#Digital circuit capacitance and switching analysis for ground bounce in ICs with a high-ohmic substrate2

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Digital Circuit Capacitance and Switching Analysis for Ground Bounce in ICs with a High-Ohmic Substrate Mustafa Badaroglu'.', Lakshmanan Balasubramanian'.', Kris Tiri3, Vincent Gravot', Piet Wambacq', Geert Van der Plas', Stephane Donnay', Georges Gielen4, and Hugo De Man'34 'IMEC, DESICS, Kapeldreef 75, B-3001 Leuven, Belgium, 'Also Ph.D. student at K.U. Leuven, Belgium 3EE Dept. - University of California at Los Angeles, CA, USA, 4ESAT, K.U. Leuven, Belgium Abstract: Ground bounce is a major c
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D ig ita l C ir c u it C a p a c ita n c e a n d S w itc h in g A n a ly s is fo r G r o u n d B o u n c e in IC s w ith a H ig h -O h m ic S u b str a te M ustafa B adaroglu . , L a k s h m a n a n B a la s u b r a m a n ia n . , K ris T iri3 , V in c e n t G ra v o t , P iet W am bacq , G eert V an der P las , S tephane D onnay , G eorges G ielen4,and H ugo D e M an 34 IM E C , D E S IC S , K a p e ld re e f 7 5 , B -3 0 0 1 L e u v e n , B e lg iu m , A lso P h .D . s tu d e n t a t K .U . L e u v e n , B e lg iu m 3E ED e p t.- U n iv e rs ity o f C a lifo rn ia a t L o s A n g e le s , C A , U S A , 4 E S A T , K .U . L e u v e n , B e lg iu m A b stract: G round b o u n c e i s a m a jo r c o n tr ib u to r to su b stra te noise generation due to the resonance caused by the in d u c ta n c e a n d th e V D D -V S S a d m itta n c e th a t c o n s is t s o f th e o n -c h ip d ig ita l c ir c u it c a p a c ita n c e o f th e M OS t r a n s is t o r s , th e d e c o u p lin g , a n d th e p a r a s itic s a r is in g f r o m th e in te r c o n n e c t. T h is p a p e r a d d r e s s e s (1 ) th e d e p e n d e n c e o f th e V D D -V S S a d m itta n c e o n the different states of the circuit and th e in t e r c o n n e c t a n d (2 ) th e c o m p u ta tio n o f to ta l s u p p ly current w ith g r o u n d bounce. T he V D D -V SS adm ittances of several test circuits are com puted w ith 1 3 % m a x im u m error relative to the m easurem ents on a test A SIC fa b r ic a te d in a0 .1 8 p m CM OSprocess on a h ig h -o h m ic su b str a te w ith 18Q cm resistivity. It is a ls o show n th a t th is a d m itta n c e d e p e n d s o n th e c o n n e c tiv ity o f th e g a te s to th e s u p p ly r a il r a th e r th a n their connectivity am ong each other. 1 . I n tr o d u c tio n W ith th e in c re a s e o f s w itc h in g s p e e d o f d ig ita l c irc u its a n d tig h te r re q u ire m e n tso n the signal-to-noise ratio in a n a lo g c irc u its , s u b s tra te n o is e is a m a jo r o b s ta c le fo r s in g le -c h ip in te g ra tio n o f m ix e d -s ig n a l s y s te m s . T h e re h a v e b e e n o n ly a fe w w o rk s a d d re s s in g th e generation m echanism s o f substrate noise. In m ost cases only the propagation m echanism s have been m easured. A g o o d o v e rv ie w o f th e s u b s tra te n o is e e x p e rim e n ts is g iv e n in [I]. Substrate n o is e e x p e rim e n ts h a v e b e e n carried outo nte s t c h ip s w ith d e d ic a te d d ig ita l s u b s tra te noise generators[ I ] o r u s in g o n ly s m a ll d ig ita l c irc u its [3 ] b y g iv in g fe w e r d e ta ilso n h o w th e n o is e is g e n e ra te d . I n [4], parallel sets of tri-state buffers w ith d iffe re n t d riv in g c a p a b ilitie s a re o p e ra te d w ith a n in te m a l/e x te m a l c lo c k in o rd e r to s tu d y th e s u b s tra te n o is e . T h e o u tp u tso f th e s e tri-s ta te b u ffe rs h a v e b in a ry -w e ig h te d lo a d s , w h ic h a re in p F ra n g e , c o n n e c te d to th e s u b s tra te . D u e to th e s e la rg e lo a d c a p a c ita n c e s in th e e x p e rim e n ts , th e s u b s tra te n o is e is d o m in a te d b y c a p a c itiv e c o u p lin g , m o s tly th e c a s e inU 0b u ffers. In reality o n ly a sm all p o rtio n o f th e d ig ita l c irc u itry c a n d riv e s u c h la rg e lo a d s s im u lta n e o u s ly , m o s tly a t a lo w e r s p e e d . T h e c o u p lin g fro mth e s u b s tra te c o n ta c ts o f th e g ro u n d ra il is th e re fo re m o re d o m in a n t in n o is e g e n e ra tio n fo r la rg e -s c a le in te g ra te d c irc u its [5 ]. T h e m o d e lin g o f th e tr a n s f e r fu n c tio n fro m th e pow er s u p p ly t o th e s u b s tr a te o r e q u iv a le n tly to th e c irc u it g ro u n d a s w e ll a s th e m o d e lin g o f th e p o w e r s u p p ly b e c o m e m o re c ru c ia l. T h e re fo re a c a re fu l s e le c tio n o f th e te s t c irc u its i s n e c e s s a ry to s tu d y th e s c a la b ility a s p e c ts o f th e m e a s u re d substrate noise to U LSI system s. For this purpose we 2 5 7 h a v e d e s ig n e d d e d ic a te d s im p le te s t c irc u its ina0 .1 8 p m 6 M C M O S p ro c e s s in o rd e r (1 ) to d e m o n s tra te th e s ta te dependent transfer fu n c tio n s ,(2 ) t o v e rify th a t th e s e tra n s fe r fu n c tio n s a r e to p o lo g y in d e p e n d e n t, a n d (3 )t o show that these transfer functions as w ell as the supply c u rre n t c a n b e lin e a rly s u p e rp o s itio n e d in o rd e r to fo rm th e m o d e ls o f la rg e d ig ita l system s. T o p o lo g y independent transfer fu n c tio n s in d ic a te th a t m o d e lin g o n ly c o n n e c tiv ity t o th e s u p p ly n e tw o rk is im p o rta n t ra th e r th a n th e c o n n e c tiv ity to o th e r g a te s . T h e p a p e r is o rg a n iz e d a s fo llo w s :I ns e c tio n2 w e in tro d u c e a lu m p e d m odel fo r g ro u n d b o u n c e a n d b rie fly d e s c rib e i t s d e p e n d e n c ie s .I ns e c tio n3 w e d e s c rib e th e te s t c irc u its used in our experim ents. In section 4 the m easurem ents are presented.I n section5 conclusions are draw n. 2 . C h ip -le v e l g r o u n d b o u n c e m a c r o m o d e l V S S - b F ig u r e1 : (a ) C h ip -le v e l g r o u n d b o u n c e g e n e r a tio n m o d e l. (b ) E q u iv a le n t p a r a lle l F U C -n e tw o r k . F ig u re 1 s h o w s th e g ro u n d b o u n c e g e n e ra tio n m o d e l fo r a n e tw o rk o f th e g a te so na b u lk s u b s tra te . In th is m o d e l th e s u p p ly lin e in d u c ta n c e a n d its s e rie s re s is ta n c e a re re p re s e n te d b y L b a n d R b re s p e c tiv e ly . A d d itio n a lo n - c h ip d e c o u p lin g c a p a c ita n c e a n d i t s s e r ie s d a m p in g resistance are represented by C d and R d respectively. For e a c h g a te : T h e c irc u it a d m itta n c e is re p re s e n te d b y a c a p a c ita n c e (C c ) in s e rie s w ith a resistance (R c). The series resistancefro mth e V S S c o n ta c t to th e s u b s tra te is represented by R s. The capacitance due to the reverse b ia s e d n -w e ll ju n c tio n d io d e a n d th e re s is tiv e p a th a re re p re s e n te d b y C w a n d R w re s p e c tiv e ly . A r e s is tiv e n e tw o rk m o d e ls th e c o u p lin g th ro u g h th e b u lk . B y ta k in g th e s u b s tra te in to a c c o u n t th e w e ll c a p a c ita n c e (C w ) a n d the substrate contact resistance(R s) are com puted as a part o f the V D D -V S S adm ittance. A s s u m in g th a t a ll g a te s u n d e r c o n s id e ra tio n b e lo n g to s in g le p o w e r d o m a in , it is p o s s ib le to c o m b in e th eV D D - V S S a d m itta n c e s (Y 1 1 ) o f e a c h g a te in th e s a m e p o w e r n e tw o rk to a s in g le a d m itta n c e .A s w ill be illu s tra te d later, th e effectiv e ad m ittan ce w ill be th e sam e fo r tw o different circuits, w hich c o n ta in th e s a m e n u m b e r a n d 0 -7 8 0 3 -8 1 0 8 -4 /0 3 /$ 1 7 .0 0 0 2 0 0 3 IE E E . Authorized licensed use limited to: University of Central Florida. Downloaded on November 21, 2008 at 12:17 from IEEE Xplore. Restrictions apply. -;3 .E / ty p e o f g a te s in a s in g le p o w e r re g io n . T h e c o n trib u tio n o f th e s u b s tra te in th e o v e ra ll Y 1 1 is n e g lig ib le fo r h ig h - ohm ic substrates. For a 2-input N A N D gate (N A N D 2) in a 0 .1 8 p m C M O S te c h n o lo g y o n a h ig h -o h m ic s u b s tra te w ith 1 8 0 c m r e s i s t i v i t y th is com parison is show n in F ig u re 2. The s u b s tr a te netlist is e x tra c te d b y u s in g S u b s tra te s to rm [6 ]. IY 1 1 1 N A N D 2 1 o v e r a ll I Y l l ld u e to th e c ir c u it a n d !h e s u b s tra te IY lllo n ly d u e to th es u b s b a te (C w ,R w . R s a n d IO I th es u b s tra te m e s h ) ? O W 1 M 1 0 M lO O M 1 G 1 0 G F re q u e n c y F ig u r e 2 : C o n tr ib u tio no f th e s u b s tr a te in th e o v e r a ll V D D - V S S a d m itta n c e(Y 1 1 ) o f a N A N D 2 g a te . B y u s in g th is m o d e l th e v o lta g e s w in g a t th e V S S n o d e (g ro u n d b o u n c e ) is c o m p u te d a s a fu n c tio n o f th e s u p p ty c u rre n t (Is u p p ly ) fo r a n e q u iv a le n t p a ra lle l R L C -n e tw o rk (F ig u re 1b ) w ith th e e le m e n t v a lu e s g iv e n b y : 1 . L- 1 - 1 ---+ R P R d (l+ Q j) 2 R b (l+ Q :) R c (l+ Q :) I . 1 c c C d C P = -+ -(l+ l/Q :) (l+ l/Q a ) Q := I/[w R d C d 1.Q ![w Lb /R b 1 ,QZ=1/ [ a R c C c ] T he resonance frequency (w ,) and the dam ping factor( 6 , ) o f th e o s c illa tio n s a re g iv e n a s fo llo w s : - W O= - 1 & = .F m y 2 R P C P In order to solvew , and5 an iterative approach can be e m p lo y e d b y firs t fin d in g a n in itia l v a lu e o fw , fo r Q d = a :, Q b=O , a n dQ c=O . T h isa , is th e n u s e d in o rd e r to u p d a te th e n e w v a lu e s o f Q d,Q b,and Q c. T hese values are again u s e d to u p d a teo , a n dt ; . T h is ite ra tiv e s o lu tio n g o e s o n u n til th e c o n v e rg e n c e inw ,a n d6 v a l u e s . 2 .1 . L ogic-state dependenceo f the circuit capacitance E q u a tio n s (1 )-(2 ) c o n ta in s o m e n o n -c o n s ta n t te rm s d u e to C c a n d R c . T h e s ig n ific a n c e o f th e s e te rm s c a n b e re d u c e d b y a d d in g fix e d d e c o u p lin g c a p a c ita n c e b u t a t th e e x p e n s e o f th e c h ip a re a . F ig u re3show s the average v a lu eo f Y 1 1 , s im u la te d in S P IC E , o v e r th e lo g ic -s ta te s fo r th e N A N D 2 g a te in c lu d in g its s u b s tra te m o d e l. F ig u re 4 a show s th e p e rc e n ta g e d iffe re n c e o f /Y 11 1 re la tiv e to its m e a n v a lu e o v e r th e s ta te s . F o r m e d iu m s iz e d c irc u its (fro m lK g a te to lM gates), the g ro u n d b o u n c e re s o n a n c e (e q u a tio n (1-2 )) o c c u rs b e tw e e n lO M H zt o 2G H z. In th is fre q u e n c y re g io n there is a m a x i m u m v a r i a t i o n o f3 0 % o v e r t h e m e a n v a l u e o f IY 11I w h ic h r e s u lts i n a 1 9 % v a ria tio n o n th e re s o n a n c e fre q u e n c y w ith n o e x tra o n -c h ip d e c o u p lin g . T h e v a lu e s of C c for a N A N D 2 gate are 1 1 .3 7 fF )9 .4 7 fF , 9 .4 7 fF , a n d 5 .9 9 s fo r th e lo g ic -s ta te s 0 0 , 0 1 , 1 0 , a n d 1 1 re s p e c tiv e ly . B y o m ittin g th e in flu e n c e o f th e in te rc o n n e c t c a p a c ita n c e s inside the gate these v a lu e s b e c o m e 9 .1 8 fF , 7 .2 8 fF , 7 .2 8 fF , a n d5 . 8 9 f F re s p e c tiv e ly . N o te th a t in te rc o n n e c t c a p a c ita n c e is a ls o lo g ic -s ta te - d e p e n d e n t. T h e in te rc o n n e c t w ill b e a m o re d o m in a n t c o n trib u to r to C c for large digital circuits w ith d e n s e in te rc o n n e c ts a n d c o m p le x p o w e r g rid a n d a ls o fo r th e fu tu re te c h n o lo g ie s w ith s m a lle r d e v ic e s . F o r th e s a k e o f preserving the linearity one can use an average value (e.g.averaged between lOOkHz and 1GHz)for theV D D - V SS a d m itta n c e o v e r th e logic-states as w e ll a s th e m axim um and average error bound. 90 8 8 [d e g re e s ] ~ Y l l F re q u e n Q F ig u r e3 : A v e r a g e v a lu eo f th e N A N D 2 V D D -V S S c ir c u it a d m itta n c e o v e r th e lo g ic -sta te s. % o a ie~ ~ ~ ~ ,n i~ iil 0 1 0 m m i o O A B .0 1 1 0 - , - - _ - - 6 - A - - - .:: m = i1 e 1 1 d 0 - L % O w I M 1 0 M IW M 1 0 1 0 G 5 0 0 2 0 4 0 6 0 8 3 1 2 1 1 1 6 1 8 2 F R C !Y e V S v w ly w ltx leM F ig u r e4 : (a ) R e la tiv e d iffe r e n c e (in% ) in th e m a g n itu d eo f the N A N D 2 V D D -V SS adm ittance for each logic-state com pared to the value averaged over the logic-states. (b) N A N D 2 c ir c u it c a p a c ita n c e v e r s u s s u p p ly v o lta g e . F ig u re4 b s h o w s th e s im u la te d c irc u it c a p a c ita n c ea s a fu n c tio n o f th e s u p p ly v o lta g e . C irc u it c a p a c ita n c e ina n o n -s w itc h in g g a te d o e s n o t c h a n g e s ig n ific a n tly o v e r th e v a ria tio n s o f th e s u p p ly v o lta g e a ro u n d its n o m in a l v a lu ed u et og ro u n d b o u n c e s in c e th e tra n s is to rs in th is g a te a re e ith e r in c u t-o ff o r in th e lin e a r re g io n . T h e d is c u s s io n in th is s e c tio n is a p p lic a b le to a ll s ta tic C M O S g a te s w ith o u t lo s so fg e n e ra lity . 2 .2 . S u p p ly c u r r e n t a n a ly s is w ithg r o u n d b o u n c e T h e lin e a r re la tio n s h ip b e tw e e n th e s u p p ly c u rre n t a n d th e n u m b e ro fs im u lta n e o u s s w itc h in g g a te s d o e s n o t o c c u r fo r th e la rg e g ro u n d b o u n c e . T he n e g a tiv e feedback from the ground bounce on the supply current o f th e b u ffe rs i s a d d re s s e d in [7 ]. T h is w o rk o n ly c o n s id e rs th e lo n g -c h a n n e l d e v ic e s a n d th e in p u tsfro m an external source w ith a clean ground. In fact it is m ore c o m m o n to h a v e th e in p u ts fro m a n o n -c h ip d riv e rI nth e sam e pow er lin e w ith th e s w itc h in g c irc u it. T h e , s a tu ra tio n c u rre n to f a s w itc h in g in v e rte r fo ra r i s i n g in p u t is d e fin e d b y : w here K i s a p ro c e s s a n d a g e o m e try d e p e n d e n t coefficient and CL is th e s h o rt c h a n n e l v e lo c ity s a tu ra tio n c o e ffic ie n t, w h ic hi sb e tw e e n 1 and2 [8]. V in p is th e in p u t v o lta g e , w h ic h m a y c o n ta in o n lo ff-c h ip n o is e , a n d V S S is th e o n -c h ip g ro u n d v o lta g e , w h ic h h a s a g ro u n d Isu p p ly= K (V in p- V S S-V th ) (3 ) 2 5 8 Authorized licensed use limited to: University of Central Florida. Downloaded on November 21, 2008 at 12:17 from IEEE Xplore. Restrictions apply.b o u n c e c o m p o n e n t. In th e c a s e o f a n o n -c h ip d riv e r th e negative feedback effect is m uch m ore than an external s ig n a l w ith a c le a n g ro u n d s in c e th e lo g ic le v e l h ig h a t th e in p u t is th e c irc u it p o s itiv e s u p p ly V D D h a v in ga s u p p ly b o u n c e , w h ic h b e c o m e s o u t o f p h a s e w ith V S S d u rin g th e tra n s itio n . F ig u re5show s the supply current and the ground bounce peak-to-peak values for a num ber o f s im u lta n e o u s s w itc h in g in v e rte rs (s h o w n a s T 1 c irc u it i nF ig u re 7 ) im p le m e n te d in a 0 .1 8 p m CM OS process, h a v in g V th o (N /P )= 0 .3 2 /-0 .4 7 V a n d w ith in p u t ris e tim e o f5 0 p s , fo r th e fo llo w in g th re e c a s e s w h e n th e c irc u it: (1) has no package parasitics, (2 ) h a s a p a c k a g e (L b = ln H , R b = O .lQ ) a n d h a s th e in p u t fro m a n e x te rn a l d riv e r(BUF)w ith a c le a n s u p p ly , (3) has a package (Lb=lnH , R b=O .ln) and has the input fro m a n in te rn a l d riv e r(B U F )o n th e s a m e s u p p ly lin e w ith the circuit. z:: [m v p p ]v s s 2 0 0 3 0 : ; i 1 0 0 C ase(3 ) C ase@ ) (b)4 0 0 0 C ase 1 0 2 4 6 8 1 0 I 2 1 4 16 N um bero f s im u lta n e c u s s w itc h in gin v e rte rs F ig u r e5 : (a ) S u p p ly c u r r e n t (b ) G r o u n d b o u n c e v o lta g e peak-to-peak values versus the num bero f s im u lta n e o u s sw itch in g in verters. T h e s u p p ly c u rre n t p e a k -to -p e a k v a lu e s ta rts to d e v ia te fro mth e lin e a r s u p e rp o s itio n w ith re s p e c tt o th e n u m b e r o f s w itc h in g in v e rte rs fo r a g ro u n d b o u n c e la rg e r th a n 7 % o f th e v o lta g e h e a d ro o m (V D D -V th = 1 .4 8 V ). T h is v a lu e c a n b e g e n e ra liz e d to o th e r g a te s p ro v id e d th a t th e input rise/fall tim e i s th e sam e/faster adthan fo r th e a b o v e c a s e . T h e lin e a rity is s till p re s e rv e d (d u e to a = 1 for short-channel devices) for cases (2) and (3) how ever w ith a s m a lle r s lo p e c o m p a re d to c a s e(1 ). The supply current peak value decreases by 3 5 % in case(3 ) with respect to case (1) w ith the generated ground bounce of 48O m V pp in case (3 ). 3 . D escrip tiono f th e test circu its The dependenceo f supply current and ground bounce h a s b e e n v e rifie d e x p e rim e n ta lly w ith te s t c irc u its th a t h a v e b e e n fa b ric a te d in a 0 .1 8 p m6 M C M O S process on a h ig h -o h m ic s u b s tra te w ith 1 8 n c m resistivity (Figure 6 ).T h e s e c irc u its a re : 1 . P a ra lle l c o n n e c tio no f 1 6 in v e rte rs (C irc u it T l ) , 2 . S e ria lly c a s c a d e d in v e rte rs in p a ra lle l (C irc u it T 3 ), 3 .A2 5 6 -g a te s s e q u e n tia l c irc u it (C irc u it T 4 ), C irc u it T 1 is c o m p o s e d o f in v e rte rs c o n n e c te d in p a ra lle l (F ig u re7 ). T h e c irc u it is c o n tro lla b le w ith fo u r in p u ts in o rd e r to o p e ra te th e p a ra lle l c o m b in a tio n s o f 1 , 2 , 4 a n d 8 inverters. Each set is driven by a buffer (B U F).T oh a v e e q u a l in p u t s lo p e a t e a c h set, each b u ffe r o u tp u t is b a la n c e d w ith several parallel connections of a lo a d c a p a c ita n c e C th a t c o rre s p o n d s to th e in p u t c a p a c ita n c e o f th e in v e rte r W (N /P )= 1 .2 1 /2 .6 0 p m . C irc u itT 1 has an equivalent area of 135-gates. C ircuit T3 is com posed of serially cascaded in v e rte rs (F ig u re 7 ). T 3 is c o n tro lla b le w ith 4 in p u ts in o rd e rt o o p e ra te th e p a ra lle l c o m b in a tio n s o f 1, 2 ,4 , a n d 8 s e ria lly c a s c a d e d in v e rte rs . E ach s e t o f s e r i a l l y c a s c a d e d in v e rte rs is d riv e n b y th e b u ffe r, w h ic hi slo a d e d w ith th e sam e load capacitance as in T1 in order to preserve the s a m e in p F ig u re 6 : M ic ro p h o to g ra p h o f th e te s t c irc u its . .U I T F F p p T p T 3 C lr c u lt F ig u r e7 : S c h e m a tico f th e c ir c u itsT 1 a n d T 3. . I I v J F ig u r e8 : S c h e m a tico f c ir c u it T 4. C ircuit T4 is composed of an 8 -b it m a x im u m -le n g th s e q u e n c e P R B S g e n e ra to r in c a s c a d e w ith a 4 -b it c o m p a ra to r (F ig u re 8 ). T h e c irc u it g e n e ra te s a trig g e r s ig n a l (T R IG O K ) in o rd e r t o s y n c h ro n iz e th e m easurem ents. T he R E S E T G E N m o d u le g e n e ra te s a s y n c h ro n o u s re s e t fo r th e c irc u it d u rin g th e firs t3c lo c k cycles after external reset. 4 . E xperim ental R esults W e c o m p u te th e a v e ra g e v a lu e o f th e V D D -V S S a d m itta n c e (T a b le 1 ) of the test circuits by sim u latin g th e m in S P IC E a n d also by u s in g the macro m o d e ls 2 5 9 Authorized licensed use limited to: University of Central Florida. Downloaded on November 21, 2008 at 12:17 from IEEE Xplore. Restrictions apply.S P IC E D IO D E LC c[ f F ] N o in te rc o n n e c t L o c a l L o c a l+ S ig n a l L o c a l+ S ig n a l+ G lo b a lI2 5 2 7 /2 5 8 1 2 3 8 7 /2 5 8 1 3 5 8 9 /3 5 0 1 M EASURED I2 3 2 4 261 1 3 0 8 5 T 1 T 3 T 4 1 4 2 4 1 1 3 9 5 1 4 2 0 /1 3 9 5 1 9 2 5 1 1 8 3 1 1 9 6 7 1 1 9 6 6 1 9 6 2 1 1 9 6 6 2 6 9 0 1 2 6 4 5 2 4 4 5 1 2 5 0 8 2 3 4 7 1 2 5 0 8 3 5 7 5 1 3 4 0 7 I T a b le1 : M e a n v a lu e s o f th e V D D -V S S c a p a c ita n c e fo r th e test circu its (fromS P I C E sim u la tio n s, s u p e r p o s itio n in g o f th e m acrom odels, and m easu rem en ts) T a b le 1 s h o w s th a t th e lo c a l in te rc o n n e c t is s ig n ific a n t in th e o v e r a ll V D D - V S S a d m itta n c e : 2 1 % in T 1 , 2 2 % i n T2, and 21% in T 4 . O m ittin g a ll th e in te rc o n n e c ts w il’l cause an error of 33% ,29% ,and 36% for T 1, T3, and T4. re s p e c tiv e lyi n the resonance frequency estim ation.F o r fu tu re te c h n o lo g ie s th is e rro r w ill b e e v e n m o re p ro n o u n c e d . N o te th a t th e V D D -V S S a d m itta n c e s o f T I and T3 are the sam e even when lo c a l in te rc o n n e c t is ta k e n in to a c c o u n t. T h is sh o w s th a t th e c o n n e c tiv ityo f th e g a te s to th e s u p p ly ra il is im p o rta n t ra th e r th a n th e c o n n e c tiv ity o f g a te s t o e a c h o th e r. T he o v e ra ll difference is lim ited to 10% from the m easurem ents. , om [m v] V D D A CP P 9 0 0 800 200 1 0 0 T 3 Y 2 4 6 6 I O I 2 1 4 I!! IS = d e n m a l((lN 4 . IN 3 . IN 2 [N I}) In p u t s w ltc h in g s ta tefo r a r is in g e d g e a t th e in p u ts F igure9 : M easured supply bounce peak-to-peak value for c ir c u itsT 1a n dT 3 v ersu s th e in p u t sw itc h in g sta te s. Figure9 show s the m easuredA C peak-to-peak valueo f th e s u p p ly v o lta g e (V D D ) o n th e d ie fo r T 1 ,3 v e rs u s th e in p u t s w itc h in g s ta te s(IS ). T3 generates 33% and 40% less noise at IS = 4 andIS = 8re s p e c tiv e ly in c o m p a ris o n to th e c a s e in T 1 . T h is s h o w s th a t th e s e ria l lo g ic is le s s n o is y th a n th e p a ra lle l lo g ic . T he negative feedback e ffe c t is d e m o n s tra te d b y th e d e v ia tio n fro m a straight line derived due to the first tw o points (at IS=O and 1). F o r th e m a x im u m num ber o f s im u lta n e o u s s w itc h in g in v e rte rsi nT 1 th is d e v ia tio n is m e a s u re d a s71‘Y O . F ig u re 1 0 s h o w s th e m e a su re d V D D -V S S a d m itta n c e o f T4 as a function of the logic-states, w hich is controlled b y th e o n -c h ipP R B S .A 3 -4 % v a ria tio n is m e a s u re d0 1 1 th e m a g n itu d e o f th e V D D -V S S a d m itta n c e o v e r 400M H z t o lG H z frequency b a n d w ith respect to the a d m itta n c e a t th e p o w e r-u p lo g ic -s ta te o f c irc u it T 4 . In o rd e r to tre a t th is lo g ic -s ta te -d e p e n d e n c e , T a b le 1 u s e s th e a v e ra g e v a lu e fo r th e V D D -V S S c irc u it a d m itta n c e a s w e ll a s f o r th e in te r c o n n e c t o v e r th e lo g ic -s ta te s . m iM ~=w & a n ~ n iY i1 1aner nw w cksw ri -U P [o g J1MOW W a n m is b c ndod+ e s wr t -w p 1 21 0 8 0 6 D 4 0 2 0 4 2 4 4 ‘‘840aM 5 0 0 M 6 W M 7w M BDO M 9O W 1 G F -W V F W ” * C .= f F ig u r e1 0 : M e a s u r e d v a r ia tio n s in th e V D D -V S S adm ittance of circuitT 4. 5 . C o n c lu s io n s T he e x p e rim e n ts o n sim ple circuits give ideas to d o fu rth e r s im p lific a tio n s fo r g ro u n d b o u n c e m o d e lin g . W e h a v e show nth a t th e c o n trib u tio n o f th e s u b s tra te in th e V D D -V S S im p e d a n c e o f th e g a te s is n e g lig ib le fo r h ig h - o h m ic substrates. The lo g ic -s ta te d e p e n d e n c y o f th e in p u ts a n d in te rc o n n e c ts o n th e g ro u n d b o u n c e s h o u ld b e ta k e n in to a c c o u n t. B o th m e a s u re m e n ts a n d s im u la tio n s h a v e s h o w n th a t th e a s s u m p tio no f lin e a r s u p e rp o s itio n o fs u p p ly c u rre n ts to o b ta in th e to ta l s u p p ly c u rre n t is v a lid o n ly fo r ground bounce v a lu e s b e lo w 1 5 % o f V D D -V th . W e e x p e rim e n ta lly v e rifie d th a t it is p o s s ib le to d e riv e th e o v e ra ll c h ip -le v e l m o d e l fo r g ro u n d b o u n c e b y d ire c tly s u m m in g th e V D D -V S S a d m itta n c e s o f th e in d iv id u a l g a te s . T h is su m is in d e p e n d e n t o f th e o v e ra ll c irc u it to p o lo g y . U sing th is to p o lo g y -in d e p e n d e n t c o m p u ta tio n fo r a m o re c o m p le x s e q u e n tia l c irc u it h a s e s tim a te d th e c irc u it c a p a c ita n c e w ith in 1 3 % e r r o r . M e a s u re m e n ts a ls o v e rifie d th a t th e s e ria l lo g ic g e n e ra te s le s s g r o u n d b o u n c e th a n d u e to th e p a ra lle l lo g ic . R eferen ces S .D o n n a y a n dG . G ie le n , e d ito rs , ” S u b s tra te n o is e c o u p lin g in m ix e d -s ig n a l IC ’s ,”K lu w e r A c a d e m ic P u b lis h e r s , 2 0 0 3 . D .K . S u , M .J. L o in a z , S . M asui, a n d B .A . W o o le y , “ E x p e rim e n ta l re s u lts a n d m o d e lin g te c h n iq u e s fo r s u b s tra te n o is e in m ix e d -s ig n a l in te g ra te d c irc u its ,”IE E E J . S o lid -S ta te C ir c u its ,V o1.28,N o.4, pp. 420-430, A pril 1993. K . M akie-Fukuda, T. A nbo,T . Tsukada, T . M atsuura, and M . H o tta , “V oltage-com parator-based m easurem ent o fe q u iv a le n tly s a m p le d s u b s tra te n o is e w a v e fo rm s in m ix e d -s ig n a l in te g ra te d c irc u its ,”IE E EJ . S o lid -S ta te C ir c u its ,V o 1 .3 1 , N O S , p p . 7 2 6 - 731,M ay 1996. M .X u,D .K . Su,D . K . Shaeffer,T .H . L ee, andB . A . W ooley, “ M e a s u rin g a n d m o d e lin g th e e ffe c ts o f s u b s tra te n o is e o n th e L N A fo r a CM OS G PS re c e iv e r,” IE E E J . o f S o lid -S ta te C ir c u its , V o 1 .3 6 , N o .3 , p p . 4 7 3 - 4 8 5 ,2 0 0 1 , M . B a d a ro g lu ,M . v a n H e ijn in g e n ,V . G ra v o t,J . C o m p ie t,S . D onnay, M . E n g e ls , G . G ie le n , a n d H . D e M an, ” M e th o d o lo g y a n d E x p e rim e n ta l V erificatio n fo r S u b s tra te N oise R e d u c tio n in CM OS M ix e d -S ig n a l IC s w ith S y n c h ro n o u s D ig ita l C irc u its ,” IE E E J . S o lid -S ta te C ir c u its , S u b s tra te s to rm fro m C a d e n c e : h ttp :/lw w w .c a d e n c e .c o m . R . S e n th in a th a n a n d J .L . P rin c e , “ S im u lta n e o u s s w itc h in g g ro u n d n o is e c a lc u la tio n fo r p a c k a g e d C M O S d e v ic e s ,” IE E EJ . S o lid -S ta te C ir c u its ,V o1.26,N o .] 1,p p . 1724-1728,N ov. 1991. T .S akurai andR . N ew ton, “A lpha-pow er law m osfet m odel and its a p p lic a tio n s to cm os in v e rte r d e la y a n d o th e r fo rm u la s ,” IE E EJ .o f S o lid -S ta te C ir c u its , V o l.2 5 , N o .2 , p p . 5 8 4 -5 9 4 , A p ril 1 9 9 0 . V 0 1 . 3 7 , N o . 1 1 , p p . 1 3 8 3 - 1 3 9 5 , N O V . 2 0 0 2 . 2 6 0 Authorized licensed use limited to: Universit of Central Florida. Downloaded on November 21, 2008 at 12:17 from IEEE X lore. Restrictions a l .
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