Delay Variation Tolerance for Domino Circuits
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1 Dy Vrt Trc r D Crcuts K-C Wu, C-T Hs, S-C C Dprtt CS, Nt Ts Hu Uvrsty, Hscu, Tw Ax@tuc.cs.tu.u.tw, s@tuc.cs.tu.u.tw, scc@cs.tu.u.tw ABSTRACT Fctrs y vrt, suc s prcss vrt s cts, y cus uctur cp t vt t pr-spc t cstrt. I ts ppr, w prps v r-sytss tcqu t trt y vrt r crcuts. Nt tt t scs s crtc pts r zr; y y t t ts zr-sc s w wrs t prrc crcut. Our sc s t crs t scs s t crtc r y pp rut uxry su-crcut t t r crcut. T uxry su-crcut c cus crtc pts t c s pts r prcpt pts [7] s s t prv t cpty y vrt trc. Exprt rsuts r vry cur. 1. Itruct Crcut y vc tcs cs crsy sstv t prcss vrt s [1][2]. Ts ctrs wu cus crcut s prrc t uctut, t wrst cs, t vt y ccur. Espcy r prrc ss, t crtc rs r t pt crcut sty. As rsut, t y vrt pr cs crtc ssu r crcuts. I ts ppr, w prps r-sytss t t trt y vrt r crcut. T scs s crtc pts r zr; y y t t ts zr-sc s w wrs t prrc crcut. T r y vrt trc [3] s rut y t ccpt scs. T utrs prps r-sytss tcqu wc crprts Trp Mu Rucy (TMR) structur t crcut s tt t crcut c trt v r y ucrtty. Tr rsuts sw tt y 40% r vr, crt r vrt trc c cv r sttc CMOS crcuts. U sttc crcuts, yc crcuts prt tw pss: t pr-cr ps t vut ps. T v t rc pr, crcuts rqur c Fur 1: A xp strt y vrt trc r crcut. ss, xcpt prry puts, t v y rs trsts ur t vut ps. Du t t rs-trst-y prprty, y vrt trc crcuts s uc sr t ccps t tt sttc crcuts. I tr wrs, rcty ppy t s t s [3] t crcuts y v ucssry r r. Our sc y vrt trc s t c (trt) crcut wt rut uxry su-crcut, wc s ustrt t w xp. A crcut Fur 1 pts c uct = (++c)+ = ++c+. Fr y trc, w cstruct uxry crcut pt F 2 = (+) = + rt w utput = +F 2. Bcus t -st pprty cvrs tt F 2 (.., F 2 ), t w uct = +F 2 s tc t t r uct. W w sw tt pp crcut s t c t uctty t r crcut ut s t ct y trc. Csr put pttr (,, c,, ) = (1, 0, 0, 1, 0) wc ucs trsts prpt crtc (t) pts t. Sc t F 2 v y rs trsts t OR t, wcvr rs s rrvs rr w t t OR t s utput. I tr wrs, t rr rrv tr r F 2 trs t utput vu st t t. Dy vrt trc s csquty cv cus t rrv ss w t uc t w crcut s y. I t t prps w structur r crcuts, ts ppr s rvs v trs wc w us t crry ut sr t ts r [3]. W s sw tt y vrt trc c pp t t tr s prry utputs t cv ttr rsuts. F 2
2 T xprts sw tt t r vr ur t s ss t tt r [3]. As, w v prr Mt-Cr xprts. T y t s v s prty sty uct sr t [6]. T rsuts sw tt ut 77% sps t r crcut C6288 c t crt y rqurt; wvr, ut 99% sps t crrsp r-sytsz crcut c stsy t s rqurt. W wu t t tt tr v svr stus [4][5][7] ttpt t ptz t sttstc t rsuts y t sz tcqus. Ts ts rqur sttstc s t v r ts. W t tt sttstc struts ts sttstc crrts ts r v prcsy, ts [4][5][7] c r ct t rut structurs s scr y ts ppr. O t tr, ts ppr s t ssu y sttstc t s. Trr, ur t w ttr w ccurt sttstc s r t v. Fr xp, vry w cps r uctur r w tcs, suc s 90 65, s t s cut t tr r t vry sttstc s r w tcs. I t t prcss vrt, y vrt u t s ssus, suc s IR rp, s t sy t. 2. Dy Vrt Trc Dupx D Systs Lt crcut ur csrt r y vrt trc. A upx syst s sw Fur 2, wc cssts t r crcut, ts upct, OR t t t utputs s ts puts. Tr r tw prprts r upx syst. Frst, t prrs t s uct s t r crcut. Scy, trst trv pt s trvs t rrr pt. Sc crcut s y 0-t-1 trsts, t OR t s utput trsts r 0 t 1 w t rr trst rrvs. Ay y crs wc s pstp tr r w t ct t vtu t rsut. Trr, c (xcpt t OR t) t Or crcut Dupct crcut F 2 Fur 2: A upx syst. upx syst s t sc. St, tr s r t 100% r vr r upx syst, t upx syst prctc. I t rr ts ppr, w w xp w t ruc w t v r y vrt trc. Lt us rst t r y vrt trc. T r y vrt trc c qut wt t sst sc ts/wrs crcut. A crcut s s v t y trc [3] t sc c t/wr s t st t. Gv y trc vu t crcut, ur ctv s t r-sytsz t crcut s tt vry t/wr t w crcut c trt t st y vrt t. T sc c t/wr upx syst s t (., t = ), wc s vr-prtctv r t y vrt prs. I r, y trc 10%~20% t r crcut y s suct r ur csrt prcss vrt s cts. 3. R-sytss r Dy Vrt Trc T ccps v y trc vu t wtut t uc r vr, prctc sc rt r upx syst s prps. Our r-sytss stps r s ws. (1) B wt upx syst Fur 2. (2) Rv y s wrs r r ruct w t t trc vu. W w scuss w t prr wr rv ct. Assu t r crcut pts t c uct, t rut uxry crcut pts F 2, t ctv utput s = +F 2. I t -st F 2 s su-st tt (.., F 2 ), w c prsrv t r uctty (= +F 2 = ). W tr r y pss B ucts wc stsy F 2, w y csr wr rv t ruc t -st F 2. Br prst ur trs, w scr wt wrs c rv t t F 2 t w. L 1: A rct put wrs t OR ts r rut c sutusy rv. Pr: Ott. Lt t y trc vu t. A pt s c t -crtc pt ts y s rtr t t t rqurt us t. I tr wrs, t y crt t -crtc pt w cus t pt s y t xc t
3 p x y q s t r w 5 w 6 w 3 w 4 w 2 w 1 p 1 p 2 w Fur 4: N s t AND-cvr t -crtc pts p 1 p 2. t -tr: {,, } t -s put: w 1 ( -> ), w 2 ( -> ), w 3 ( -> ), w 4 (r -> ), w 5 (p -> ), w 6 (q -> ) Fur 3: T r crcut. t rqurt. I t, w sy tt s t -crtc t s t -crtc pt. O c s tt t sc t -crtc s sr t t. Csr t xp Fur 3, wr t y c t s 1. Supps t y trc t s 1 t t rqurt r s 6. I ts xp, t t rqurt s qu t t t t st pt. Pt {s------} s t -crtc pt cus ts y s 6, rtr t r - t (6-1=5). I ct, t pts Fur 3 r t -crtc pts. N s t -crtc cus t s t -crtc pt. Bss, t s {,,,,,,,, } r t -crtc s. Nt tt t scs ts t -crtc s r 0, sr t t. A s t t -tr t s t -crtc t -crtc pts t prry utput ust pss tru t. A wr 1 -> 2 s t -s put 1 s t t -crtc ut 2 s t -crtc. I t s xp, s {,, } r t -trs cus t -crtc pts t t prry utput ust pss tru ts s. Wr w 1 ( -> ) s t -s put cus s t t -crtc ut s. Sry, wrs {w 2, w 3, w 4, w 5, w 6 } r s t -s puts. Tr 1 [3]: A t -s put wr w t OR t -tr c rv (rpc y -ctr vu,.. c 0) wtut vt t rqurt t y trc. Pr: Ott. T t r crcut Fur 3 s xp. A upx syst c cstruct y tw upcts ( ) t r crcut. Accr t Tr 1, w c rv wr w 1 y rpc t wt c 0 sc t s t -s put t OR t -tr. W sy tt s trstv ut wr w tr s pt r wr w t t. I t, Fur 4, tw pts y cvr, wc s c t cvr t tw pts. W t t AND-cvr tw t -crtc pts ts tw pts cvr s AND t. Fr xp Fur 4, t -crtc pts p 1 p 2 cvr AND t s s t AND-cvr p 1 p 2. W v t w tr. Tr 2: Lt wr w t -s put t OR t. I tr s AND-cvr t -crtc pts wr w s trstv ut, wr w c rv wtut vt t y trc. Pr: Ott. Fr xp, wr w 3 ( -> ) c rv ccr t Tr 2. Frst, wr w 3 s t -s put t OR t. T trstv ut s w 3 csst {,,, }, wc OR t s t y cvr t -crtc pts. Sc tr s AND-cvr w 3 s trstv ut, wr w 3 c rv. I ct, wrs {w 3, w 5, w 6 } stsy t ct Tr 2 s wrs {w 3, w 5, w 6 } r rv. T rsutt crcut tr rv wrs w 1 (y Tr 1), w 3, w 5, w 6 s sw Fur 5. W c s pt s sr s [3] t urtr ruc t r vr. Tw ss wc pt t Fur 5: T r-sytsz crcut tr wr rv. 2
4 quvt B uct ut t t t -crtc pts c sr. Fr xp Fur 5, t utput tt 2 v t s uctty. W c sr t utput ss 2, s strt Fur 6. Supps quvt ss r w t sr wtut vt t rqurt t y trc. T crcut s sw Fur 6. A pt s s t prcpt pt y c (crs r crs) t pt s y c vr ct t crcut y [7]. Tr 3: Atr wr rv ccr t Tr 1 Tr 2, t -crtc pts r tr s pts r prcpt pts [7]. Pr: Ott. T tut r ts tr s s ws. Our wr rv trs urt tt tr wr rv, crcuts st v t s utput vu wvr t -crtc pts r r ctvt. Trr, y y crt t -crtc pt w t ct crcut s y. I Fur 6, t pts r tr s pts r prcpt pts. W w scuss scs s tr r-sytss. Csr Fur 6. T st tru pt pss tru s {----} ws pt t s 5. Assu t t rqurt s 6. Trr, s t sc 1 t r-sytsz crcut Fur 6 w t s t sc 0 t r crcut Fur 3. I tr xp, sc pts pss tru r s pts, t sc s t. Gry, tr r-sytss, pts ws ys r rtr t 5 c tr s pts r prcpt pts; tt s, t st tru pt t r-sytsz crcut s t y 5. As rsut, t sc c t r-sytsz crcut s t st 1 (= t ). 4. Dy Trc Itr Ss T r-sytss ty scr prvusy s pp t prry utputs ws rrv t s suscpt t y vrt. W c s py tc pprc t prtct t rrv t tr ss r y vrt. Dy trc tr ss c v t vt r ruct. I Fur 7, csr t crcut wc s st t s s tt Fur 3 xcpt Fur 7 s AND t. B s Fur 7 rprst t -crtc s t -crtc pts. I t r-sytss tcqu s pp t y t prry utput, y t -s put wr w 1 c rv t rsutt crcut s sw Fur 8. I ts xp, t r vr s r cus tr s y rv t -s put wr. W w sw tt y py y trc tr s w, t r pty c ruc. T rsut tr prr r-sytss w s sw t ry cs Fur 9. Accr t Tr 3, pt st {s---} cs tr s pt (st) r prcpt pt (st). Tus, pt {s----x---} pss tru s pt (st) {s---} s s s pt. Sry, tr pts pss tru {t---}, {s }, {t } r tr s pts r prcpt pts. Ts s t c Fur 7: A xp strt y trc tr ss. w w Fur 6: T r-sytsz crcut tr s sr. Fur 8: T r-sytsz crcut y ppy y trc t prry utput Fur 7.
5 s t s 2 t 2 Fur 9: T r-sytsz crcut y ppy y trc tr s w Fur 7. s s pts r prcpt pts r t t -crtc pts. Csquty, s {,,,,, } Fur 9 c t -trs. W w ctu t prr y trc t prry utput, t -s put wrs t tr OR t -trs {,, } c rv. T r-sytsz crcut s sw Fur 10. T tt r vr t r-sytsz crcut Fur 10 s 7 (ts), wrs tt t r-sytsz crcut Fur 8 wtut y trc tr ss s 9 (ts). 5. Exprt Rsuts x W v pt t r-sytss t [3] urs SIS vrt, s xprt st MCNC ISCAS crs. T 1 prvs t cprs t r vr tw t t [3] urs. T 2 strts t vts y vrt trc r crcuts. W rst ptz crcut wt scrpt.y, t us y trc vus 10% 15% t r crcut y t r-sytsz crcut. T t rqurt r c x w w Fur 10: T r-sytsz crcut y ppy y trc t prry utput Fur r-sytsz crcut s st t t y t crrsp r crcut. I T 1, cu sts t t r crcut. Cus tw tr prv t r y t r crcut, rspctvy. Cus ur v sw t rsuts r 10% y trc cus sx t sv r 15% y trc. Fr v y trc rqurt, w r-sytsz t r crcut y t t [3] urs vuy. T w cpr t r vr tw t r-sytsz crcuts. Fr xp, crcut C880 s t r 3569 t y W t y trc s 3.36 (= 10%*33.6), t r-sytsz crcut y [3] s t r vr 31.2% t r crcut s r. O t tr, t r-sytsz crcut y ur t s t r vr 14.9% t r crcut s r. W t y trc s 5.04(=15%*33.6), t r-sytsz crcut y [3] s t r vr 53.1% w y ur t s t r vr 25.4%. O t vr, r 10% (15%) y trc, t r vr r [3] urs s 29% (48%) 12% (21%), rspctvy. Bt t ts usuy sp w scs r c crcut. W v s prr Mt-Cr xprts t strt t ct y vrt trc T 2. I t xprt, t y t s v s prty sty uct sr t [6]. W t 1000 sps r crcut 1000 sps ts r-sytsz crcut wt 10% y trc r Mt-Cr xprts. Atr tt, t y c sp s ccut. I T 2, cu sts t t r crcut. Lt r t y t crcut. Cu tw sws t ur crcut sps ws ys r sr t {0.8* r } r t r crcut, cu tr sws t ur r ts r-sytsz crcut. Sry, cus ur t v rprt t urs sps ws ys r sr t {0.9* r }, {1.0* r }, {1.1* r }, {1.2* r } r t t r crcut ts r-sytsz crcut. T crcut t481 s xp. Lt t t rqurt 1.1* r (1.1*34.1 = 37.51), 815 sps t r crcut t t t rqurt w 963 sps t r-sytsz crcut stsy t s rqurt. I Fur 11, w rw t strut curvs Mt-Cr sps crcut t481 ts r-sytsz crcut wt 10% y trc. T str vt
6 T 1: Cprs tw [3] ur t Or crcut 10% y 15% y trc trc Crcut [3] Ours [3] Ours Ar Dy Ar Ar Ar Ar vr vr vr vr (%) (%) (%) (%) C C C C C C C C pr rt t sy u px px Av t r crcut s 2.39 w tt t r-sytsz crcut s T curvs s rv tt t r-sytsz crcut s r st t vr t t r crcut. 6. Ccuss W v prps rwr t r-sytsz v crcut r t y trc. Our t s wt upx syst; w t pt wr rv s sr t ruc t r vr t y trc structur. Tw v trs r urtr r ruct r prst. Exprt rsuts strt t vts y vrt trc r r-sytsz crcut. Rrcs [1] K. Br, G. Grtu, M. Lusr, I. Scstr, C. Hws, Dct-s y tst rsstv vs-ctcts, crtc vut, Prc. Itrt Tst Crc, pp , Spt [2] M. A. Brur, C. Gs, S. Gupt, Nw vt tst prs r prrc p su-cr VLSI crcuts, Tutr Nts, VLSI Tst Sypsu, Apr [3] S-C C, C-T Hs, K-C Wu, R-sytss r y vrt trc, Prc. Ds Autt Crc, pp , Ju [4] Su H C, Bpu C. Pu, Kus Ry, Nv sz rt r y prvt ur T 2: Sttstc rsuts Mt-Cr xprts 0.8* r 0.9* r 1.0* r 1.1* r 1.2* Crcut r O R O R O R O R O R C C C C C C C C pr rt t sy u px px Av O: Or crcut R: R-sytsz crcut prcss vrt tr tcy, Prc. Ds Autt C., pp , Ju 7-11, [5] E.T.A.F. Jcs M.R.C.M. Brr, Gt sz us sttstc y, Prc. DATE, pp , [6] J-J Lu, A. Krstc, L-C. W, Kw-T C, Fs-pt-wr sttstc t yss ct pt sct r y tst t vt, Prc. Ds Autt Crc, pp , Ju [7] Sr R, Sr B. K. Vruu, Jt W, A ty t prv t y t prsc prcss vrts, Prc. Ds Autt C., pp , Ju 7-11, [8] Axr S, Fuct t ptzt, Prc. Itrt Crc Cputr-A Ds, pp , Nv Fur 11: T strut curvs Mt-Cr sps crcut t481 ts r-sytsz crcut.
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