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VRMModeling:AStrategytoSurvivetheCollisionofThreeWorlds

LarrySmith,Qualcomm,SteveSandler,Picotest,EricBogatin,TeledyneLeCroy

AnOverallPerspectiveInanyelectronicproduct,thePowerDistributionNetwork(PDN)consistsofthreeelements:thepowergeneratoroftenreferredtoastheVoltageRegulatorModule(VRM),powerconsumers,whicharetheactivedevices,andapassivenetworkofinterconnectslinkingthetwo.TheVRMistheessentialpowergenerationcomponent.ItconvertssomeACorDCinputvoltageintotheDCvoltagesrequiredbyactivedevices.Theseactivedevicesultimatelytransformelectricalenergyintoactionssuchasinformationprocessing,sensing,actuating,displaying,orcommunicating.Thepassivenetworkofinterconnectsincludestheboard,packages,anddecouplingcapacitors.

Inmanydesignteams,differentengineers,differentgroups,orevendifferentcompaniesaresometimesresponsiblefordevelopingoneofthesethreeelements,oftenwithoutsufficientknowledgeoftheotherelements.Althougheachelementmayhaveaspecificationthatdefinesitsinputandoutputperformance,rarelydoesthespecificationalonecontainenoughdetailtoguaranteethecorrect,integratedperformanceoftheentirenetworkbecausetheotherelementscanvaryoverawideperformancerange.

TheunfortunateproductmanagerisultimatelyresponsibleforensuringthefinalproductworkswhenallthreeelementsofthePDNareintegratedtogether.Howcantheproductmanagerbeconfident,beforetheproductisbuilt,thattheVRM,interconnects,andactivedevices,whichinteract,meetstheproductperformancespecs,margintests,andcosttargetsinalloperatingconditions?

Onepracticalapproachistousesomelevelofmodelingforeachelement.Thisallowsanalysisofnominalandworst-casesituationsand,ifnecessary,explorationofalternativedesignsbeforefinaldesigndecisionsaremade.Anaddedbenefitofthisapproachisthateachdesigngroupcanexaminethemodelsoftheotherelementsandgainanunderstandingofhowtheirelementmightinteractwiththerestofthesystem.

Selectingamodeltouseforeachelementrequiresestablishingadynamicbalancebetweenacceptablesimulationaccuracyandthecostsineffort,expertise,time,risk,anddollarsrequiredtoattainthataccuracy.

Althoughmoredetailedandaccuratemodelsofeachelementmayincreasetheaccuracyofthesimulations,higheraccuracycomesatsomecost.Generally,themoreaccuratethemodel,themorecomplexitis,themoreexpertiseisrequiredtouseitcorrectly,themoretimeitmighttaketorunthroughscenarios,andthemoredifficultitmightbetodebugtheresultsandbuildconfidenceintheiraccuracy.

Ifthemodelissocomplexthatonlyafewexpertscanunderstanditanduseitwithoutintroducingartifacts,theriskofgeneratinginaccurateresultsishighwhenless-experiencedengineersusethemodel.Ontheotherhand,ifthemodelissosimplethatitdoesnotincludefeaturesthatmightaffectperformancedramatically,itwouldhavelittlevalue.

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Thedesignprocessstillreliesonengineeringintuition.Althoughthefinaldesignsignoffcanbebasedonadetailedsystem-levelsimulation,theinitialcreationandoptimizationofadesignisoftenbasedonthejudgementofanexperiencedengineer.Anappropriatelycomplexmodelthatisstillsimpleenoughtograspcanbeapowerfultooltoguideinitialdesigndecisions.

AcompletePDNcontainsmanysourcesofnoise.Someelementsactasaggressorsandsomeasvictims.Ultimately,theproductmanagerisresponsibleforidentifyingallsourcesofnoisethathavethepotentialtocauseanerrorinanyoperatingconditions.

Inpractice,onlythosewithhighlevelsofexpertisecanidentifyandminimizeallpossibleself-aggressionandmutual-aggressionnoisesources,soinmostsituationsonlythemostcommonnoisesourcesareanalyzed.Thisapproachresultsinsomeriskthatanoisesourcenotincludedintheanalysismightcauseaproductfailure.

ThispaperreviewsfourlevelsofVRMmodelsthatVRMdesigners,boardlevelinterconnectdesigners,semiconductordesigners,andproductmanagersoftenusetoexploredesigntradeoffsthroughoutthePDNsystem.Thechoiceofwhichonetouseinvolvesconsideringengineers’levelsofexpertiseandwhatproblemstheyexpecttoanalyze.Sometradeoffsandrelativemeritsofthemodelsaredescribed.

FromtheCoreLogic’sPerspectiveToguidetheinvestigationofthefourmodels,westartwithaworldviewfromthecorelogiccircuit’sperspective.Althoughthisisonlyoneperspective,ithelpsidentifyself-aggressionnoisecausedbytransientcurrentsinthecorelogiccircuits,asviewedbythesilicontransistorsthatdrawcurrentfromthePDN.Figure1showsaroughschematicoftherestofthePDNsystemasseenbythepadsonthecorelogicrailsonthedie,andthesmallsignalimpedanceprofilelookingintothePDN.

Figure1:PDNcomponentsthatcontrolfrequencydomainimpedance,fromtheperspectiveofthepadsofthedie.

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TheVddself-aggressionnoisedependsonthepropertiesoftheboard-leveldecouplingcapacitors,boardpowerplanesandvias,thepackageballs,packagevias,powerplanesandpackagecaps,andthediebumps,theon-diepowergrid,andtheon-diecapacitanceforthesiliconloadasshowninthebottomportionofFigure1.ThisistheremainderofthePDNsystembeyondtheVRM.TheVRMisalsoknownasthepowermanagementintegratedcircuit(PMIC).

TheboardandchiplevelPDNcomponentsareimportantinthe1MHzto500MHzfrequencyband,whichisbeyondthebandwidthoftheVRMorPMICasindicatedinthetopportionofFigure1.Theboardlevelcomponentsofthebulkcap,highfrequencycaps,packagecaps,andon-diecapacitancesupplythecurrentandchargeconsumedbythesiliconloadabovethebandwidthoftheVRM.

Siliconloadsarecapableofconsumingfullcurrentstepsinjustafewclockcycles.A3GHzmicroprocessoridlingat2Amightsuddenlyrequire7Aonenanosecondlater.FaststepcurrentsmustcomefromenergyandchargestoredinPDNcapacitance.ItmustcomethroughinductivePDNstructuressuchasthediebumps,packagevias,powerplanesandballs,andboardvias,powerplanes,andcapacitormountingstructures.Eventually,severalmicrosecondslater,therequiredpowerisdeliveredfromtheVRMorPMIC.

TargetimpedanceisveryusefulfigureofmeritwhendesigningtheboardlevelPDNelementstocontrolself-aggressionnoiseonthecorelogic.Inthesituationdescribedabove,themicroprocessordemandeda5Astepcurrent(7A–2A)witha1nSecrisetime.Thevoltagetoleranceforthemicroprocessormaybe5%;thatis,itisexpectedtofunctionproperlywitha3GHzclockfrequencyifthevoltagestayswithinthe±5%tolerance.

AsimpleOhmslawcalculationrevealsthatthePDNsystemimpedanceshouldbeapproximately10mOhmswhenthenominalPDNvoltageis1.2V.Usingtheruleofthumbthatthefrequencycontentis

,thePDNshouldmeetthetargetimpedanceupto350MHz.

AllPDNsystemsoperateinthismanner.AserversystemmayrelymoreonlargeelectrolyticbulkcapacitorsandlowerbandwidthVRM,andamobilesystemmayrelyonahigherbandwidthPMICandsmallceramiccapacitors;thisisthestructureofallPDNsystemsthatsupplycurrenttosiliconloads.ItisfromthisperspectivethatwelookatsomeoftheVRMmodels.

WhatisMissingThetargetimpedanceprovidesaguidelinefordesigningPDNelements.Whenusinga5%noisetoleranceonthecorelogicrail,itisassumedallthenoiseisself-aggressionnoise.Butmutual-aggressionnoisesources,suchasvoltagetransientsfromtheVRM,orfromotherswitchingcurrentsthroughtheboardlevelimpedance,canaddtotheVddon-dierailnoise.

Thepackageleadinductanceandon-diecapacitanceactaslow-passfiltersandgenerallyfilterouthigherfrequencycomponentsfromtheboardontothedieabovethepolefrequencyoftheBandiniMountainfrequency.However,lowfrequencynoisebelow10-100MHzcanmakeitswayonthedie.Thisadditionalnoisewilladdtothe5%noisefromtheself-aggressionsources.

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Inthisinitiallook,wewillfocusonself-aggressionnoisefromVddtransientcurrents.ThesimpleVRMmodelsintroducedtoguidethedesignofPDNsinwhichVddself-aggressionnoiseisanalyzedwillnotpredictanyofthemutual-aggressionnoise,suchastheswitchingnoisefromtheVRM,thenoisecouplingoverfromtheexternalpowersourcethatisnotblockedbythepowersupplyrejectionratio(PSRR)oftheVRM,ortheringingnoisefromthetransientresponseoftheVRMreactingtostepcurrentloadschanges.Anon-linearVRMmodelisrequiredtomodelthesesourcesofnoise,asdetailedbelow.

TheSimplestVRMModel:AnIdealVoltageSourceThesimplestVRMmodelisanidealvoltagesource.Thisrepresentationhaszerooutputresistanceandistheworstmodeltouseinanycontextbecauseitdoesnotpredictanyofthemostimportantnoisebehaviors.

Unfortunately,anidealvoltagesourceisusedtorepresenttheVRMinmanytimedomainpowerintegrity(PI)simulations.Theproblemwiththeidealvoltagesourceisthatitiszeroimpedanceandshortsout(DCandAC)anyPIcomponentitisacross.

ThePIdesignflowofteninvolvesextractionofS-parametermodelsfortheprintedcircuitboard.TheextractiontooloffersportstoattachtheVRM,boardcaps,andpackagedsiliconcomponents(microprocessorload).ThenacircuitsimulationtoolusesaschematictoconnectPDNcomponentstotheportsofextractedboardandpackagemodels.AnexampleoftwomodelsisshowninFigure2.

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Figure2:Schematicontheleftshowstheimpedancesimulationofon-diecapacitance,packageimpedance,andboardbulkcapacitance,andproducestheblueimpedancecurveonthegraph.Theschematicontherightisidentical,buthasanidealvoltagesourceshuntingtheboardcapandproducesthegreenimpedancecurve.

TheschematicontheleftinFigure2showsanimpedancemodelofsomePDNcomponents.AnACcurrentamplitudeof1Aisforcedintothe50nFon-diecapacitancewith5mOhmESR.Thereisapackageconnection(20pH,1mOhm)toaboardbulkcapacitorrepresentedbyalossytransmissionlinemodel[2].Thesimulatedimpedanceversusfrequencyforthistopologyisshowninthebluecurve(bulkcapalone).TheBandiniMountainimpedancepeakisclearlyseenat100MHz,aswellastheprofileproducedbythecapmodelandpackage.Thisisexpectedbehavior.

Softwaretoolsareoftenusedtoextracttheimpedancepropertiesofaprintedcircuitboard.ThereisatemptationtoattachanidealvoltagesourceattheextractedportterminalsfortheVRMasshownintheschematicontherightinFigure2.

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WehaveattendedmanydesignreviewsandfoundthatthistendencyofattachinganidealvoltagesourceastheVRMtotheboardlevelS-parametermodelisalltoocommon.ItisanunfortunatemistakemadebymanyPIengineers.

Attachingazero-impedancevoltagesourcetothePMICorVRMportoftheextractedPCBeffectivelyshortsoutallthePDNcomponentsontheboardwithsomesmallequivalentinductanceandresistanceassociatedwiththeboardportconnections.ThisisshownintheschematicontherightinFigure2.AsseeninthegraphinFigure2,thezero-impedanceidealvoltagesourcecreatesaflatlinebelow1MHzandeliminatesthesignatureofthebulkcap.Thebulkcaphasbeenshortedout.

ThegoalinthePDNdesignandsimulationforself-aggressionnoiseistoevaluatetheeffectivenessofbulkcaps,highfrequencycaps,boardpowerplaneconnections,andsoforth;therefore,shortingthemoutwithanidealvoltagesourceisamajorerror.Unfortunately,manyPIanalyseshavebeencorruptedbyusinganidealvoltagesource.

ItisveryimportantthatidealvoltagesourcesareneverusedinPDNsimulations,especiallywhenimpedanceortransientresponsestofaststepcurrentloadsarebeingevaluated.

AFirst-OrderLinearRLModelforaVRMThesimplestlinearmodelthatrepresentstheVRMoutputimpedancebehavior,andiscommonlyusedforfrequencydomainsimulations,isaseriesRLmodel.ThismodelhastheadvantageofbeingeasytoimplementandaccountingforsomeoftheinteractionsoftheVRMwiththerestofthePDN,fromthedie’sperspective,whensimulatingVddself-aggressionnoise.Ofcourse,thissimplemodelcannotbegintoaddressthenon-linear,stability,noiseripple,andsaturationpropertiesofarealVRM.

Figure3:RLmodelforVRM.

AsillustratedinFigure3,theoutputimpedanceriseoftheVRMduetotheinternalfeedbackresponsebandwidth,iswellrepresentedbyaninductorandresistor.TheresistorrepresentstheVRMvoltagedropthatisproportionaltoDCcurrent.Theinductorprovidesanincreasingimpedancewithfrequencybeyondsomecornerfrequency.

TheinductancevalueiscalculatedfromthecurrentrampresponsetimeorbymatchingtheresonantfrequencybetweentheVRMinductanceandbulk(output)capacitance.NotethattheinductancevalueforthesimplelinearmodelisnotrelatedtotheinductorvalueintheSMPSmodel.Theinductorofthe

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linearRLmodelsimplycapturesthebehavioroftheregulationloop(eitherSMPSorLDO),anddoesnotrepresentanyphysicalelement.Theresistancevalue(R)intheVRMmodel(R_VRM)issimplytheresistanceatDCorsomeverylowfrequency(100Hz)atwhichtheimpedancecurvebottomsout.

AfrequencydomaincalculationfortheinductanceoftheinductorintheVRMmodel(L_VRM)isbasedonthefrequencyoftheVRMimpedancepeak.ThiscanbefoundbymeasuringtheimpedanceofaVRMsystemasafunctionoffrequency.Duetothenon-linearnatureofallVRMs,thefrequencyandheightoftheVRMimpedancepeakarenotuniqueandchangeslightlyaccordingtoloadconditions.Propertieschangefromlightlyloadedconditions(smallsignalandlinear)tofullloadtransientconditionsinwhichdampingishighlyloaddependent.Nonetheless,thefrequencyoftheVRMimpedancepeakisrelativelystable.

Figure4:Two-elementRLmodelandRLCbulkcapmodelshowhighVRMimpedancepeak.ThepeakfrequencyisusedtofindtheequivalentVRMinductance.

Figure4showsaVRMimpedancepeakatabout22kHzbecauseoftheresonancebetweenthebulkcapacitanceandtheeffectiveVRMinductance.ThecapacitanceisextractedfromthemeasuredimpedancewiththeVRMturnedoff,orfromknowledgeofthecapacitancecomponentsused.Althoughthisisthetotalon-boardcapacitance,itisdominatedbythebulkcapacitance.TheeffectiveVRMinductanceiscalculatedfromtheresonantfrequencyandon-boardcapacitance.

and

Thisistheinductanceintheresonantloopthatcausestheimpedancepeakat22kHz.TheschematicparametersindicatethatthesimulatedparameterfortheVRMwas50nHandtheinductanceofthebulkcapacitorwas2nH,thesumofwhichis52nH.ThisdemonstratesthattheresonantpeakfrequencycanbeusedtodeterminewhattheequivalentVRMinductancemusthavebeen.TheVRMresonantpeakcanbemeasured.

Itishighlydesirablethattheinductorimpedancecrossthecapacitorimpedanceexactlyatthetargetimpedanceline.Intheliterature,thisisknownasimpedancematching[3]orthecharacteristicimpedancethatgivesagoodPDNstepresponse[4].Thisimpedanceisthespecialpointatwhich

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inductivereactancecrossesthecapacitivereactanceandthetargetimpedanceline.Wewantthe

characteristicimpedanceoftheVRMpeak, ,tobethesameasthetargetimpedanceto

keepthestepresponseatorbelowthevoltagedrooptolerance,withalowq-factortodampoutanyringing.Thisresultsinamaximallyflatimpedanceprofilethatissufficientlylowtodeliverthefulltransientcurrentwithadroopthatiswithinthevoltagetolerance.

Atimedomaincalculationoftheinductanceparametercomesfromthe property.Whentheloaddemandsafaststepofcurrent,theoutputoftheVRMislimitedbyamaximumcurrentrisetime(di/dtrate).TherisetimefortheloadfromaVddrailtransientcurrentstepisoftenexpressedinamps/nSec;thetimefortheVRMresponseisoftengiveninamps/uSec,1000timesslower.

TheequivalentinductanceforthelinearVRMmodelcanbedeterminedusingthisproperty.WhentheVRMisdrivenbyarampcurrentload,thevoltageresponseoftheVRMisameasureoftheoutputinductance.TheequivalentlargesignalinductanceoftheVRMiscalculatedfrom .InthespecialcaseinwhichtheVRMinductivereactancecrossesthecapacitivereactanceatthetargetimpedance,thevoltagedropforastepcurrentoftheworst-casetransientVddcurrentwillbethesameasthevoltagetoleranceusedinthetargetimpedancecalculation.

Figure5:TheheightoftheimpedancepeakcanbeadjustedbyincreasingVRMresistance,butthiswouldincreasetheDCresistanceandcontributetoanundesirableDCIRdrop.

TheheightoftheimpedancepeakintheparallelresonanceoftheVRMoutputinductanceandthebulkcapacitor’scapacitanceisdeterminedbysystemlosses,includingthelossesattributedtothebulkcap.ItistemptingtochooseRfora2-elementseriesRLmodeltoproperlydamptheimpedancepeak,butasshowninFigure5,thiswouldleadtoexcessiveresistanceinthepathfromtheidealvoltagesourceandtoomuchDCIRdrop.

TheRintheRLmodelneedstosatisfytwoproperties:providethecorrectdampingfortheparallelresonantpeakandprovidethecorrectDCoutputimpedance.Onesinglevaluecanrarelydothis.Amoreaccuratemodelmustincludetwovaluesofresistance,andtobeeffectiveinthecircuit,twoseriesinductorvalues.Thisisa4-elementRLmodel.

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SecondOrderModeloftheVRM:A4-elementRLModelModelingtheVRMastheparallelcombinationoftwoseriesRLcircuits,asshowninFigure6,offersasimple,linearcircuitmodelforaVRMthatincludesamoreaccuraterepresentationoftheDCorlowfrequencyimpedance,theequivalentinductanceofthefeedbackloop,andthedampingresistanceneededtoaccountforthefirstparallelresonantpeak.

Figure6:Asimple,linear,4-elementVRMmodelisolatestheidealvoltagesourcefromtherestofthePDNcomponentsandproducestheredimpedancecurve.Theimpedancepeakatabout300kHzisduetotheVRMoutputinductanceinteractingwiththeon-boardbulkcapacitor.Theimpedancepeakbetweenon-diecapacitanceandbump-packageloopinductanceappearsatabout100MHzasitshould.

This4-elementRLmodelhaslittleimpactonthehigherfrequencyBandiniMountainpeakbutwillaffectthelowerfrequencyparallelresonancebetweentheVRMandthebulkcapacitor.Thismodelisuseful

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whenanalyzingon-dieVddself-aggressionnoise.Theelementparameterscanbechosentogivereasonablyaccuratesimulationresultsinbothfrequencyandtimedomainswiththislinearmodel.

IftheVRMfeedbackpointsareinternaltotheVRM,thentheVRMmaybeattachedschematicallytotheVRMportontheextractedPCB.TheportmaybeforaSMPSinductorifthebulkcapismountedonthePCBpowerplanes.

If,however,thereareexternalfeedbacksenselinesfortheVRMthatextendtosomepointinthePDNsystem(oftensomelocationontheboardunderneathahigh-powerconsumingload),themountpointfortheVRMmodelshouldnotbeattheVRMport.SpecialPCBportsshouldbecreatedtomountthelinearVRMmodelwithlowresistanceandinductanceconnectionsclosetothesenselineterminations.

ArealVRMwithexternalsensepointswillregulatethevoltageatthesensepoints.AsimplelinearVRMmodelhasnoprovisionforfeedbackcompensation.IfthesimpleVRMmodelismountedattheextractedPCBportlocations,DCIRvoltagedropfromtheVRMporttothePCBfeedbackpointwillnotbecompensated.

Thesecondresistor(R_damp)isusedtoindependentlydamptheimpedancepeakwhilethefirstresistorisusedtosettheproperDCIRdrop.AgoodstartingvalueforR_dampisthetargetimpedance,whichwouldresultinaq-factorof1.ThiscanberefinedbyPDNmeasurementofanactiveVRMwithaVNA.TheVRMwillnotdeliversignificantcurrentathighfrequency,soasecondinductorwithavalueofapproximatelyL_VRM/10isusedtomodeltheblockedhighfrequencycurrent.The4-elementVRMmodeldeliversthebluecurveseeninthegraphinFigure7.ItprovidesthedampingthatbringstheVRMimpedancepeakdowntothetargetimpedancewithoutimpactingtheDCIRdropatlowfrequency.

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Figure7:ProperDCIRdropanddampingfortheVRMpeakisachievedatthesametimebyaddinganadditionalRandLtothe2-elementmodel.

ModelingOtherNoiseSources:VRMSelf-AggressionNoneoftheselinearmodelscanaccountforanyofthenoiseontheVddrailfromVRM-aggression,whichcanbecausedbyaninadequatePSRRandnoiseontheprimarypowersource,switchingnoisefromtheinternalVRMoperation,ornonlineartransientresponsefromchangingcurrentloads.

AnyoftheseeffectswillgeneratemorenoiseonthepinsoftheVRMandappearontheVddrailpadsiftheirfrequencycomponentsarebelowthepolefrequencyoftheBandiniMountain.ThesenoisesourceswilladdtotheVddself-aggressionnoisecausedbyVddtransientcurrents.Inextremecases,VRMandotheraggressornoisecanexceedtheself-aggressionnoisetoleranceandcauselargerproblems.

ThefactorsthatcontributetothesenoisesourcesareoftennotrelatedtothePDNdesignfeaturesthatweoptimizedtoreducetheVddself-aggressionnoise.ThesefactorsmustbeanalyzedandaddressedindependentlyofdesignfeaturesintroducedtoreducetheVddself-aggressionnoise.

Amodelthatincludesthenon-linearfeedbackandPSRRoftheVRMisrequired.RecentadvancesinVRMmodelingtechniques,whichincludeharmonicbalanceandstatespaceequations,havegreatlyreducedthecomplexityofVRMmodelsandenabledfastersimulation[1].

AnaccurateVRMmodelreflectsthenon-linearpropertiesoftransistorsandfeedbackloopsthatoccurwhenloadcurrentstransitionfromverylowtoveryhighvaluesandtheVRMisatthelimitofitscurrentdeliveryrange.TheaccurateVRMmodelalsotakesintoaccountswitchingnoiseandPSRReffects,aswellassmall-andlarge-signalimpedanceeffects.Accuratemodelsarerequiredforclosedloopfeedbacksimulationstodeterminethebestcircuitelementsandparametersforstabilityanalysis.AccurateVRMmodelsarerequiredforoptimalVRMdesignandintegrationintotheentirePDNsystem.

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Asanexample,asimpleSMPSbuckconverterschematicisshowninFigure8.ItconvertssomehigherDCvoltagetoaDCvoltageappropriateforCMOSlogic,oftenabout1V.Itinvolvescomplexcircuitrytosenseandregulatetheoutputvoltage,monitorcurrent,openandcloseswitchesatappropriatetimes,andmaintainstabilityoverdifferentloadconditions.

Basically,thetopswitchremainscloseduntiltheworkinginductorisfullychargedwithcurrent.Thebottomswitchisthenclosedtoallowcurrenttocontinuethroughtheinductorloopwhiletheloopcurrentandenergystoredintheworkinginductordiminishes.Complexcircuitryandalgorithmsenablethisclassofregulatorstofunction.SimulationandmodelingoftheSMPSisamajordisciplineinitselfandsignificantdesigneffortsandcomputerresourceshavebeendedicatedtotheseefforts.Ultimately,itiswithsuchmodelsthattheinteractionsoftheVRMwiththerestofthePDNcanbeanalyzedandeachelementoptimized.

Figure8:BuckconverterVRM.

ConclusionItisimportanttouseaproperVRMmodelinPIsimulations.AnidealvoltagesourceshouldneverbeattachedtoaportofanextractedprintedcircuitboardS-parametermodel,asisoftendone,becauseitshortsoutasignificantportionofthePDNwithzeroimpedance.

TheidealvoltagesourcemustbeisolatedfromtheboardpowerplanesanddiscretecapacitorsbyanimpedancethatrepresentstheVRM.Preferably,theVRMmodelistunedandcorrelatedtoregulatorspecsheetsandactualVRMmeasurements.Ifthisinformationisnotavailable,a4-elementRLRLmodelwithanimpedancepeakatapproximatelytherightmagnitudeandfrequencymaybeused.TheRLRL

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parametervaluesmaybedeterminedfromthepropertiesoftheimpedancepeak.TheVRMmodelaffectsthePDNimpedancecurveinacertainfrequencyband,often20kHzto20MHz.

AlthoughlinearmodelsfortheVRMarecriticalforoptimizingtheboardlevelPDNtomanageVddself-aggressionnoise,theycannotprovideanyinsightintonoisethatoriginateswiththeVRM.

ForacompletedescriptionofthenoiseinthePDN,includingtheVRMself-aggressionnoise,anon-linearmodelisneededandcanbeimplementedusingastatespacemodel.

References

[1] S.Sandler,HowtoDesignforPowerIntegrity:DC-DCConverterModelingandSimulation.2018.

[2] V.Sriboonlue,L.Smith,J.Mohamed,J.Shin,andT.Michalka,“NovelParallelResonancePeakMeasurementandLossyTransmissionLineModelingof2-Tand3-TMLCCcapacitorsforPDNApplication.”

[3] H.Barnes,J.Carrel,andS.Sandler,“PowerIntegrityfor32Gb/sSERDESTransceivers,”inDesignCon,2018.

[4] L.SmithandE.Bogatin,PrinciplesofPowerIntegrityforPDNDesign.PrenticeHall,2017.

[5] S.Sun,A.Corp,L.D.Smith,andP.Boyle,“On-ChipPDNNoiseCharacterizationandModeling,”inSantaClara,CA,DesignCon,2010,no.408,pp.1–21.