08 1 912E-01 . * * • 0 264 5 450E-08 1 503E-01 . * t. + . • 0 263 5 5O0E-08 1 212E-01 .* * . . + • 0 266 5 550E-08 9 334E-02 .• $ . . • 0 267 3 6OOE-08 7 73BE-02 .• * • 0 268 9 650E-OB 6 I42E-02 • $ + • 0 269 3 7O0E-O8 S 022E-02 • > o 270 3 750E-O8 4 117E-02 • s + • 0 271 3 800E-08 3 319E-02 * % •• 0 272 3 850E-08 2 7B4E-02 t X 0 273 5 9O0E-O8 2 248E-02 • $ X 0 274 3 950E-08 1 909E-02 « $ 0 275 6 OOOE-08 1 594E-02 • » " +0 276 277 278 279 Y 280 0 281 JOB CONCLUDED 282 0 TOTAL JOB TIME 0.0 10 160 Appendix B : SPICE o u t p u t s f o r s i m u l a t i o n s of m u l t i p l i e r c e l l s I n t h i s a p p e n d i x , some o u t p u t waveforms of the m u l t i p l i e r c e l l s a r e p r e s e n t e d . The SPICE s i m u l a t i o n s a r e run on the Metheus w o r k s t a t i o n . The i n p u t l i s t i n g s of the programs a r e o b t a i n e d t h r o u g h the l a y o u t e x t r a c t o r . The l e v e l 2 MOSFET param e t e r s of the N o r t h e r n Telecom 3um CMOS p r o c e s s a r e used i n the s i m u l a t i o n s . Output waveforms of a re c o d e r CIRCUIT: RECOO DATE: TUE APR 8 0B:13:28 1986 (F i l e : recod) T I M E GROUP 1 : V(subn) V(_sub)_ . V( xn2 ) V(x2) V(xnl) V U U _ V m kl_) V(bml) 162 Output waveforms of a m u l t i p l e x e r CIRCUIT: HUXR DflTt: lilt APR 6 25:51:30 19Hb (F i l e : muxa) 5.24- 1 ^ 4.71- \ / / / 4.17-\ ' \ i \ i 3.64-\ i 3.11- \ ; 2.57-\ i \ i 2.04-\ i \ i \ i \ i 1.51-\ i \ i \ > 0.97- / \ R 41 / \ 0 1 0 ~ 0 n 5.0n 10.0n 15.00 20.0n 25.0n 30 0n 35.00 40.'0n 45.0n 50.0n TIME GROUP 1: VCppl) V(ppnl) V(Clkl) V(lx) 163 Output waveforms of a c a r r y l o o k - a h e a d c e l l CIRCUIT: CL5 DRTE: UED RPR 9 00:48:59 1986 ( r i l e : ct5) TIME GROUP 1: V(c?) V(_cn2)_ VCClkl) V( Cwl) 164 Output waveforms of a f u l l adder CIRCUIT: FA DATE: SftT APR 5 21:35:16 1586 ( f i l e : FA) TIME GROUP 1 : VCcar) V(_cBrn) V(suw) V(sumn) VCClki) V(_c) 1 6 5 Output waveforms of a h a l f adder CIRCUIT: HH UHTt: HON FEB IP 23:51:10 1986 ( F i l e : HFD T I M E GROUP 1: V( car ) V(_cBrn_) V(sum) V( sumn ) V(Clkl ) V( b ) \ 166 Output waveform of an i n p u t d r i v e r c e l l CIRCUIT: INLflT DATE: SRT JHN 25 20:38:21 1985 ( F i l e : i n l e t ) T I M E GROUP 1: V( tnp) V(_ouO V(n l ) V(n2) V(Clk) 1 6 7 Output waveform of an ou t p u t d r i v e r c e l l CIRCUIT: DUTDR DRTb: HON FEB 17 21:50:11 19B6 ( F i l e : outdr) T I M E GROUP 1: V( inp) V(_out_) V(n l ) V(Clk) 168 Output waveform of an output pad 169 Appendix C : Layo u t s of some major c e l l s of the m u l t i p l i e r In t h i s a ppendix, the l a y o u t s of some im p o r t a n t c e l l s a r e shown. The d e s i g n r u l e s used a r e tho s e f o r the N o r t h e r n Telecom 3um CMOS p r o c e s s . The f o l l o w i n g l a y e r r e p r e s e n t a t i o n i s used i n a l l t he l a y o u t s : M e t a l P - w e l l C o n t a c t c u t 1 7 0 Layout of a r e c o d e r c e l l 171 Layout of a m u l t i p l e x e r c e l l 172 Layout of a c a r r y l o o k - a h e a d c e l l 173 Layout of a f u l l adder 174 Layout of a h a l f adder 175 Layout of an i n p u t d r i v e r c e l l 177 Layout of an o u t p u t pad 178 Layout of an i n p u t pad 

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