蒙特卡洛分析

MonteCarlosimulation……forbetteryieldandperformance--Atutorial2021/5/91start

SystemrequirementStatisticalanalysisincludeprocess,mismatcheffectsInitialdesignDesignmeetsthegoal?endNOYESMonteCarlosimulation

……forbetteryieldandperformance

SomedesignmaydegradeinperformanceOveralldesignyieldcouldbeunexpectedlylowIffabricationprocessparameteranddevicemismatcheffectonsamediearenottakenintoaccountthenHencestatisticalanalysismustfindahighplaceindesigncycle2021/5/92WewillperformMonteCarloanalysisonanRF-frontendLNAandcomparetheresultifnostatisticalanalysisisdone.WewillalsoseehowtoanalyzeyieldandscalardatainMonteCarlowiththehelpofLowpassfilterexample.MonteCarlosimulation2021/5/93MonteCarlosimulation(example)LinearityInputmatchingBiasN/WOutputmatchingCascodearch.toreducefeedbackcapacitanceRF-frontend(LNA)

KnowingSystemrequirement

Initialdesignbasedonrequirementlikenoise,gain,narroworwideband.2021/5/94MonteCarlosimulationCadencesimulationsetup(Normal)Choosingaffirmaanalogartist2.

ChoosingSpectresimulator2021/5/95Choosingmodelfile,whichcontainsallMOS,reg.,capmodelparameters.MonteCarlosimulation1.Choosesetupmodellibraries2.BrowseandchoosemodelfileinthedirectoryCadencesimulationsetup(Normal)2021/5/96Setupanalysis(dc,ac,spetc.),createnetlistandrunsimulatorMonteCarlosimulation1.Chooseanalysistorun2.Chooseoutputtoplot3.CreatenetlistandrunCadencesimulationsetup(Normal)2021/5/97PlottingresultsMonteCarlosimulation1.Choosedirectplotforanalysis2.Clicktoviewthedesiredresult3.AnalyzewaveformCadencesimulationsetup(Normal)2021/5/98MonteCarlomodelinginCadencespectresimulator

ProcessSection

-describesmanufacturingparameter,theirstatisticalvariationandamodelfordevicethatcalculatesits(width,length,cap,res.Etc.)accordingtoprocessparameter.Design-SpecificSection–designeraccordingtohisneedcanspecifyMonteCarloanalysis.Forexampleinacurrentmirrorcircuit,matchedtransistorsareusedanddesignercangivesomecorrelationfactorbetweenthesematchedtransistor.MonteCarlosimulationCadencesimulationsetup(MonteCarlo)2021/5/99TypicalModelFileProcessSectionAllparametersetstotheirnominalvalue,nostatisticalvariationdefinedModel(NMOS’sRg)iscalculatedusingnominalparametervalue21MonteCarlosimulationCadencesimulationsetup(MonteCarlo)2021/5/910Definingprocess,mismatchparameterasstatisticallyassignedvalueAssessesthedevicemismatchondifferentdie,whichcouldhavegonethroughsomedifferentprocessparametersduringfabrication.Assessesthedevicemismatchonsamedie,whichcouldhavegonethroughsomedifferentprocessparameter.VariationdefinedasadistributedfunctionMonteCarlosimulationProcessSectionCadencesimulationsetup(MonteCarlo)2021/5/911DesignSpecificSectionThisincludesthecircuitconnectivity(tworesistors,andcorrespondingcurrentsourcesthatfeedthem)Definingcorrelationbetweentwodevices(R1,R2)†Note:AlternativelythisinformationcanalsobeinsertedthroughArtistMonteCarloTool.MonteCarlosimulationCadencesimulationsetup(MonteCarlo)2021/5/912MonteCarlosimulationModelfileusedforLNAexampleNoteThisisnotbasedonfoundrydatabutmodeledforillustrativepurposes.Cadencesimulationsetup(MonteCarlo)2021/5/913MonteCarlosimulation

AfterInitialdesignthatmeetsthesystemrequirement,statisticalanalysismusthavetobecarriedout.Makesuretheadditionofprocessandmismatchparametersectioninmodelfile.Makecertaintoincludetheparticularsection(forexa.Statsinspectre)insimulationmodellibraryGototoolMonteCarloinaffirmaanalogartistCadencesimulationsetup(MonteCarlo)2021/5/914MonteCarlosimulationChoosenoofiteration(default=100)1.ChoosewhichvariationtoincludeProcessdevicemismatcheffectontwodiff.dieMismatchdevicemismatcheffectonsamedie

2.Clickifyouwanttoseethefamilyofcurvei.e.curvefromeachiteration3.Definetheexpressions/signalsonwhichMonteCarloanalysiswillbeperformed.Note:calculatorcanalsobeusedtogettheseexpressionFinallyruntheanalysisCadencesimulationsetup(MonteCarlo)2021/5/915MonteCarlosimulation(Analyzingwaveform)MatchingNormalsimulation(withoutstatisticalvariation)MonteCarloSimulation(withstatisticalvariation)Processparameterandmismatcheffect

Input&OutputmatchingN/WDEGRADESOveralldesignperformance(noise,gainetc.)DEGRADESS11S222021/5/916MonteCarlosimulation(Analyzingwaveform)Matching(VSWR):IttellshowwellinputandoutputN/Warematched.MonteCarlosimulationNormalsimulationVSWR1VSWR2VariationsinVSWR2021/5/917MonteCarlosimulation(Analyzingwaveform)Matching(forwardandreversetransmissiongain)Ithasdeterioratedtheperformancesignificantly,asaminimumS12andmaximumS21valueisdesirable.NormalsimulationMonteCarlosimulationS12S212021/5/918MonteCarlosimulation(Analyzingwaveform)NormalsimulationMonteCarlosimulationStability:AKfvalue>1,isdesiredforanstableamplifierKfvaluehasbecome<1,andconsequentlycreatingapotentialunstability,hencealargemarginisrequiredatinitialdesignphase.Stabilityfactor2021/5/919MonteCarlosimulation(Analyzingwaveform)NormalsimulationMonteCarlosimulationNoisePerformanceAsvisible,designhasarobustnoiseperformanceatdesiredband(2.4-2.5GHz)BUT….NoisefigurePeriodicOutputnoise2021/5/920MonteCarlosimulation(Analyzingwaveform)But…

LNAasanRF-frontendhastoprovideenoughgainwithmaximumnoisesuppressiontomaintainanallowableSNRatdemodulator'sinput.ItfailstomeetthegainrequirementGain2021/5/921MonteCarlosimulationWewillquicklygooveranotherexampleoflowpassfilterandseehowtoanalyzescalardataandyieldthroughMonteCarlosimulation2021/5/922MonteCarlosimulationInitialDesign:CircuitdesigningaccordingtosystemrequirementLow-PassFilter2021/5/923MonteCarlosimulation1.Runningnormalanalysis2.Specifyingstatisticalvariationinmodelfile3.RunningMonteCarloanalysis123Cadencesimulationsetup(MonteCarlo)2021/5/924MonteCarlosimulationSimulationshowsdb20andphasevaluesaregreatlyaffectedbystatisticalvariationsintroducedintransistor.Hencetheneedforredesigningthecircuit(Analyzingresults)2021/5/925MonteCarlosimulation(AnalyzingScalardata)1.ChooseresultsplotHistogram2.Chooseparameterstoplot3.Analyzethehistogramappearedinwaveformwindow2021/5/926MonteCarlosimulation1.Chooseresultsspecificationlimits2.Setboundsandlimits3.ChooseResultsyieldsimpleinanalysiswindow4.Setsuppressionvalueforyield5.AnalyzeyieldOnly64%iterationspassesthespecifiedlimitsforbandwidthandymax(AnalyzingYield)2021/5/927MonteCarlosimulation

(PLLComponents)OverviewReferenceclockDetectoroutputLoopfilterresponseOscillatoroutputClockdivideroutput•Phase/frequencydetectordeterminesthedifferencebetweenthephaseorfrequencyoftwosignals•Theloopfilterremovesthehigh-frequenciesfromthevoltage-controlledoscillator(VCO)controllingvoltage•TheVCOproducesandoutputfrequencycontrolledbyavoltage2021/5/928MonteCarlosimulation

(PLLComponents)NoiseSourcesDetectornoiseVCOnoiseΣ-ΔQuantizationnoiseInPLLdesignitishighlydesirabletobeabletoseetheimpactofallnoisesources,whichinturnaffectstheoverallPLLperformance.DuetoreferencejitterDuetovariationincontrolvoltageDuetouncertaintyinvolvedindiscretization2021/5/929MonteCarlosimulation

(VCO)Anoscillatorisacircuitcapableofmaintainingelectricoscillations.Frequencyofoscillation=1/(LC)1/2Controlledbyvoltagedependentcapacitance(varactor)

Powerefficientsincebiascurrentissharedbetweenthetwotransconductors.ComplimentaryCross-CoupledLCVCOequivalentForoperationincurrent-limitedregime:VO=(4/π).Ibias.Req

(Idealswitching)VO(apx)=Ibias.Req(Highfrequency)2021/5/930Causesofspectralpuritydegradation(phasenoise):1.)Randomnoiseinthereferenceinput,thePFD,loopfilterandVCO(alsodividersifthePLLisafrequencysynthesizer)2.)Spurioussidebands–highenergysidebandswithnoharmonicrelationshiptothegeneratedoutputsignal.Itissystematicinorigin.Whyisspectralpurityimportant?MonteCarlosimulation

(VCO–PhaseNoise)PhasenoiseproducesadjacentchannelinterferencePhasenoisecandegradethesensitivityofareceiverduetoreciprocalmixing2021/5/931MonteCarlosimulation

(VCO–PhaseNoise)Howdotheprocessandmismatchvariationaffectphasenoise?--wewillperformmontecarloanalysistoassessthis.

Step1–Varyingtheprocessparameteronly

Step2–investigatingthedevicemismatch(indiffVCOonesidemismatchedtotheother)inpresenceofprocessvariationThestatisticsblockcontainsthedistributionsforparameters:DistributionsspecifiedintheprocessblockaresampledonceperMonteCarlorun,areappliedatglobalscope,andareusedtypicallytorepresentbatch-to-batch(process)variations.Distributionsspecifiedinthemismatchblockareappliedonaper-subcircuitinstancebasis,aresampledoncepersubcircuitinstance,andareusedtypicallytorepresentdevice-to-device(onchip)mismatchfordevicesonthesamechip.CadenceSpectremodeling:2021/5/932MonteCarlosimulation

(VCO–PhaseNoise)modelfileDefinestatisticalblocksinthemodelfile(ideallyitshouldbeprovidedfromthefoundry)ProcesssectionMismatchsection2021/5/933MonteCarlosimulation

(VCO–PhaseNoise)STEP-1RunningMonteCarloforprocessvariationonlyNormalsimulationMonteCarlosimulationWithappliedstatisticalvariation(inmodelfile)anincreaseinnoisecanbeobserved,andatthisrunresultednoiseisworstandunacceptable.2021/5/934MonteCarlosimulation

(VCO–PhaseNoise)STEP-2RunningMonteCarloformismatchin2sidesofDiff.VCONormalsimulationMonteCarlosimulationAgainsimilarlookingbutnotthesameresultsappearsandnoiseatthisrunisunacceptable.Note:

Whenthesameparameterissubjecttobothprocessandmismatchvariations,thesampledprocessvaluebecomesthemeanforthemismatchrandomnumbergeneratorforthatparticularparameter.2021/5/935MonteCarlosimulation

(VCO–PhaseNoise)--moreinsightTogetmoreinsightwewillvaryonlyfewparameterandcheckhowvaluesareassignedfordifferentrunaswellasthesimulationresultDefiningvariationforonlytwoparametersinthemodelfile--Vth -tox2021/5/936MonteCarlosimulation

(VCO–PhaseNoise)--moreinsightHerebothnmos(pmos)transistorshavebeenassignedsameprocessvariation.IneachruntheytakeondifferentparameteraccordingtodistributiondefinedProcessvariationonlyNM0NM1PM1PM02021/5/937MonteCarlosimulation

(VCO–PhaseNoise)--moreinsightProcessandMismatchbothvariationtogether,withcorrelationof0.2betweenthetwonmos(pmos)transistorAsconspicuouseachnmos(pmos)transistorisgettingdifferentparametervalueineachrun.2021/5/938MonteCarlosimulation

(VCO–PhaseNoise)--moreinsightProcessvariationonlyProcess&mismatchvariationAsvisibleinthecaseofprocessvariationwithdevicemismatchnoisehasbeenincreased.2021/5/939MonteCarlosimulation

(PLLataglance)

InaPLLalltheseprocessvariationcandegradeit’soverallperformancesignificantly.Toseetheimpactofprocessvariationweprobetheoutputaftertheloopfilter.MonteCarlosimulationAsclearinonecasecontrolvoltage(i.e.loopfilteroutput)isrampingrapidlycomparetootherandthuswillresultindifferentperformance.2021/5/940MonteCarlosimulationInourdesignPLLhasasettlingtimeof65us.Tosimplyruntheanalysis(transistorlevel)forthismuchperiodmaytake2-3daysonasinglemachine.Todomontecarlosimulationevenfor10runwillmakethesituationworse.TospeedupMonteCarloanalyses—tomakethemruninminutesasopposedtodays—--WeneedtoreducetheruntimeandcanutilizeParallelsimulation.--Suchasvariancereductiontechniquecanbeemployed.2021/5/941MonteCarlosimulation

(Seedno¶llelsimulation)Note:(1)Inputfileshouldhave‘.scs’extension(forexa.input.scs)(2)InspectreonecannotspecifydifferentseedfromGUI(bydefaultitalwaystakesseed=1).IfMonteCarlosimulationfordifferentseedisrequiredthen…..Step1.Createnetlist(inputfile)a)Eitherfromanalogartistor

b)Toolsmontecarlosimulationcreate_input_filesSeed2021/5/942MonteCarlosimulationMonteCarlosimulation

(Seedno¶llelsimulation)Step2.Editinput.scsfilemanuallyeditSEED=?line(numberyouwant)Seed2021/5/943MonteCarlosimulationMonteCarlosimulation

(Seedno¶llelsimulation)Step3.Runspectrefromcommandlinewithoptionforexample…..spectre-envartist4.4.6+log../psf/spectre.out-formatpsfbin-raw../psfinput.scsHereoneshouldexecutespectrecommand(orexecutablefile)fromthenetlistdirectory.Forexampleonewantstosimulate“PLL”designfromcommandlineThengotoyoursimulationdirectorycd…/simulation/pll/spectre/schematic/netlistandhereexecutespectrecommandSeed2021/5/944MonteCarlosimulationMonteCarlosimulation

(Seedno¶llelsimulation)Step4.ResultscanbeplottedwitheitherfromcalculatororfromMonteCarlotool…..Seed=1Seed=11Seed=3Fig:PlotsfordifferentseedvaluesimulationSeed2021/5/945MonteCarlosimulation

(Seedno¶llelsimulation)Anotherwayofdoingsimilarthing(givingdifferentseedvalue)fromGUIwouldbetostartsimulationfromdifferentrun,orsaytoskipsomeinitialrunasshowninthefig.ButbewareskippingtheserunscouldtakemuchlongertimeforacomplexdesignHereitwillskipfirst10runsandsimulatefrom11’thto110’thrunfor100iterationThisisquitesimilartoassigningdifferentseedvalue.AwayaroundfromGUI2021/5/946MonteCarlosimulation

(Seedno¶llelsimulation)Runningmultipleanalysisfromonefile

ThiscanbedonebydefiningmultiplemontecarloanalysisstatementintheinputfileasshownbelowNote:Foreachanalysisadifferentnametochildanalysis(forexampleac,dc,tran)andtooutputfilehastobeassigned.Analysis1Analysis22021/5/947MonteCarlosimulation

(Seedno¶llelsimulation)Runningscriptforexecutingmultiplefiles(sequentially)

Thiscanbedonebymakinganexecutablefileass