su m e t h at all d ela y e d ges in t h e d esign are e q ually su bj ect to v ariation , w e can ac h ie v e m a x im
Uncertainty-Aware Circuit Optimization Xiaoliang Bai University of California at San Diego La Jolla, CA 92037
Chandu Visweswariah IBM Thomas J. Watson Research Center Yorktown Heights, NY 10598 ! "#
Philip N. Strenski IBM Thomas J. Watson Research Center Yorktown Heights, NY 10598 $ %& "! "#
David J. Hathaway IBM Microelectronics Essex Junction, VT 05452 & ! "#
ABSTRACT
')(+*-,./1024357698;:@A5#(+(+BC/=D8;53-3:FE:N./HG/=:FIr/=:+*-:+8;EsG."."D*-U/=:+,8.fG893t*iG8DRuGIP/=DJ=:+8;E LGJ=:FG/=:F,8;.gG(+()IGD."5`/=K;5QUO5PJ"RX,J=*iG8I#5f/=,vLGJ"2sRwJ=,*xUJ=5#3:+IPB /=:+,8qbmy:+*-U(F5k./HG/=:+./=:+IG(UJ=:+8;I#:+U;(+5#.l/=5P(F( D.z/=K;G/l/=K5mLGJ=:FG/=:+,8 ,Rz/=K5g(+:+*-::/=KD;.M5PGIP5PJ=09G/=:F8E-/=K;5VUJ=,0;(+5#*`bM!K5PJ=5m:+.eG(+.",|G UJHGIP/=:+IG(*iG/"/=5PJ?/=K9G/&."IHK;5P*iG/=:+I J=5#./"J=D;IP/=DJ=:+8;E)3,@M8;./"J=5#G*T:F8 /=K5e35#.":+E8|*-5P/=K;,3,(+,E2i:+.!5G.":+5PJ\/=,kI#,8;I#5#:+L
[email protected];5P8|/=K5PJ=5eGJ=5 RX5P@!57Jz5#SD;G(+(>>>>bon~/qK9G.q(+,8;E)0O5#5#8N."UO5PI#D;(FG/=5#3 /=K;G/iGEEJ=5#.".":+L 5`,U/=:+*-:F#G/=:+,8,RlG{I#:ÿEDGFYHZ1J K9pÿEMCNPOQ;=RF 8:9$SUTCV28WVÿXK Þ*) Ñ+) [ 1W\] .1"ÿED^1W`_ .ba c+dYefga Þ*) Ñ+)h[ >Z\]Ri 1 > ÿED > `_ 8:9 } H+1 >} .1} i 1> } ;= } ;7M} MCN } / } v } l qjrsc*mtmtfjqja } l m c+dYefjqga } .ac+dYefja} i a c+dYefga } l m nIo^fjd } l x*yy*fjd } z m nIo^fjd } z x*yy*fjd } |ux*yy*fjd}
}
}
ÔØú×+Ò+×wÔÏ"Ó-ßÔÏ=×FÔÝÒFÐ\Ñ=â;ÔÑÏ=Ð#ÛÏ=ÐPÞ"Ð#ÖÑ=Þ1ÍPÓÍ#Ò+Ð\Ñ=×+á-Ð ÔÏ"Ï=×+ßÔÒ;Ñ=×+á-Ð!ßÔÏ=×FÔÝ;Ò+Ð#ÞT?S?Y+zÒFÔØ;Ö;ÍHâ;×+Öã ÍPÒFÎÍHÕ4Ð#ÜãÐ Ï=Ð#ðØ×
[email protected]!@M2BRCzaIBRD!XIJPl XdF^?!FPJ`dCD!@GdW/JCSBMQ
[email protected]D!OW?QBREJ BR?!F#JXIO2KpG@G @SW4lzµ&l XIF#JCSBMQXI@JD!O)WR?QBEJ^@GD!XI@JVJFPMLD!@O)G KjF:?!F.ad?!O&H4`IMPFPH®`dJ@GIWEFLD!XIO&HáuOiV`IGdMPFL?DQB@GTDgZ´B2KjBR?!FPGdFPJJPí EFLD!XdO&H1µ/?!FLJ`IC8D!JrCOTO)1±T`BRC@DQBxD!@A\FPC8ZJ@E@C²Bx?2ly{CD!XdO)`dW)XD!XIF `IGdMPFL?
[email protected]Z4hBPKoBx?!F#D!`dGI@GIWXIBJrBC@E@D!@GdWJCSBMQ.D!XIBRDr@JÔaIJ KjOR?!JF D!XBRGD!XdFGdO)E@GBRCCZ.D!`IGIFPH1ML@?!ML`
[email protected]>D!XdF
[email protected]XTDrOisD!XIF KoBRCC7XBRJpU FPFPG?!FPHd`IMLF2H@G/EOR?!FbD!XBRG XBRC8igl ysJ>¹}BGHÆBR?!FsM:XIBGdW)F2HYTD!XIFsBEO)`dGTDjOiJFPaIBR?QBRD!@OG M2BRGU F MPOG&D?!OCCSFPH YnUI`4DVBRDVad?!O)WR?!FPJJ@A\FPC8Z
[email protected]XIFL?cMPOJDr@G.D!XdFCS@E@8D!@GIW JCSBMQ l @Wdl JXdOxKpJsD!XIF3FLÅFPMLDbOiABR?Z4@GIW}¹BRD|BrI~4F2H/ÆBRGH JCSBMQ3XI@JD!O)WR?QBEJO)U4DQB@GIFPHVUTZ3A)Bx?
[email protected]Æ
[email protected]FoXdO)CSHd@GIWb¹3d~4F2H BR?!FcJXIO2KpG@G @Wdl ï4l XIFLJFVFL~4a FL?!@EFPGTD!JjK>FL?!FVa F:?i*O?!EFPH/O)G D!XIFbJ!BEFcÄIR)â¨rFL~4FPMP`dD!@OGdh`IGd@DjE}BML?!OBRJ @SW4l7ul
4.2 Degradation due to variations
140
120
# s ig nals
100
80 P re-tuning 60
Normal-tuning S igma=5 S igma=10
40
S igma=20 20
0 -60
-40
-20
0
20
40
60
80
100
S la ck (ps)
øpùkúû7üxýÿþ û)ý& ü ù
7 ù úü "!#Iüxý$2ûù%7ú&
Iü.ù
ø{ù²ú û7üxý$µ*),+zý-.²i0-Iüù 7ú¥±&
140
120
# s ig nals
100
80 P re-tuning 60
Normal-tuning k=10
40
k=50 k=100
20
0 -60
-40
-20
0
20
40
60
80
100
S la ck (ps)
øpùkúû7üxý('*),+zý-./,0-Iü7ù%7ú213&
465,798,:;=@A5CB> 5EDF8 @>5C79HJIKL:?> INM3J7=I ;9;WVrM3