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DC–DC Converter-Aware Power Management for Low-Power Embedded Systems

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IEEETRANSACTIONSONCOMPUTER-AIDEDDESIGNOFINTEGRATEDCIRCUITSANDSYSTEMS,VOL.26,NO.8,AUGUST20071367

DC–DCConverter-AwarePowerManagementfor

Low-PowerEmbeddedSystems

YongseokChoi,StudentMember,IEEE,NaehyuckChang,SeniorMember,IEEE,andTaewhanKim,Member,IEEE

Abstract—Mostdigitalsystemsareequippedwithdc–dccon-verterstosupplyvariouslevelsofvoltagesfrombatteriestologicdevices.DC–DCconvertersmaintainlegalvoltagerangesregardlessoftheloadcurrentvariationaswellasbatteryvoltagedrop.Althoughtheefﬁciencyofdc–dcconvertersischangedbytheoutputvoltagelevelandtheloadcurrent,mostexistingpowermanagementtechniquessimplyignoretheefﬁciencyvariationofdc–dcconverters.However,withoutacarefulconsiderationoftheefﬁciencyvariationofdc–dcconverters,ﬁndingatrueoptimalpowermanagementwillbeimpossible.Inthispaper,wesolvetheproblemofenergyminimizationwiththeconsiderationofthecharacteristicsofpowerconsumptionofdc–dcconverters.Specif-ically,thecontributionsofourworkareasfollows:1)Weanalyzetheeffectsoftheefﬁciencyvariationofdc–dcconvertersonasingle-taskexecutionindynamicvoltagescaling(DVS)schemeandproposetheDC_DVStechniquefordc–dcconverter-awareenergy-minimalDVS.2)DC_DVSisthenextendedtoembedanawarenessofthecharacteristicsofdc–dcconvertersingeneralDVStechniquesformultipletasks.3)WegoontoproposeatechniquecalledDC_CONFforgeneratingadc–dcconverterthatismostenergyefﬁcientforaparticularapplication.4)Wealsopresentanintegratedframework,i.e.,DC-lp,basedonDC_DVSandDC_CONF,whichaddressesdc–dcconverterconﬁgurationandDVSsimultaneously.ExperimentalresultsshowthatDC-lpisabletosaveupto24.8%ofenergycomparedwithpreviouspowermanagementschemes,whichdonotconsidertheefﬁciencyvariationofdc–dcconverters.

IndexTerms—DC–DCconverter,lowpower,voltagescaling.

I.INTRODUCTION

LMOSTallmoderndigitalsystemsaresuppliedwithpowerthroughdc–dcconvertersbecausehigh-performanceCMOSdevicesareoptimizedtospeciﬁcsupplyvoltageranges.DC–DCconvertersaregenerallyclassiﬁedintotwotypes,namely:1)linearvoltageregulatorsand2)switchingvoltageregulators,accordingtothecircuitimplementation.However,nontrivialpowerdissipationisunavoidableinbothtypesofvoltageconversionanddirectlyaffectsbatterylife.Fig.1showsthepathofcurrentﬂowthroughadc–dcconverter

ManuscriptreceivedJuly25,2005;revisedAugust4,2006.ThisworkwassupportedbytheInformationTechnologyResearchandDevelopmentProjectfundedbytheKoreanMinistryofInformationandCommunications.TheworkofT.KimwassupportedinpartbytheNanoIP/SoCPromotionGroup,SeoulResearchandBusinessDevelopmentProgram,andinpartbytheMinistryofScienceandTechnology/KoreaScienceandEngineeringFoundationthroughtheAdvancedInformationTechnologyResearchCenter.Thispaperwaspre-sentedinpartattheDesignAutomationConference2005,Anaheim,CA,June2005.ThispaperwasrecommendedbyAssociateEditorM.Pedram.Y.ChoiandN.ChangarewiththeSchoolofComputerScienceandEngineering,SeoulNationalUniversity,Seoul151-742,Korea.

T.KimiswiththeSchoolofElectricalEngineeringandComputerScience,SeoulNationalUniversity,Seoul151-742,Korea.

DigitalObjectIdentiﬁer10.1109/TCAD.2007.890837

1368IEEETRANSACTIONSONCOMPUTER-AIDEDDESIGNOFINTEGRATEDCIRCUITSANDSYSTEMS,VOL.26,NO.8,AUGUST2007

workisasfollows:Althoughaneffectivepowermanagementschemecanreducethepowerconsumptionofadevicetoalargeextent,itdoesnotalwaysmeanthatitalsoreducesthepowerconsumptionofadc–dcconverterminimally,insomecasesoperatingveryinefﬁciently,resultinginapoorbatterylifeenhancement.Consequently,itisquitenecessarytosolvethetwoproblems,namely:1)theproblemof(output)voltagescalingofadc–dcconverterand2)theproblemofvoltagescalingthatisappliedtothedevicesotherthanthedc–dcconverterinanintegratedfashion,sothatthetotalenergyconsumptionisgloballyminimized.

DVSisacceptedasoneofthemosteffectiveandwell-studiedpowermanagementtechniques.Assumingthattheprocessorsupplyvoltageisdynamicallyandcontinuouslyvariable,thereareoptimalalgorithmsforschedulingnonperiodictasksandselectingthebestvoltageforeachtask[11],andtherearealsovoltagescalingtechniqueswithﬁxedpriorityscheduling,whichareapplicabletoperiodictasks[12].Essentially,moststudiessuggestedDVSalgorithmsbasedondynamicorstaticpriorities.Thesealgorithmsaredifferentiatedbyhowslacktimesareestimatedandredistributed[13]–[17].SomeDVSschemesadjustthesupplyvoltagewithinanindividualtaskboundary(i.e.,intratask),notontask-by-taskbasis[18]–[20].In[21],practicalDVSschemeswiththeconsiderationofdis-cretesupplyvoltageandnonuniformloadcapacitancesweresuggested.However,whilealltheseDVSschemesdosaveenergy,noneofthemtakeintoaccounttheeffectsofvoltagescalingonthedc–dcconverter,theresultingchangesinloadcurrent,andtheireffectontheefﬁciencyofthedc–dcconverteritself.Toovercomethislimitationinpreviouspowerman-agementtechniques,wewillnowaddresstheissueofdc–dcconverter-awarepowermanagement.Speciﬁcally,weapproachtheproblemintwoaspectstocoverthecorepartsoftheproblemofdc–dcconverter-awarepowermanagement.

1)Theconverter-awarevoltagescalingproblem.Forasin-gletaskwithexecutioncyclesandadeadline,wederivethepowerconsumptionmodelofadc–dcconverterbyanalyzinghowpowerconsumptionisrelatedtooutputvoltageandproposearobustvoltagescalingtechnique1thatminimizesthesumoftheenergyconsumedbytheexecutionofthetaskandtheenergydissipatedbythedc–dcconverter.Theproposedtechniqueisthenextendedtohandlemultipletasks.Wethenaddresstheotherproblem.

2)Theapplication-drivenconverteroptimizationproblem.Thisinvolvesﬁndingthedc–dcconverterconﬁgurationthatisbestsuitedtotheapplicationandsystem,intermsofminimizingthetotalenergyconsumption.

SectionIIstartswithabriefsummaryofthefunctionofdc–dcconverters,followedbythedevelopmentofamodeloftheirpowerconsumptionandthederivationofpowerequations.InSectionIII,wepresentanintegrateddc–dcconverter-awareenergyminimizationalgorithm,whichessentiallysolvesthetwocoreproblems,namely:1)converter-awarevoltagescaling

1Note

thatourproposedvoltagescalingtechniqueisﬂexibleenoughtobe

incorporatedintomostoftheexistingDVSmethodswithminimalmodiﬁcation.SectionIII-Dcoverssuchageneralapplicability.

Fig.2.DC–DCconvertersgeneratedifferentsupplyvoltagesfortheCPU,memory,andharddiskdrivefromasinglebattery.

and2)application-drivenconverteroptimization.SectionIVpresentsasetofexperimentalresultsthatshowtheeffectivenessoftheproposedtechniques.Finally,concludingremarksaremadeinSectionV.

II.DC–DCCONVERTERS

A.VoltageRegulation

Theproliferationofdigitaldevicesandconstanttechnologi-calinnovationmakeitimpossibletouseasinglesupplyvoltageforalldevices,andoften,multiplelevelsarerequiredinasingledevice.Sinceallsupplyvoltagesaregenerallyderivedfromasinglebattery,voltageregulators(dc–dcconverters)areneededtocontrolthesupplyvoltageforeachdevice,asindicatedinFig.2,whichshowsasimpliﬁedpowersupplynetworkforatypicalbattery-operatedembeddedsystem.

Theprimaryroleofadc–dcconverteristoprovidearegu-latedpowersource.Unlikepassivecomponents,logicdevicesdonotdrawaconstantcurrentfromtheirpowersupply.Thepowersupplycurrentchangesrapidlywithchangesinthedevices’internalstates.AnunregulatedpowersupplyislikelytosufferanIRdropcorrespondingtotheloadcurrent,whereasaregulatedpowersupplyaimstokeeptheoutputvoltageconstantregardlessofvariationintheloadcurrent.ThephenomenonofIRdropiscausedbyinternalresistanceofthepowersupply.Therefore,adc–dcconverterisstillneededforvoltageregula-tionevenifthereisonlyonesupplyvoltage.B.SwitchingRegulatorBasics

Wefocusonminimizingthepowerdissipationofastep-downswitchingregulator,whichisthetypemostfrequentlyusedinlow-powerapplications.Aswitchingregulatorusesaninductor,atransformer,oracapacitorasanenergy-storageelementtotransferenergyfromthepowersourcetothesys-tem.Theamountofpowerdissipatedbyvoltageconversioninaswitchingregulatorisrelativelylow,mainlyduetotheuseoflow-resistanceMOSFETswitchesandenergy-storageelements.However,theamountofpowerdissipatedbyalinearregulatorisratherhigh,mainlybecausethereisanupperboundontheefﬁciencyofalinearregulator,whichisequaltotheoutputvoltagedividedbytheinputvoltage.Inaddition,switchingregulatorscanincrease(i.e.,boost),decrease(i.e.,buck),andinvertinputvoltagewithasimplemodiﬁcationtotheconvertertopology,unlikelinearregulators.Fig.3(a)showsthebasicstructureofthestep-down(buck)switchingregulator.Aswitchingregulatorcontainsacircuit,locatedonthepathbetweentheexternalpowersupplyandtheenergy-storage

CHOIetal.:DC–DCCONVERTER-AWAREPOWERMANAGEMENTFORLOW-POWEREMBEDDEDSYSTEMS1369

󰀃󰀄∆IL(PWM)2··(D·RSW1+(1−D)·RSW2+RL+RC)32(2)

whereVI,VO,andIOaretheinputvoltage,outputvoltage,andoutputcurrent(i.e.,theloadcurrent)ofthedc–dcconverter,respectively;andRSW1,RSW2,RL,andRCaretheturn-onresistanceofthetopMOSFET(SW1),theturn-onresistanceof

1370IEEETRANSACTIONSONCOMPUTER-AIDEDDESIGNOFINTEGRATEDCIRCUITSANDSYSTEMS,VOL.26,NO.8,AUGUST2007

thebottomMOSFET(SW2),theequivalentseriesresistanceoftheinductorL,andtheequivalentseriesresistanceofthecapac-itorC,respectively.Dand∆IL(PWM)arethedutyratio(timewhenthecurrentactuallyﬂowsthroughthecomponent/totaltime)andtherippleofthecurrentﬂowingthroughtheinductor,respectively,whichcanbeexpressedasfollows:

,∆IL(PWM)=

VO·(1−D)Lf·f(3)

whereLfisthevalueoftheinductor,andfSistheswitching

frequency,whichisassumedtobeconstantinaPWMdc–dcconverter.

Pconduction(PWM)consistsoftwoterms.Theﬁrstandsecondtermsrepresenttheconductionpowerconsumptionsduetothedccomponentandtheaccomponent(orcurrentripple),respectively,ofthecurrentﬂowingthroughallcomponents(i.e.,SWP1,SW2,L,andC)ontheRcurrentpath.Intheﬁrsttermofconduction(PWM)in(2),D·istheeffectiveresistanceoftheSW1+(1−D)·RcurrentpathofSWthe2+Rdc–dcLconverter,consideringthedutyratioofeachcomponentonthatpath.ThedutyratiosforSW1,SW2,andLareD,(1−D),and1,respectively.(SincethedccomponentofthecurrentﬂowingthroughtheCiszero,thetermrelatedtoCisomitted.)ItiswellknownthattheconductionpowerconsumptionofsomesystemscanbeexpressedbyI2·R,whereIisthecurrentﬂowingthroughthesystemandRistheresistivecomponentofthesystem.Therefore,theproductofthiseffectiveresistance

andI2

,whereIﬂowingthroughOisequivalenttothedccomponentofthecurrentO

eachcomponent,canbeusedtomodelthedccomponentoftheconductionpowerconsumptionofthePWMdc–dcconverter.Inthesecondterm,D·R(1−D)·RSW1+SW2+RL+RCistheeffectiveresistance,and(1/3)·(∆IL(PWM)/2)2isthesquareoftheaccomponent(orcurrentripple)ofthecurrentﬂowingthroughthecomponents.APFMdc–dcconverterhasavariableswitchingfrequencythatdependsontheoutputcurrent,theoutputvoltage,andotherfactors.Therefore,theswitchingfrequencyshouldbecharac-terizedaccuratelytodeterminetheamountoftheconductionpowerdissipationofaPFMdc–dcconverter.From[7],theswitchingfrequencycanbedescribedas

fS(PFM)=

T=2·IOIpeak·(TSW1+TSW2)(4)

whereIpeakisthepeakinductorcurrentallowedinagivenPFMdc–dcconverter,andTSW1andTandtheSWbottom2aretheturn-ontimesofthetopMOSFET(SW1)MOSFET(SW2),respectively.TSW1andTSW2canbedeterminedasfollows:

TSW1

=Ipeak·LfVI−VO

,TSW2

=Ipeak·LfVO

(5)

Pconduction(PFM)in(6)ismodeledinthesamewayasP(Iconduction(PWM).Intheﬁrstterm,((TSW1+TSW2)/T)·peak/2)2isthesquareofthedccomponentofthecurrent

ﬂowingthrougheachcomponent,andinthesecondterm,(1/3)·((TaccomponentSW1+TofSWthat2)/T)·(∆Icurrent.LThe(PFM)duty/2)2isthesquareoftheratiosforSW1andSW2are(TSW1/(TTheseSW1+expressionsTSW2))andfor(TtheSW2current/(TSW1and+TdutySW2)),respectively.ratioscanbefoundin(orderivedfrom)manyreferences(e.g.,[7]and[25]).ReplacingTsionsfrom(5),wecanalsoconstructSW1andTthealternativeSW2withtheexpres-expressionshowninthelasttwolinesofthefollowingequation:Pconduction(PFM)=

TSW1+TSW2

󰀅󰀃T·Ipeak󰀄2󰀃TSW1·RSW1TSW2󰀄2·TSW1+TSW2+·RSW2TSW1+TSW2

+RL

󰀃+13·∆IL(PFM)

󰀄2󰀃2·TSW1·RSW1󰀄󰀆TSW1+TSW2+TSW2·RSW2TSW1+TSW2+RL+RC=

2·IOI󰀅peak󰀃·Ipeak󰀄2󰀃VO·RSW1(VI−VO)·RSW2󰀄2·VI+VI

+RL

󰀃󰀄2󰀃

+1Ipeak

VO·RSW1(VI−VO)·RSW2󰀄󰀆3·2·VI+VI

+RL+RC(6)

where∆IL(PFM)istherippleoftheinductorcurrent,whichisalmostthesameasIpeakinthePFMdc–dcconverter.

2)GateDrivePowerDissipation:ThegatecapacitanceoftwoMOSFETswitchesisanothersourceofpowerdissipationindc–dcconverters.Adc–dcconvertercontrolstheoutputvoltageandmaintainstherequiredloadcurrentbyopeningandclosingtwoswitchesalternately.Thisprocessrequiresrepeatedchargingofthegatecapacitancesofthetwoswitches.Thus,thegatedrivepowerdissipationisdirectlyaffectedbytheamountofswitchingperunittime,whichistheswitchingfrequency.Consequently,PWMdc–dcconverterswithaconstantswitch-ingfrequencyconsumeaﬁxedgatedrivepowerthatisinde-pendentoftheloadcondition,whereasPFMdc–dcconvertersconsumelessgatedrivepowerastheoutputcurrentdiminishes.Gatedrivepowerdissipationisroughlyproportionaltotheinputvoltage,theswitchingfrequency,andthegatechargeofMOSFETs,asshowninthefollowingequation[25]:

Pgate_drive=VI·fS·(QSW1+QSW2)

(7)

whereQSW1andQSW2arethegatechargesofthetopMOSFETandthebottomMOSFET,respectively.

ThisgatedrivepowermodelcanbeappliedtobothPWMandPFMdc–dcconvertersinthesameway,exceptthatfinthePWMmodel,butavariableinthePFMmodel.Sisaconstant3)ControllerPowerDissipation:Besidesthegatedrivepowerdissipationofthecontrolcircuit,thestaticpower

CHOIetal.:DC–DCCONVERTER-AWAREPOWERMANAGEMENTFORLOW-POWEREMBEDDEDSYSTEMS1371

dissipationofthePWMorPFMcontrolcircuit,andthepowerlostinmiscellaneouscircuitsinadc–dcconvertershouldbeconsidered.Generally,controllerpowerdissipationisindepen-dentoftheloadcondition,whichmakesthispowerdissipationadominantoneunderlightloads.Wecharacterizethecontrollerpowerdissipationas

Pcontroller=VI·Icontroller

(8)

whereIcontrolleristhecurrentﬂowingintothecontrollerofthedc–dcconverter,excludingthecurrentchargingthegatecapacitance.

Almostallmanufacturingparameters(i.e.,RSW1,RSW2,RL,RC,fS,Ipeak,Icontroller,etc.)canbeobtainedfromdatasheetsprovidedbythemanufacturerofeachcomponent.Wecanbuildapowerconsumptionmodelforthedc–dccon-verterwiththisinformation.Wethenvalidateourpowermodelbycomparingthepowerestimatedbythemodelwithﬁguresfromthedc–dcconvertermanufacturer’sdatasheetsoracircuitsimulation.

Ifwehaveoneparameterwhosevalueisnotknown,forexample,Icontroller,wecanestimateitsvaluefromthedif-ferencebetweentheenergyconsumptioncalculatedbyourenergymodelexcludingonlyIcontrollertermsandtheenergyconsumptionobtainedfromthecurveofloadcurrentversusefﬁciency(orpowerconsumption),whichisprovidedbythemanufacturersforaspeciﬁccondition,asfollows:

Pdcdc(PWM)(v)

󰀃=iO(v)2·

v󰀃󰀄󰀄·RSW1+1−v·RSW2+RL󰀃VI󰀃󰀄󰀄VI+1󰀃3·12·vv

2Lf·fS·1−󰀃󰀄VI󰀄·vVI·RSW1+1−vVI

·RSW2+RL+RC

+VI·fS·(QSW1+QSW2)+VI·Icontroller=Pdcdc_except_Icontroller(PWM)(v)+VI·Icontroller

(9)

Icontroller󰀁=Pv)−P󰀂dcdc(PWM)(dcdc_except_Icontroller(PWM)(v)VI

(10)

SinceallcircuitparametersexceptIcontrolleraregiven,wecanobtainthevalueofPdcdc_except_ImodelandthevalueofPcontroller(PWM)(v)fromourpowerdcdc(PWM)(v)fromthedatasheetforaspeciﬁcoutputvoltage(vinthepreviousequations)and,thus,estimatethevalueofIcontroller.Finally,toverifythevalidityofourpowermodelandtheestimatedparameter,weincorporatethisparametervalueintoourpowermodelandthenseewhetheritestimatesthepowerconsumptionofthedc–dcconverteraccuratelyfordifferentoutputvoltagesandchangedvaluesofotherparameters.

Tovalidatethesepowermodels,wecomparedtheefﬁciencycurvesprovidedbymanufacturerswiththecurvesestimated

byourmodelfortwocommercialdc–dcconverters,namely:1)theTPS40009[26]and2)TPS62100[27],whichusePWMandPWM/PFMhybridcontrol,respectively.Allmanufacturingparametershavebeenextractedfromdatasheets.AsshowninFig.4,thepowermodelsforboththePWMandPFMconvertersareaccurateenoughtoallowustoestimatethepowerdissipationofrealdc–dcconverters.D.EffectsofMOSFETGateWidthSizing

Asshowninprevioussections,powerdissipationindc–dcconvertersisaffectedbyvariousparameters.Theseconsistofthemanufacturingparameters,whichcannotbechangedatruntime,andload-dependentparameters,suchastheoutputvoltageandcurrentofthedc–dcconverter,whichcanbechangedtosuittherun-timeworkload,orbyhigh-levelpowermanagementtechniques.

Sincewearetryingtoreducethetotalsystemenergycon-sumptionbymeansofDVSwhenusingagivendc–dccon-verter,ratherthanproposingmodiﬁcationtodc–dcconvertersthemselves,weconsidermostmanufacturingparameterstobeﬁxedandfocusontheeffectsoftherun-timeloadvariationinthepowerdissipation.However,unlikeothermanufacturingparameters,thegatewidthoftheMOSFETswitchesshowsinterestingbehavior,especiallyinsystemsequippedwithaPWMdc–dcconverter.AsthegatewidthoftheMOSFETgetssmaller,theturn-onresistanceoftheMOSFETincreases,whereasthegatechargeisreduced[2],[7].Morespeciﬁcally,theturn-onresistanceRSWandthegatechargeQwidthofWSWoftheMOSFETswitcheswithagateas

SWcanbeestimatedRSW=

R0SW

WSW

,QSW=

WWQ0(11)

whereR0andQ0aretheturn-onresistanceandthegatecharge,respectively,ofaMOSFETwithagatewidthofW0.

ThismeansthattheoptimalvalueofthegatewidthW,intermsoftheenergyconsumption,willvarywiththeloadcondi-tionbecausetheturn-onresistanceandthegatechargeaffecttheload-dependentpower(i.e.,conductionpowerdissipation)andtheload-independentpower(i.e.,gatedrivepowerdissipation),respectively,inaPWMdc–dcconverter.SinceDVScausesadrasticvariationoftheloadconditionfromoneapplicationtoanother,theoptimalgatewidthoftheMOSFETswitchesmayvarywiththeapplicationinaDVS-enabledsystem.Fig.5showsthatthechangeofWaffectstheconversionefﬁciencyinoppositewaysunderlightandheavyloads.

III.DC–DCCONVERTER-AWAREENERGY

MANAGEMENTTECHNIQUES

A.ProposedAlgorithm:AnOverview

Conﬁguringadc–dcconverterandaDVSschemetomin-imizetheoverallenergyconsumptionisacomplexproblem,asitwillbecomeapparentinthefollowingsection.Tomaketheproblemmoretractable,sothatitcanbeinvolvedina

1372IEEETRANSACTIONSONCOMPUTER-AIDEDDESIGNOFINTEGRATEDCIRCUITSANDSYSTEMS,VOL.26,NO.8,AUGUST2007

Fig.5.Conversionefﬁciencyofadc–dcconverterfordifferentvaluesoftheparameterW.(TheefﬁciencycurvewithW=W0isequivalenttothatofaTPS40009[26].)

systematicway,weproposeasimplebutrobustframework,whichiscalledDC-lp,forourconverter-awareenergymini-mizationalgorithm.DC-lpessentiallycombinestwocoretech-niques,namely:1)DC_DVS(SectionIII-B)and2)DC_CONF(SectionIII-C).DC_DVSreﬁnestheDVSresultbyconsideringtheenergyefﬁciencyofthedc–dcconvertertobeused,whereasDC_CONFreﬁnestheconﬁgurationofthedc–dcconverter(i.e.,determinestheoptimalvalueoftheparameterW)from

CHOIetal.:DC–DCCONVERTER-AWAREPOWERMANAGEMENTFORLOW-POWEREMBEDDEDSYSTEMS1373

Thefollowingsectionsdescribethetwosteps,eachofwhichsolvesthedc–dcconverterenergyminimizationproblems.Step1istheconverter-awarevoltagescalingproblem,whichistodeterminetaskandvoltageschedulesthatminimizethetotalenergyconsumptionofasystem,includingthatofthedc–dcconverter.Step2istheapplication-drivendc–dcconverteroptimizationproblem,whichistoﬁndthemostenergy-efﬁcientconﬁgurationofthedc–dcconverterfortheapplication.B.Converter-AwareVoltageScalingTechnique

ForaCMOScircuit,itiswellknownthattheCPUpowerPiandtheenergyconsumptionEiforataskJicanbecomputed(assumingaﬁxedsupplyvoltage)by

Pi=CCPU,i·Ei=Ri·Pi

2Vdd,i

duringaunittimeperiod,startingatt.Then,thetotalenergyconsumedbythevoltagescalingAioftaskJiisgiven[11]by

ti,2󰀉

E(Ai)=Pi(fi(t))dt

ti,1

(14)

whereti,1andti,2arethestartingandendingtimes,respec-tively,oftheexecutionoftaskJi.Thus,thetotalCPUenergy

consumptionECPU,excludingthatofthedc–dcconverter,forNtasks(J1,J2,...,JN)is

N󰀉󰀈i=1t

ti,2

ECPU=Pi(fi(t))dt.(15)

·fi+Vdd,i·Istatic+Pon

(12)

i,1

whereCCPU,iistheaverageswitchedcapacitanceperclock

cycleforthetask,fiistheoperatingfrequency,Vdd,iisthesupplyvoltageusedfortheexecutionofthetask,Istaticisthefrequency-independentstaticcurrent(consistingmainlyofthesubthresholdleakagecurrent),Ponistheinherentpowerconsumption(whichisindependentofthescalablesupplyvoltageoftheCPU),andRiisthetotalnumberofcyclesrequiredfortheexecutionoftaskJi.

However,supplyvoltagescalingincursonecrucialpenalty,i.e.,thereducedvoltageincreasescircuitdelay,whichisap-proximatelylinearlyproportionaltothesupplyvoltagesincethecircuitdelayTdcanbeexpressed[22]as

Td=

CLVdd

µCox(D/L)(Vdd−Vt)α

(13)

Combiningthisequationwith(1),thetotalenergyconsump-tion,includingthatofthedc–dcconverter,forthetaskscanbeexpressedas

N󰀉󰀈i=1t

ti,2

Etot=ECPU+Pdcdcdt.(16)

i,1

whereCLrepresentsthetotalnodecapacitance,µisthemo-bility,Coxistheoxidecapacitance,Vtisthethresholdvoltage,

Vddisthesupplyvoltageforthetask,αisaconstantsatisfying1<α<2,andDandLrepresentthewidthandlengthofthetransistors,respectively.

Aninstanceofataskschedulingandavoltageallocationprobleminasystemconsistsofasetoftasks(orjobs)J={J1,J2,...,JN}andavariablevoltagerange[Vmin,Vmax],whereNisthenumberoftasks.

EachtaskJi∈Jisassociatedwiththefollowingparameters:aidiRi

arrivaltimeofJi;

deadlineofJi(ai≤di);

numberofprocessorcyclesrequiredtocompleteJi.

Notethatthevaluesofai,di,andRiaregivenfortaskJi,andthevaluesoffi(t)andPi(fi(t))varywiththedynamicallyscaledvoltagesusedinrunningJiand,thus,directlyaffecttheenergyconsumption.Ascheduleoftasksisreferredtoasafeasiblescheduleifallthetimingconstraintsofthetasksaresatisﬁed.Then,thetaskschedulingandvoltagescalingproblembecomesasfollows.

Problem1:Givenaninstanceoftasks,adc–dcconverter,andthevoltagerangeofaprocessor,ﬁndafeasibletaskscheduleandvoltagescalingthatminimizesEtotin(16).

ToreducethecomplexityofProblem1,weﬁrstproposeatechniqueforsolvingarestrictedversionoftheproblemandthenextendittoafullsolution.

SolutiontoProblem1withasingletask:From(1)and(12),wecanderivethetotalpowerequationintermsofthesupplyvoltagevariablealonebecauseasystemwithDVShasthemaximumoperatingfrequency,whichisproportionaltoitsoperatingvoltage.Thatis,f=αV,whereαisasystem-3

+Vdd·dependentconstant,andthus,PCPU=CCPU·α·Vdd

Istatic+Pon.Furthermore,sincepowerconsumptioncanalsobeexpressedasaproductofloadcurrentandsupplyvoltage(i.e.,P=VI),wehave

Idd=CCPU·α·Vdd+Istatic+

=CCPU·α·VO+Istatic+

Pon

VddPon

=IOVO

(17)

Sincethesupplyvoltagedirectlydeterminestheprocessor’sclockfrequency[asimpliedin(13)],itisoftenconvenienttoconsidertheenergyconsumptiontobeafunctionoftheclockfrequency.Letfi(t)betheclockfrequencyassignedtotaskJiattimet,andletPi(fi(t))betheenergyconsumedintaskJi

whereIddisthesupplycurrentﬂowingintotheCPU.IOistheoutputcurrent,andVOistheoutputvoltageofthedc–dcconverter.

1374IEEETRANSACTIONSONCOMPUTER-AIDEDDESIGNOFINTEGRATEDCIRCUITSANDSYSTEMS,VOL.26,NO.8,AUGUST2007

FixingthevalueofWin(1)and(17),wecanexpressthetotalpowerconsumptionPtot,includingthatofthedc–dcconverter,foreachcontroltechnique,asPtot(PWM)(v)

=PCPU(v)+Pdcdc(PWM)(v)

=CCPU·α·v3+Istatic·v+Pon+iO(v)2󰀃󰀃·vVI·RSW1+1−v󰀄󰀄·RSW2+RL󰀃󰀃VI

󰀄+1·1󰀄2·vv󰀃32Lf·fS·1−VI·v󰀃VI·RSW1+1−v󰀄󰀄VI·RSW2+RL+RC+VI·fS·(QSW1+QSW2)+VI·Icontroller(18)

Ptot(PFM)(v)

=PCPU(v)+Pdcdc(PFM)(v)=CCPU·α·v3+Istatic·v+Pon+

2·iO(v)

󰀅Ipeak

󰀃󰀃󰀄·Ipeak󰀄2󰀃2·vVI·RSW1+1−v󰀄VI

·RSW2+RL

󰀃󰀄2󰀃

󰀃󰀄󰀄󰀆+13·Ipeak2·vVI·RSW1+1−v

·RSW2+RL+RC+VI·

2·iO(v)(VI−v)·Ipeak·

Ipeak·Lf·VI

·(QSW1+QSW2)+VI·Icontroller

(19)

wherevisthescalablevoltage,theonlyvariablecontrolledbyDVS,whichisequivalenttoboththesupplyvoltageVoutputvoltageVddoftheCPUandthe·α·v2+IOofthedc–dcconverter,andiO(v)=CCPUstatic+(PonForataskwithanexecutiontimeT/vand).

adeadlineD,thevalueofEtotfortheexecutionofthetaskcanbeobtainedbysimplymultiplyingthetotalpowerconsumptionPtot(v)bytheexecutiontimebecausethepowerlossinthedc–dcconverterduringstandbystateisnegligible,i.e.,

󰀉D

󰀉T

Etot(v)=

Ptot(v)dt=

Ptot(v)dt=T·Ptot(v).(20)

Then,applyingT=R/f=R/αV,whereRisthenumberofcyclesforthetaskandVisitssupplyvoltage,toEtot(v)gives

Etot(v)=

Rα·Ptot(v)v

.(21)

Etot(v)isnotamonotonicallyincreasingfunctionofthe

outputvoltage.Thismeansthatusingthelowestfeasiblevoltage(orfrequency)forataskdoesnotalwaysminimizethetotalenergyconsumption.Fig.7showstherelationship

Fig.7.Energyconsumptionagainstsupplyvoltageforthesystemconﬁgura-tionC1,whichisdescribedinSectionIV(v∝CPUclockfrequency).

CHOIetal.:DC–DCCONVERTER-AWAREPOWERMANAGEMENTFORLOW-POWEREMBEDDEDSYSTEMS1375

Fig.10.TotalenergyconsumptionagainstW.

1376IEEETRANSACTIONSONCOMPUTER-AIDEDDESIGNOFINTEGRATEDCIRCUITSANDSYSTEMS,VOL.26,NO.8,AUGUST2007

Fig.13.Determinationofthediscretevoltages(frequencies)byDC_DISC_DVS-1.(a)fOPTfmax.(c)fmin≤fOPT≤fmaxandEtot(vL)≥Etot(vH).(d)fmin≤fOPT≤fmax,Etot(vL)valueofWin[Wmin,Wmax]thatminimizesthetotalenergyconsumptionofthesystem.NotethatWintheconverterdesignmustbekeptwithin[Wmin,Wmax]toavoidviolatingtheconstraintsofworst-casepowerdeliveryandthemaximumsizeoftheMOSFETs.Moreparticularly,letv1,v2,...,vkbethevoltagesappliedtoa(scheduled)sequenceofunitexecutiontimesofmultipletasksproducedbyaDVSscheme,andletEtot(vi,W)bethetotalenergyconsumptioninthecorrespondingtimeforasupplyvoltagevi.Then,thetotalenergycanbeexpressedsolelyintermsofw,whichrepresentsthegatewidthWoftheMOSFETs,asfollows:

Etot(w)=Etot(v1,w)+···+Etot(vk,w)

=γ1·w+γ2·

+γ3w

(23)

whereγ1,γ2,andγ3areconstants.Notethatthisequationisconvexwithrespecttow.Consequently,todeterminetheenergy-optimalvalueofWin[Wmin,Wmax],weﬁrstderiveaWvaluewOPTthatminimizesEtotandthensimplycheckwhetherwOPTisintherange[Wmin,Wmax]andﬁnallysettheminimum-energyvalueofWaccordingly.Thissolutionprocedure,whichiscalledDC_CONF,isshowninFig.11.D.DC–DCConverter-AwareDVSforDiscreteSupplyVoltages

ToshowthatDC-lpisapplicabletoawiderangeofDVSproblems,wewillnowconsidertheproblemofdc–dcconverter-awareDVSwithdiscretelyvariablesupplyvoltages(oroperatingfrequencies).ByexaminingtheﬂowofDC-lpinFig.6,wecanseethatweneed,attheleast,toupdateStep1(i.e.,DC_DVS),whichsolvestheDVSproblemforcontinuouslyvariablesupplyvoltages.Inmoredetail,weneedtointroducetheconstraintofdiscretevoltagesintoDC_DVS-1,whichsolvesthedc–dcconverter-awareDVSproblemforasingletask.Oncewehavedevelopedatechnique(whichwewillcallDC_DISC_DVS-1)tosolvethedc–dcconverter-awareDVSproblemforasingletaskusingdiscretevoltages,

DC_DVS-mcanrepeatedlyuseDC_DISC_DVS-1foreachofthescheduledtasks.(NotethattheexecutionscheduleoftaskswillhavealreadybeenobtainedusinganexistingDVStechnique.)WenowexplainDC_DISC_DVS-1,whichisalsosummarizedinFig.12.

Let(f1,f2,...,fK)bethesetofavailableoperatingfre-quencies,assumingf1fmax,thenwehavenochoiceexcepttousetheextremefrequencies[thecasesinFig.13(a)and(b)].2However,ifthevalueoffOPTisinbetweenfminandfmax,thenwefocusonthetwofrequencies,whicharetheneighborsoffOPTin(f1,f2,...,fK).LetfLandfHdenotethesetwofrequencies,wherefLIV.EXPERIMENTALRESULTS

Weimplementedourproposeddc–dcconverter-awarepowermanagementtechniquesinC++andtestedthemonaset

representsthevoltagecorrespondingtothefrequencyfx.

CHOIetal.:DC–DCCONVERTER-AWAREPOWERMANAGEMENTFORLOW-POWEREMBEDDEDSYSTEMS1377

TABLEI

EXPERIMENTALSYSTEMCONFIGURATIONS

1378IEEETRANSACTIONSONCOMPUTER-AIDEDDESIGNOFINTEGRATEDCIRCUITSANDSYSTEMS,VOL.26,NO.8,AUGUST2007

TABLEIV

COMPARISONSOFENERGYCONSUMEDBYNODVS(NO_DVS),ACONVENTIONALDVSSCHEME(DVS_ONLY),ANDOURDC–DCCONVERTER-AWARE

DVSTECHNIQUE(DC_DVS)FORBENCHMARKPROGRAMS.SYSTEMCONFIGURATIONISC2,

ANDwISTHECONFIGURATIONPARAMETEROFTHEDC–DCCONVERTERUSED

CHOIetal.:DC–DCCONVERTER-AWAREPOWERMANAGEMENTFORLOW-POWEREMBEDDEDSYSTEMS1379

TABLEVI

ENERGYCONSUMPTIONUSINGDC_DISC_DVSCOMPAREDWITHACONVENTIONALDVSMETHOD[21],

USING{0.8V,1.4V,2.0V,2.6V,3.2V},FORTHECONFIGURATIONC1

1380IEEETRANSACTIONSONCOMPUTER-AIDEDDESIGNOFINTEGRATEDCIRCUITSANDSYSTEMS,VOL.26,NO.8,AUGUST2007

TABLEVIII

ENERGYCONSUMPTIONUSINGDC_DISC-lpCOMPAREDWITHACONVENTIONALDVSMETHOD[21],

USING{0.8V,1.4V,2.0V,2.6V,3.2V},FORTHECONFIGURATIONC1

YongseokChoi(S’01)receivedtheB.S.andM.S.degreesincomputerscienceandengineeringfromSeoulNationalUniversity,Seoul,Korea,in2000and2002,respectively.HeiscurrentlyworkingtowardthePh.D.degreeattheSchoolofComputerScienceandEngineering,SeoulNationalUniversity.

Hisresearchinterestsincludeembeddedsystemsdesignandsystem-levellow-powerdesign.

CHOIetal.:DC–DCCONVERTER-AWAREPOWERMANAGEMENTFORLOW-POWEREMBEDDEDSYSTEMS1381

NaehyuckChang(M’97–SM’05)receivedtheB.S.,M.S.,andPh.D.degreesfromSeoulNationalUni-versity,Seoul,Korea,in1989,1992,and1996,re-spectively.

HehasbeenwiththeSchoolofComputerScienceandEngineering,SeoulNationalUniversity,since1997,whereheiscurrentlyanAssociateProfessor.Hisresearchinterestincludesembeddedsystemsandlow-powersystems.Hehaspublishedmorethan70technicalpapersintheseareas.

Dr.ChangisamemberoftheAssociationfor

ComputingMachinery/SpecialInterestGrouponDesignAutomation(ACMSIGDA).HecurrentlyservesontheTechnicalProgramCommitteeofACMSIGDAandtheIEEECircuitsandSystemsSocietyconferencesandsym-posiumssuchasDAC,ICCAD,ISLPED,andISQED.HeiscurrentlyanAssociateEditoroftheIEEETRANSACTIONSONCOMPUTER-AIDEDDESIGNOFINTEGRATEDCIRCUITSANDSYSTEMS,theJournalofLow-PowerElec-tronics,andtheJournalofEmbeddedComputing.

TaewhanKim(M’93)receivedtheB.S.degreeincomputerscienceandstatisticsandtheM.S.degreeincomputersciencefromSeoulNationalUniversity,Seoul,Korea,in1985and1987,respectively,andthePh.D.degreeincomputersciencefromtheUniver-sityofIllinois,Urbana–Champaign,in1993.

From1993to1998,hewaswithLatticeSemicon-ductorCorporationandSynopsysInc.,wherehewasinvolvedinlogicandhigh-levelsynthesis,andfromAugust1998to2003,hewaswiththeDepartmentofElectricalEngineeringandComputerScience,Korea

AdvancedInstituteofScienceandTechnology,Daejeon,Korea.Currently,heisaProfessorwiththeSchoolofElectricalEngineeringandComputerScience,SeoulNationalUniversity.Hisresearchinterestsareintheareaofcomputer-aideddesignofintegratedcircuitsandcombinatorialoptimizations.

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