PowerDistributionNetwork(PDN)ImpedanceandTargetImpedance

SteveSandler,Picotest,EricBogatin,TeledyneLeCroy,LarrySmith,PDNpowerintegrity.com

IntroductionThepurposeofthepowerdistributionnetwork,thePDN,istodeliveraDCvoltage,within

regulationlimits,withanacceptablenoise,toeachactivedevice.Ultimately,thefinaldesignisabalancebetweenmanagingtheacceptableperformancewithsufficientmarginandanacceptablelevelofriskgiventheever-shrinkingscheduleandcosttargetconstraints.

Whenstartingoutwithadesign,usingatargetimpedance,asthemaximumimpedancedesigngoalforthePDNimpedance,isausefulmetrictoguidethedesign.But,justusingatargetimpedancealoneasthedesignrequirementisnotenough.ThereareafewsignificantnoisesourcesfromthePDNelementsthatasimpletargetimpedancedoesnotadequatelyaddress.Tobeclear,thevoltageregulationlimitsthatmustbemaintainedincluderipple,noise,DCregulation,IRdrop,andthevoltageexcursionsduetodynamictransients.Forthispaper,weareonlydiscussingthevoltageexcursionsduetodynamiccurrenttransientsasthe‘noisesource’thatisbeingmanagedbythePDNimpedancecontrol.

TheTargetImpedanceAsimplifiedmodelofthePDNincludingthepowergeneratorelement,orvoltageregulator

module(VRM),thepowerconsumerelements,suchastheICdevices,andthepassiveinterconnects,includingthevariousdecouplingcapacitors,isshowninFigure1.ThismodelcanbeusedforboththeI/Opowerrails,oftenlabeledastheVccrailsandthecorelogicrails,oftenlabeledastheVddrails.

Figure1AsimplifiedmodelofthePDNasseenbythepadsofthediepowerrail.

TherecanbemultiplesourcesofnoiseonthepowerrailsoftheIC,butseparatedintotwogeneralcategories:

• self-aggressionnoisecausedbythechip’sowntransientcurrentspassingthroughtheimpedanceofthePDN

• mutualaggressionnoise,orcrosstalk,fromthePDNinterconnectsontothevoltagerailsoftheIC.ThispollutionnoisecancomefromtheVRM,fromotherpowerrails,oreven

fromsignalspassingthroughtheimpedanceofthePDNinterconnects,aspartofthereturnpathofthesignals.

Targetimpedanceisausefulmetrictoaddressthefirstproblem,inafewsituations,butdoesnotaddressdirectlythesecondproblem.

Whenanalyzingtheself-aggressionnoisefromtheVddrailtransientcurrentontheVddrail,weconsiderthevoltagenoisegeneratedonthePDNinterconnectsduetothetransientcurrentsfromthecorelogicswitching.ThetransientcorelogicpowercurrentthroughthePDNimpedancecreatesthevoltagenoiseonthecorelogicpowerrails.

Tokeepthevoltage-dropfromthetransientcurrentbelowtheacceptablevoltagenoisethreshold,theimpedanceofthePDNmustbebelowacertainlevel,thetargetimpedance.Initssimplestformthetargetimpedanceisgivenby:

IftheimpedanceprofileofthePDN,asseenbytheICpads,isaflatimpedanceprofilefromDCtothehighestfrequencycomponentsofthetransientcurrent,andwekeeptheflatPDNimpedancebelowthetargetimpedance,thentheworst-casevoltagenoise,duetodynamiccurrent,onthepadsoftheICrailwillbelessthanthemaximumacceptablevoltagenoise.

AnimportantPDNdesigngoalistoengineeraflatimpedanceprofileforthePDN,belowthetargetimpedance.Thisisthebasiccriterionfora‘robust’PDN.Inthiscase,theworst-casevoltagenoise,duetodynamiccurrentexcitation,foramaximumtransientcurrentwillalwaysbelessthanthemaximumacceptablenoise.

Whileaflatimpedanceprofileisanimportantgoal,inmanycases,aflatimpedanceprofileacrosstheentirefrequencyrangeistooexpensivetoimplement.Theremaybepeaksintheimpedanceprofile.Theseusuallyariseattheinterfacestotheboundariesbetweenthedifferentinterconnectelements,suchas

• betweentheVRMandbulkdecouplingcapacitors• betweenthebulkdecouplingcapacitorsandtheMLCCcapacitors• betweenthepackageleadinductanceandtheon-diecapacitance

Figure2showsanexampleofatypicalimpedanceprofileofthePDN,asseenbythepadsoftheVddrailshowingafewpeaks,somelargerthanothers.

Figure2.AnexampleoftheimpedanceprofileofthePDNasviewedfromthepadsonthediepowerrail.

Usingatargetimpedanceasadesigngoal,isarobustsolutioninthespecificcaseofaflatimpedanceprofile.Whentherearepeaksintheimpedanceprofile,theworst-casevoltagenoiseisnotaccuratelypredictedbyjustatargetimpedance.

ToengineerthepeakimpedancesbelowthetargetimpedancemaymakethePDNveryexpensive.ThiswouldrequiremanyMLCCcapacitors,andthindielectricbetweenthepowerandgroundplanes,forexample.Instead,asecondcriterionisintroducedforacceptableperformancewherepeaksoccur.

TheFeaturesofanImpedancePeakinthePDNEveryimpedancepeakinthePDNiscreatedbyaparallelRLCcircuit.Fourtermscharacterize

eachpeak:

• Theparallelresonantfrequency• Thecharacteristicimpedance• Thepeakimpedance• Theq-factor

Theparallelresonantfrequencyisthefrequencyatwhichtheinductivereactanceequalsthecapacitivereactance.Thisiscalculatedfrom

ThecharacteristicimpedanceisanimpedancethatcharacterizestheRLCcircuit.ItisnottobeconfusedwiththecharacteristicimpedanceofatransmissionlinebutisjustanotherimpedancethatcharacterizestheRLCcircuit.Thischaracteristicimpedanceistheimpedanceatwhichthereactiveimpedanceofthecapacitorequalsthereactiveimpedanceoftheinductor,whichoccursattheparallelresonantfrequency.Theimpedancewheretheycross,thecharacteristicimpedance,isgivenby

Theq-factorofthepeakisrelatedtothedampingcreatedbyanyequivalentseriesresistance,theRterm,fromleadresistance,dielectriclossorotherinterconnectresistance,andisgivenby

Inthecaseofaq-factorgreaterthan1,thepeakimpedanceisrelatedtoeachofthesetermsby

Theimportanceofthesetermsisseenwhenanalyzingthevoltageacrossthecapacitorfromtwoimportantcurrentwaveforms,astepresponseandasquarewaveresponse.

StepResponseofanImpedancePeakAsafirstordermodel,thecurrentdrawfromadiecanbemodeledasacurrentsource.The

bandwidthofastepcurrentchange,foraspecificrisetimeisgivenby

Whenthecurrentsourcehasastepcurrentchangewitharisetimeshorterthan3.5nsec,thebandwidthisgreaterthan100MHz.Iftheparallelresonantfrequencyisbelow100MHz,thenthevoltageresponseoftheRLCcircuittoastepcurrentchangeisadampedsinewave.Thefrequencyofthedampedsinewaveistheparallelresonantfrequency.Thepeakamplitudeofthedampedsinewaveisgivenby

AnexampleofthisresponseisshowninFigure3.Thissuggestswhenthereisastepcurrentchange,tokeepthepeakvoltagenoiseonthePDNbelowtheacceptablenoisevoltage,thecharacteristicimpedanceofeachpeakshouldbebelowthetargetimpedance.Ifthisisthecase,thentheworst-casevoltagenoiseonthePDNwillbelessthanthemaximumacceptablelevel.ThisisthenextmostrestrictivecriterionforarobustPDN.

Figure3.Anexampleofthemeasuredon-dievoltagenoiseofapowerrailasthecorelogiccurrentundergoesastepchangeincurrentload.Superimposedonthestepcurrentaretheindividualclockedgenoiseresponses.Notethedampedsinewaveduringtherelease.

Often,engineeringthecharacteristicimpedancetobebelowthetargetimpedanceisalsoanexpensivechoice.Someriskmightbeacceptablethateithertherewillneverbeaworsecasetransientcurrentwithashortenoughrisetimetoexcitethefullpeak,orthispeakvoltagenoisemightbeacceptableifitisonlypresentforashortperiodoftime.

ButanothercurrentwaveformmaygenerateevenmorenoisefromapeakimpedanceinthePDN.

ResonantResponseWhenthetransientcurrentisintheshapeofasquarewave,witharepeatfrequencyexactlyat

theresonantpeakfrequency,thepeaktopeakvoltagenoisegeneratedbythesinewavefrequencycomponentofthesquarewaveofcurrentattheparallelresonantfrequencyis

Ifthevoltageonthedierailisatthenominalvalue,thenthissinewaveresonantresponsewillbecenteredatthenominalvalueminussomeIRdrop.Thenoiseexcursionwillbejusttheamplitude,whichishalfofthispeaktopeakvalue.Thevoltageaboveandbelowthenominalis:

Forthesametransientpeaktopeakcurrent,butattheresonantfrequency,theresultingvoltagenoiseexcursioncanbe0.64xtheq-factortimesthestepresponsevoltagenoise,bothaboveandbelownominalvoltage.Insomecriticalmissionindustries,themaximumvoltageisimportantbecausethecircuitsarenotallowedtobeelectricallyoverstressed.Inotherindustries,theminimum

voltageisimportantbecauseset-uptimerequirements,VminandFmaxconsiderations.Ittakesaboutaq-factorofcyclesfortheresonantsquarewaveofcurrenttodrivethevoltagenoisetothepeakvoltage.Aq-factorof1/0.64=1.57ormorewillresultinapeaknoisevoltageexceedingthemaximumallowablenoisewhentheZ0characteristicimpedancemeetsthetargetimpedance.But,tomeetthiscriterion,notonlymustthemaximumworstcasetransientcurrentmodulateattheparallelresonantfrequency,butitmustbepresentforaq-factorofcyclestoreachthisworstcase.

Thelargertheq-factoroftheparallelresonance,i.e.,thesharperthepeakduetosmallerdamping,thelargertheresonantresponsecanbe,butthelongerthePDNmustbedriventoreachthefullpeaknoise.Figure4isanexampleofthemeasuredresonantresponsevoltageonthediewhenasquarewaveoftransientcurrentdrivestheon-diePDN.

Figure4.Measuredvoltagenoiseonadiewhenthecorelogiccurrentisasquarewaveatthepeakimpedancefrequency.

InaPDNdesignedtobefullyrobustandimmunetoresonantpeakexcitation,sotheworst-casevoltageisbelowtheacceptablenoisethreshold,theparallelresonantpeakimpedancemustbebelow1.57xtargetimpedance.The1.57factorcomesbecausethepositiveandnegativeresonantexcursions

are andthefullvoltagetoleranceisreachedatresonantconditionswhenan

impedancepeakis1/0.64=1.57xZtarget.ThewholeresonantwaveformisbiasedandreducedbyDCIRdropsothevoltageminimumsmaybefartherawayfromnominalvoltagethanthevoltagemaximums.Reducingtheimpedancepeakbelowthislevelwillkeeptheworst-casepeak-to-peaknoisebelowtheacceptablelevelwhentheresonanceisfullystimulated.Butthisisoftenveryexpensive,especiallywhentheresonantpeakisfromtheon-diecapacitanceandpackageleadinductance.

Often,someriskisacceptedbasedontheunlikelypossibilityoftheworst-casetransientcurrentoccurringexactlyattheparallelresonantfrequencyandlastingforaq-factorofcycles.Manysuccessfullydeployedproductshaveapeakheightaslargeas3xthetargetimpedance.Thisisanimpedancepeakheight2xhigherthanafullyrobustPDN.

ButevenafullyrobustPDN,withallofitspeaksbelow1.56xthetargetimpedance,maystillhavePDNvoltagenoiseabovetheacceptablelimitunderaspecialsetofconditions.Thisiswhenroguewavesmaydevelop.

RogueWavesIfthePDNimpedanceprofilehastwoormorehighq-factorparallelresonantpeaks,eachof

whichisbelowthetargetimpedance,noneofthepeaks,ifexcitedindividually,mightgenerateexcessivevoltagenoiseunderworstcaseconditions.

However,itispossibleforaspecificcombinationofresonantresponsestosequentiallybuildupexactlyinphasetoexcitethelowestfrequencypeak,andthenatitspeakresponse,thesecondhighestfrequencypeak,andatitspeak,thehighestfrequencypeak.

Whenmultiple-frequencyoceanwavesaddupexactlyinphase,theycanproduceexceptionallylargewaveheights,whichhavebeentermedroguewaves.Whenmultiplecurrentwaveformsaresequencedtoexcitemultiplehighq-factorpeaks,thevoltagenoiseonPDNscanshowlargepeaks,whichhavebeentermedroguewaves.

Figure5isanexampleoftheimpedanceprofileofaPDNwiththreehighq-factorparallelresonances.

Figure5.Exampleofanimpedanceprofilewiththree,highq-factorparallelresonantpeaks.TheseoccurattheboundariesofvariousPDNelements.

WhenthisPDNisexcitedbyatleasttwosequentialgroupsofsquarewavesofcurrent,withadurationandphaseexactlyoptimized,theycanexciteroguewavesonthePDN.Eachsquarewaveexcitesadifferentresonanceandthepeakvoltagesbuildoneachother.Evenifeachpeakwerebelow1.56xthetargetimpedance,meetingthefullyrobustrequirementforacceptablenoise,theresulting

roguewaveofvoltagecaneasilyexceedtheacceptablelevelofnoise.Figure6isanexampleofthesimulatedroguewaveonthisPDN.

Figure6.Exampleoftheroguewavecreatedbysequentiallyexcitingtwooftheresonantpeaks,bythecurrentwaveformshowninthelowergraph.

Howlikelyisitthatthetransientcurrentwaveformsfromthecorelogiccircuitswouldexactlymatchthespecificresonantfrequenciesandstayonresonancelongenoughtoexcitethepeakamplitudeperfectlyphased?Inacriticalapplication,itonlymusthappenonce,causingthevoltagerequirementstobeexceeded.Thiscanresultinanoverstresscondition,orintermittentoperation.Figure7isanexampleofthemeasuredroguewaveresponseonaPDNfromtheunfortunateoccurrenceofexactlytherightcurrentwaveform.

Figure7.AnexampleofthemeasuredvoltagenoiseonaPDNfromtwodifferentsquarewavesofcurrentwiththesameamplitude,excitingeachresonance.Inthefar-rightscreen,thesetwoexcitationsarephasedexactlyrighttoexcitetheroguewavewitharesponselargerthaneitherofthetwootherresponses.

OtherSourcesofNoiseThisanalysishassofaronlyconsideredonesourceofnoise,theself-aggressionnoisefrom

transientcurrentsontheVddrailthroughthePDNimpedanceprofile.Targetimpedanceisausefulmetricagainstwhichtojudgetheimpedanceprofile,ifitisappliedwiththeappropriatebalanceofperformance,riskandcost.ButtherearealsoothersourcesofnoisewhichcanbeuncorrelatedandaddtotheVddnoise.

NoiseontheVddrail,forexample,cancomefromself-inducednoiseandmutualsourcesfromthenoisepollutionontheboardlevelinterconnects.TheboardlevelnoisecanarisefromtheVRM,fromthetransientcurrentsfromotherconsumerICsandevenfromsignalstransitioningthroughthepowerrails.Thisnoiseisindependentofatargetimpedanceguideline.Intheworstcase,allthesenoisesourceswilladdtogetherwiththeself-aggressionnoiseontheVddrails.AfullyrobustPDNshouldconsiderthisworstcasenoise.

ConclusionArobustPDNisengineeredtohaveaflatimpedanceprofilewithanimpedancebelowthe

targetimpedance.ThisshouldalwaysbethedesigngoalineveryPDN.Aflatimpedanceprofilewilleliminatethechanceofresonantresponses,roguewavesandprovideadeterministicnoisefromtheself-aggressionVddcurrents.

Whentheimpedanceprofileisnotflat,buthasparallelresonantpeaks,keepingthepeakimpedancesbelowthetargetimpedanceisnotenoughofacriterionforafullyrobustPDN.

Manydesignsareabalancebetweentheperformance,theriskandthecost.Whencostisanimportantdrivingforce,anacceptableriskmightbewhenaparallelresonance’scharacteristicimpedanceisengineeredtobebelowthetargetimpedance.Thiswouldkeepthepeakvoltagenoiseresponsefromastepcurrenttobewithintheacceptablenoiselimit.

Buteventhiscriterionisnotrobustenoughforrarecurrentwaveforms.Whenresonantdrivingofpeaksispossible,allimpedancepeakheightsshouldbebelow1.56xthetargetimpedance.

Withmultiplehighq-factorpeaks,eventhisconditionisnotenoughforafullyrobustPDN.Underrareconditions,aroguewavewithavoltageamplitudeabovetheacceptablevoltagenoiselimitsmaybecreatedwhenmultiplepeaksaresequentiallyexcitedinphase.

Finally,afullyrobustPDNwouldneedtoincludetheworst-casecombinationofallnoisesourcesoneachrail,fromself-aggressionnoiseandmutual-aggressionnoise.

Alldesignsareatradeoffbetweentheperformance,thecosttheriskandmeetingthescheduletargets.Eachtypeofproducthasadifferentappropriatebalancebetweenthesefactors.Inmanyconsumerproductscostisthebiggestdrivingfactorandsomeriskisaccepted.Inhighreliabilityproducts,lowriskisthedrivingforceandalloftheseeffectsmustbeincludedinanyPDNanalysis.Thetargetimpedanceisastartingplacetoguidethedesignineachdesign,butinlowriskproductsnotenoughofacriteriontobaseadesign.

References

1) LarryD.Smith,EricBogatin,“PrinciplesofPowerIntegrityforPDNDesign--Simplified:RobustandCostEffectiveDesignforHighSpeedDigitalProducts”(PrenticeHallModernSemiconductorDesign),ISBN-13:978-0132735551,April6,2017

2) Sandler,S,“PowerIntegrity:Measuring,Optimizing,andTroubleshootingPowerRelatedParametersinElectronicsSystems”,Nov18,2014