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1、JointSupply,ThresholdVoltageandSizingOptimizationforDesignofRobustDigitalCircuitsDineshPatil,MarkHorowitzStanfordUniversity(ddpatil,horowitz)@stanford.eduAbstractmanceconstraint.Giventheimportanceofcreatingoptimizeddesigns,Inthispaper,wedescribeamethodforjointsupply,manyapproacheshavebeendevelopedto
2、addressjointthresholdvoltageandsizingoptimization,inpresenceoptimization.Someofthesemethodstweakthecir-ofuncertaintransistorparameters,toobtainrobustcuitlocallyusingsensitivityinformation[16],whileenergy-delayoptimaldesigns.Weextendourprevi-someoptimizersuseonlypartofthedesignspaceousworkonrobusttra
3、nsistorsizing,whichaccounted({sizing,Vth,Vdd})[19].fortheaddeddelaycausedbytransistorvariationsUnfortunately,aswescaletosub-90nmfeaturesize,byaddingmarginsoneachgatedelayproportionalbothintrinsicdevicevariationsandlithographycontroltotheestimateddelayvariabilityandusinga“softissuesareincreasingthest
4、atisticalvariabilityofeachmaximum”functiontocombinepathdelaysatcon-gateinthecircuit.Thesevariationscausealargespreadvergingnodes[13],tooptimizeVdd,andVthvaluesintheoveralldelayandleakageenergyofthecircuit,aswell,andtoincludethecostofuncertaintyinadverselyaffectingtheparametricyield[5].Thusitenergy.U
5、singposynomialanalyticmodelstopredicttheisimportantforcircuitoptimizationroutinestotakemeansandvariancesofdelayandenergy,wecreateanvariationintoaccountduringoptimization.Approachesoptimizationproblemthatcanbeefficientlysolvedviathatdofulljointenergy-delayoptimizationtunethede-GeometricProgramming.Mon
6、te-Carlosimulationsonsignvariablessequentially[7]and/orusesimpledeter-representativedatapathcircuitsshowthatourheuris-ministicmodels,notaccountingforprocessvariationsticstomodeluncertaintyimprovetheresultingoptimal[1],[11].Somerecentlydevelopedstatisticalmethodsenergy-delaycurvesbyroughly10%.address
7、variationsinleakagebutdonotconsiderjointsizing[10],whileothersthatperformdualVdd-Vthandsizingoptimizationuselocalsensitivitybasedtweakingofthecircuit[17].Fortruerobustenergy-delayoptimalI.Introduction
