EECS 427 Lecture 5: Logical Effort. Reminders

Transcription

1 9//009 EES 47 Lecure 5: Local Eor Readn: handou Remnders Semnar announcemen: Dr. Mchael Mcorquodale, TO and ounder, Mobus Mcrosysems Toc: Srah Down he rooked Pah The Dynamc Process o ommercalzn Research Frday 9/5, :0-:0 m, 00 EES AD wll be done n eams. AD s due nex Wednesday Sar early Try no o sk lecure Lookn ahead: HW Projec roosal due Wednesday 0/7, weeks away Quz Wednesday 0/4, weeks away

2 9//009 Inro o local eor : Local eor : Elecrcal eor : Parasc delay Las Tme Delay comonens revew Normalzed Delay 5 4 Inverer: = ; = -nu NAND: = 4/; = Eor Delay 0( ) Inrnsc Delay 4 5 Fanou I. Suherland, e al, Local Eor, Academc Press, 999

3 9//009 More comlex crcu Every ae s szed accordn o a : mn-szed nverer nand 4 nand 4 ae, nor ( nand 4 ae, nv ae, nand 4 nand 4 ae, nand 4 ) 0 0 Mulsae eor Pah eecve an-ou F F F

4 9//009 4 Mnmum delay Toal delay Subsue F F Subsue F Mnmze he delay Solve or he mnmum delay 0 mn F 0 Solve or he mnmum delay Delay s omal when sae eors are equal h h 0 Gae eor Branchn h h H ) ( ) ( Dene ah eor H GF G ) ( ) ( G: ah local eor F: ah eecve an-ou ah on ah o ah on b b ah o ah on Branchn eor

5 9//009 Equvalen Pah Eors F B FB G ou n b H Pah Eor GFB Pah Eor: Does no chane wh added nverers Does no deend on szes, bu on ooloy Mnmum Delay Sae eor o sae : Omal sae eor: For N saes: Mnmum Delay: H GFB h hˆ h H hˆ N 0 0 ( hˆ ( H N NH ) / N ) 5

6 9//009 Examle o comue mn. delay Un szed nand ae G a F L n 4 0 B H GFB 47.4 hˆ H.6 0 b 6.9 c ( 0 nand hˆ).7 Sae szn Aer comun ĥ hˆ n hˆ ou ou n Work backwards o sze each ae n, c nand ˆ h L 6

7 9//009 Sae szn examle nand L n, c hˆ 4 0 un _ nand n, c un _ nand Sae szn Aer comun ĥ hˆ ou h ˆ n ou n an also work orward o sze each ae h ˆ.6 n, a un _ nand n, b n, b. 6 un _ nand nand 4 / 7

8 9//009 alculan omal # o saes Pah eor H can be used o deermne he omal number o saes Assumn we add n nverers New number o saes N=n +n G, F, B don chane H s xed Bu nrnsc delay ncreases ( n n ) ( n n) F n n Omum s echnoloy deenden nv Summary o he ermnoloy Gae level Parasc delay Local eor Elecrcal eor Sae eor Sae delay h n ou h Pah elecrcal eor Pah local eor Branch eor Branchn acor Pah F G B ou ah n ah b b BF on ah on ah o ah 8

9 9//009 Mehod Pah eor Omal sae eor Omal ah delay Sae szn H GFB N hˆ H ou, NH n, N hˆ n,. omue ah eor. omue omal sae eor. Add buers (deermne omal number o saes) 4. omue an-ou o each sae 5. Sze ndvdual aes (workn backward or orward) Mehod examle / b = because s he same ye o ae G 9 B F 60 6 H GFB. Nˆ 5 5 hˆ.. 0 (5. 6 ) 4 0 hoose # o saes such ha sae eor s close o 4. Add nverers o he exsn saes 9

10 9//009 Mehod examle: Szn / ˆ. h ˆ.9 h / / n, e n, d n, c n, b n, a ou, e Branchn Always check hs Mehod examle: Gae szn / e) (/)x(8.75) (/)x(8.75)(8 c) a) 4/5x.05 4/5x.05 /5x /5x /5x /5x /5x /5x.05 /5x.05 /5x 0

11 9//009 Wron number o saes 5 4 Hher number o saes han omal s less bad D^(N) D^(N^ ) N N^ Wron ae sze.6.5 D(s) D() Penaly s he same n any szn drecon Snle ae s szed wron s

12 9//009 0 or our 0nm echnoloy Inverer Delays Tau's Delay (s) Nom nal Fasas Slow -slow Tau (s) Nom nal Fasas Slow -slow Fanou 0 D()-D(0) D()-D() D()-D() D(4)-D() D(5)-D(4) Tau and Inrnsc Delay (Pnv) or 0nm Tech P_nv P_nv /60 560/80 0/560 Nom nal Fasas Slowslow Averae Tau value Averae Pnv W/Wn No Fas slow m 0/ / / / / / W/Wn

13 9//009 Bes number o saes nv.8 Pah eor H Bes number o Mn. delay saes Sae eor h IBM 0.um haracerscs har / Un dsance NMOS j PMOS j NMOS PMOS NMOS R eq PMOS R eq Parameer.06F/um (W).0F/um (W).57F/um (W).44F/um (W) 4.4 k/um (W) k/um (W) * All values obaned rom devce smulaon

14 9//009 Devce Smulaons I DB I G Juncon aacance Gae aacance I d Q jv I d Q V Devce Smulaons R ull eq R eq V I DD ull D ull hal Req Req R hal eq V I DD hal D 4

15 9//009 IBM 0.um haracerscs har / Un dsance Poly Ressance M Ressance Parameer 58./um (l) 0.44/um (l) M-M6 Ressance 0./um (l) Uer layer Meals 0.09/um (l) Plae Above, Below Isolaed Poly aacance 0.69 F/um 0.9 F/um M aacance 0.69 F/um F/um M-M6 aacance 0.4 F/um 0.59 F/um Uer layer Meals F/um 0.50 F/um * All values obaned rom desn manual IBM 0nm haracerscs MOS Tye Parameer alculaed Smulaed % Error NMOS.0F/um.57F/um.7% PMOS.94F/um.44F/um 5.8% NMOS j.09f/um.06f/um.% PMOS j.44f/um.0f/um 7.% NMOS (FO4) 4.8s 5.5s % PMOS (FO4) 86.s 68.s 6% * alculaed = 0.69 * R eq * L L = 4,P + 4,N + j,n + j,p * Smulaed = 50% - 50% ranson 5

16 9//009 Why use P/N =? P/N rao Nose marns are balanced Equal sloes How abou P/N =.5? Lmaons Inernal caacance aacance n nernal nodes Body eec 6

17 9//009 Lmaons - Taern Transsor szes n sack are deren The laes arrvn nu should be closes o ouu node Wha sze s he bes choce? ca n nernal node Lmaons Branchn Assume ha he sze o he o-ah ae racks he sze o he ae on-ah o-ah h o h on on-ah Szn one crcal ah o a branch may make he oher ahs worse 7

18 9//009 Lmaons Seres Devces Models seres devces o sze o be equvalen n drve srenh o a snle devce o sze No very accurae Soluon smulae aes o drecly nd local eors Lmaons Sloe & Inerconnec Inores mac o nu sloe on sae delay Inerconnec caacances are sde loads. They do no necessary scale wh aes and canno be lumed n he local eor ormulaon 8

19 9//009 Lmaons - Scaln Scaln s no lnear wh wdh k S R c k S R R R k S k S R c k v k Permeer Narrow wdh eecs Process varaons Parasc delay o mul-nu aes usually much less han smle model redcs Duson sharn, nu deendences Szn ool Tool: TILOS [Dunlo 89] Sar wh all ranssors o mn. sze Fnd crcal ah (Omze ah) omue delays Increase sze o ranssors n crcal ah Sze ah wh bes sensvy Reea Goal o ah dsrbuon All ahs equal n lenh 9

20 9//009 Area - Delay Bu he mac o rocess varaons can be worse or he omzed ahs more on hs laer n he course Summary Local eor s useul or hnkn o delay n crcus NANDs are aser han NORs n MOS Pahs are ases when eor delays are ~4 Pah delay s weakly sensve o saes, szes Bu usn ewer saes doesn mean aser ahs Delay o ah s abou lo 4 F FO4 nverer delays Inverers and NAND bes or drvn lare cas Provdes lanuae or dscussn as crcus Bu requres racce o maser 0