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首页 两级OTA的设计举例_688504330

两级OTA的设计举例_688504330.pdf

两级OTA的设计举例_688504330

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2011-07-11 0人阅读 举报 0 0 暂无简介

简介:本文档为《两级OTA的设计举例_688504330pdf》,可适用于高等教育领域

Reference:C:DocumentsandSettingsMurmannMyDocumentslibMathcaddefaultsmcdStageOTADesignExample("SimpleApproach")CsVsdVodCsCfCfCLCLVidMa,bMa,bMa,bMa,b(Millercompensation,neutralizationcapsandCMFBnotshown)CggCsCf:=βestCfCfCsCgg:=βest=avoεsβest⋅:=avo×=Forsimplicity,assumethateachstagecontributessamegain(notnecessarilyaccurateoptimal)avostageavo:=avostage=Forsimplicity,assumethatintrinsicgainofbothsignalpathdevicesisxstagegain(notnecessarilyaccurateoptimal)Intrinsicgainrequirements:gmroavostage:=gmro=Basedongmrodesigncharts,wedecide:Lμm:=Lμm:=Forsimplicity,choosesamelengthsforpmosnmosloads(notnecessarilyoptimal)LL:=LL:=TechnologyDataVDDV:=γ:=gmID,gmCgglookuptables:Reference:C:DocumentsandSettingsMurmannMyDocumentsteachingeeautumnotaexamplegmDesignObjectivesfcMHz:=PMdeg:=DR:=(dB)G:=εs:=GivenComponentValuesCsfF:=CLfF:=CfCsG:=DesignDecision:ChannellengthsReturnfactorestimateassumingCggis~equaltosumoffeedbackcapsCcpF=CcβestkB⋅Tr⋅γ⋅g()⋅NtotkBTr⋅Cγg()⋅⎡⎣⎤⎦⋅−⋅:=NtotβkBTr⋅Cc⋅γ⋅g()⋅kBTr⋅CLγg()⋅⎡⎣⎤⎦⋅⎡⎢⎣⎤⎥⎦⋅=NtotμV=NtotVodmax⋅DR:=TotalstageloadCfF=CCLβest−()Cf⋅:=Step:CalculateCcbasedonDRspec(Differentialpeakamplitude)VodmaxVDDVDSmin⋅−:=VDSminmV:=AllocatedVdsminforMandMandresultingoutputswing:g:=ggmIDgmID=g:=ggmIDgmID=RatioofgmIDinloaddevicesvssignalpath(oftenwantg,tobe<,tominimizenoiseandCjunctionhowever,verysmallg,mayimposeDRlimitations)DesignDecision:RelativegmIDofactiveloads,outputswinggmIDSA:=gmIDSA:=DesignDecision:gmID==Wμm=Wμm=WWw⋅:=WWw⋅:=w=wnidwLgmID,()pidwLgmIDg⋅,():=w=wpidwLgmID,()nidwLgmIDg⋅,():=Calculatethewidthratios(w=WW)forthechosengmIDWμm=Wμm=WIDIDW:=WIDIDW:=IDWAm=IDWAm=IDWnidwLgmID,():=IDWpidwLgmID,():=IDmA=IDmA=IDgmgmID:=IDgmgmID:=Step:FindID,WgmmS=(approx)gmk⋅π⋅fc⋅C⋅:=k=ktanπPMdeg⋅⎛⎜⎝⎞⎟⎠:=gmmS=gmβest⋅π⋅fc⋅Cc⋅:=Step:CalculatetransconductancesOTAcircuitforsimulation(feedbacknetwork,CMFB,Cc,etcnotshown)Ma,bMa,bMa,bMa,buAuAuAuAM=M=M=uAMdMcMdMcSimulationresults(firstrun,withoutanytweaking):fc=MHz,PM=deg,T=fMHzMagnitudedBfMHzPhasedegreesfHzPSDVHzfHzSqrt(Integral)μVrmsIntegral=uVrms,DR=dB(forVodmax=V)Loopcrossoverandphasemarginarewayoff!WhyLookatopoutput:gm=mSgm=mSNotbadWhat'swrongJunctioncapsarefairlylargeandcomparabletoothercapsEgCdb~fFthiswillsignificantlyimpactnondominantpoleCgg=fF,meansthatbetaissmallerthanwhatwehadbudgetdabove(beta,est)Bottomline:Hardtoget"reasonable"matchingbetweenhandcalculationsandSpiceusingsimplifiedexpressionsandignoringjunctionscapsLet'sfixthissubcktxxxxxxelement:ma:mb:ma:mb:md:mcmodel:pch:pch:nch:nch:nch:nchregionSaturatiSaturatiSaturatiSaturatiSaturatiSaturatiiduuuuuuibsibdvgsmmmmvdsmvbsmmvthmmmmmmvdsatmmmmmmvodmmmmmmbetammmmmmgameffmmmmmmgmmmmmmmgdsuuuuuugmbuuuuuucdtotffffffcgtotffffffcstotffffffcbtotffffffcgsffffffcgdffffffsubcktxxxxxxelement:mb:ma:md:mc:mb:mamodel:nch:nch:pch:pch:pch:pchregionSaturatiSaturatiSaturatiSaturatiSaturatiSaturatiiduuumuuibsibdvgsmmvdsmmmvbsvthmmmmmmvdsatmmmmmmvodmmmmmmbetammmmmmgameffmmmmmmgmmmummmgdsuuuuuugmbmmumuucdtotffffffcgtotffffffcstotffffffcbtotffffffcgsffffffcgdffffffReference:C:DocumentsandSettingsMurmannMyDocumentslibMathcaddefaultsmcdStageOTADesignExample("AccurateApproach")CsVsdVodCsCfCfCLCLVidMa,bMa,bMa,bMa,b(Millercompensation,neutralizationcapsandCMFBnotshown)CLfF:=CfCsG:=DesignDecision:ChannellengthsReturnfactorestimateassumingCggis~equaltosumoffeedbackcapsCggCsCf:=βestCfCfCsCgg:=βest=avoεsβest⋅:=avo×=Forsimplicity,assumethateachstagecontributessamegain(notnecessarilyaccurateoptimal)avostageavo:=avostage=Forsimplicity,assumethatintrinsicgainofbothsignalpathdevicesisxstagegain(notnecessarilyaccurateoptimal)Intrinsicgainrequirements:gmroavostage:=gmro=Basedongmrodesigncharts,wedecide:Lμm:=Lμm:=TechnologyDataVDDV:=γ:=Lminμm:=kdbn:=kdbp:=(approximateratiosofCdbCggforminimumlengthdevice)gmID,gmCgglookuptables:Reference:C:DocumentsandSettingsMurmannMyDocumentsteachingeeautumnotaexamplegmDesignObjectivesfcMHz:=PMdeg:=DR:=(dB)G:=εs:=GivenComponentValuesCsfF:=CggfF=CggcCL⋅:=CggfF=CggcCsCf()⋅:=β=βCfCfCs()c()⋅:=Step:Estimatecalculatereturnfactorandallcapacitancesc:=(goodstartingpoint:c=)cCggCL=c:=(goodstartingpoint:c=)cCggCsCf=AdjustfollowingparameterstominimizetotalcurrentcomputedinstepITERATIONUsuallyhavetoleavemarginsforPVTandgaindropatswingDependingonfinaldesignoutcome(optimumgmID),itmaybeworthrevisitingthisassumtion(Differentialpeakamplitude)VodmaxVDDVDSmin⋅−:=VDSminmV:=AllocatedVdsminforMandMandresultingoutputswing:g:=ggmIDgmID=g:=ggmIDgmID=RatioofgmIDinloaddevicesvssignalpath(oftenwantg,tobe<,tominimizenoiseandCjunctionhowever,verysmallg,mayimposeDRlimitations)DesignDecision:RelativegmIDofactiveloads,outputswingLL:=LL:=Forsimplicity,choosesamelengthsforpmosnmosloads(notnecessarilyoptimal)(Note:forlowDRdesigns,Ccisnotneccesarilysetbynoiseandbecomespartoftheoptimizationprocess(egaddvariablec=ccCLtotheiterationloop)CcpF=CcβkB⋅Tr⋅γ⋅g()⋅NtotkBTr⋅Cγg()⋅⎡⎣⎤⎦⋅−⋅:=NtotβkBTr⋅Cc⋅γ⋅g()⋅kBTr⋅CLγg()⋅⎡⎣⎤⎦⋅⎡⎢⎣⎤⎥⎦⋅=NtotμV=NtotVodmax⋅DR:=Step:CalculateCcbasedonDRspecTotalstageloadC×fF=CCLCdbCdbβ−()Cf⋅:=TotalstageloadCfF=CCdbCdbCgg:=CdbfF=CdbwCdb⋅kdbpkdbn⋅:=w=wnidwLSA,⎛⎜⎝⎞⎟⎠pidwLSAg⋅,⎛⎜⎝⎞⎟⎠:=CdbfF=CdbkdbnCgg⋅LminL⋅:=CdbfF=CdbwCdb⋅kdbnkdbp⋅:=w=wpidwLSA,⎛⎜⎝⎞⎟⎠nidwLSAg⋅,⎛⎜⎝⎞⎟⎠:=TofindCdb,weestimatethewidthratiow=WW,assuminggmID=SA(notknownatthispointalsowon'tmattermuch)CdbfF=CdbkdbpCgg⋅LminL⋅:=Thisdesign(withc=,c=>IDtotal=mA)willcertainlywork,butthere'slotsofroomforpoweroptimizationWiththeabovescript,itisquiteeasytoiterativelystepcandcupdowntosearchforapowerminimumForc=,c=,itisinterestingtonotethatthereislotsofselfloading(TheCdb'spresentalargefractionofthecapsthatsetfcandfp)Hence,goingtosmallercandorcmayhelplowerpowerAnothertrywithc=,c=yieldsIDtotal=mAMakingthepmossmallerreducesitscontributedcapacitancefasterthangmIDdropsbetaalsoimprovesforsmallcHence,thereisanetreductioninpowerSimilarly,usingyetanothertrywithc=,c=yieldsIDtotal=mAManualiterationsareveryusefulfordevelopingintuitionbutitisalsopossibletoautomatethesearchprocessusinganoptimizationfunction:IDtotalmA=IDtotalIDID:=IDmA=IDmA=IDgmgmID:=IDgmgmID:=gmIDV=gmIDV=gmIDngmidLfT,():=gmIDpgmidLfT,():=Step:FindgmID,IDfTGHz=fTπ⋅gmCgg⋅:=fTGHz=fTπ⋅gmCgg⋅:=gmmS=gmk⋅π⋅fc⋅CC⋅CcCC⎛⎜⎝⎞⎟⎠⋅:=k=ktanπPMdeg⋅⎛⎜⎝⎞⎟⎠:=gmmS=gmβ⋅π⋅fc⋅Cc⋅:=Step:Calculatetransconductancesandtransitfrequenciesfcc,()βCfCfCs()c()⋅←CggcCsCf()⋅←CggcCL⋅←CdbkdbpCgg⋅LminL⋅←CdbpidwLSA,⎛⎜⎝⎞⎟⎠nidwLSAg⋅,⎛⎜⎝⎞⎟⎠Cdb⋅kdbnkdbp⋅←CdbkdbnCgg⋅LminL⋅←CdbnidwLSA,⎛⎜⎝⎞⎟⎠pidwLSAg⋅,⎛⎜⎝⎞⎟⎠Cdb⋅kdbpkdbn⋅←CCdbCdbCgg←CCLCdbCdbβ−()Cf⋅←CcβkB⋅Tr⋅γ⋅g()⋅NtotkBTr⋅Cγg()⋅⎡⎣⎤⎦⋅−⋅←gmβ⋅π⋅fc⋅Cc⋅←ktanπPMdeg⋅⋅⎛⎜⎝⎞⎟⎠←gmk⋅π⋅fc⋅CC⋅CcCC⎛⎜⎝⎞⎟⎠⋅←fTπ⋅gmCgg⋅←fTπ⋅gmCgg⋅←gmIDifpgmidLfT,()V⋅>pgmidLfT,(),V⋅,⎛⎜⎝⎞⎟⎠←⎛⎞:=gmIDifngmidLfT,()V⋅>ngmidLfT,(),V⋅,⎛⎜⎝⎞⎟⎠←IDtotalgmgmIDgmgmID←IDtotalInitialguessforoptimizationc:=c:=Givenc>c>CoptMinimizefc,c,():=fCoptCopt,⎛⎝⎞⎠mA=Copt⎛⎜⎝⎞⎟⎠=MCreateMeshf,,,,,,():=MComments:Shallowpowerminimumforsmallcandctheoptimumisclosetothe"steepcliff"imposedbylimitinggmIDtopracticalvalues>SAintheobjectivefunction(inthepowerminimum,gmID=SA,gmID=SA)CcpF=CcβkB⋅Tr⋅γ⋅g()⋅NtotkBTr⋅Cγg()⋅⎡⎣⎤⎦⋅−⋅:=Step:CalculateCcbasedonDRspecTotalstageloadCfF=CCLCdbCdbβ−()Cf⋅:=TotalstageloadCfF=CCdbCdbCgg:=CdbfF=CdbwCdb⋅kdbpkdbn⋅:=w=wnidwLSA,⎛⎜⎝⎞⎟⎠pidwLSAg⋅,⎛⎜⎝⎞⎟⎠:=CdbfF=CdbkdbnCgg⋅LminL⋅:=CdbfF=CdbwCdb⋅kdbnkdbp⋅:=w=wpidwLSA,⎛⎜⎝⎞⎟⎠nidwLSAg⋅,⎛⎜⎝⎞⎟⎠:=CdbfF=CdbkdbpCgg⋅LminL⋅:=CggfF=CggcCL⋅:=CggfF=CggcCsCf()⋅:=β=βCfCfCs()c()⋅:=EstimatecalculatereturnfactorandallcapacitancescCopt:=cCopt:=Recalculatecomponentswithoptimizerresult:Wμm=Wμm=WWw⋅:=WWw⋅:=Wμm=Wμm=WIDIDW:=WIDIDW:=IDWAm=IDWAm=IDWnidwLgmID,():=IDWpidwLgmID,():=Step:CalculatedevicewidthsIDmA=IDmA=IDgmgmID:=Step:Calculatetransconductancesandtransitfrequenciesgmβ⋅π⋅fc⋅Cc⋅:=gmmS=ktanπPMdeg⋅⎛⎜⎝⎞⎟⎠:=k=gmk⋅π⋅fc⋅CC⋅CcCC⎛⎜⎝⎞⎟⎠⋅:=gmmS=fTπ⋅gmCgg⋅:=fTGHz=fTπ⋅gmCgg⋅:=fTGHz=Step:FindgmID,IDgmIDpgmidLfT,():=gmIDngmidLfT,():=gmIDV=gmIDV=IDgmgmID:=OTAcircuitforsimulation(feedbacknetwork,CMFB,Cc,etcnotshown)Ma,bMa,bMa,bMa,buAuAuAuAM=M=M=uAMdMcMdMcM=Simulationresults(firstrun,withoutanytweaking):fc=MHz,PM=deg,T=fMHzMagnitudedBfMHzPhasedegreesfHzPSDVHzfHzSqrt(Integral)μVrmsIntegral=uVrms,DR=dB(forVodmax=V)Veryclosetospecs!fcisaboutlowerthanexpectedThisismostlyduetothedominantpoleapproximationthesecondpolepullsfctolowerfrequenciesAlso,CgdofMaddsadditionalcompensationcapacitance,whichalsoreducesfcPMandDRareessentiallyrightontargetThediscrepancies,ingeneral,canberesolvedintwoways:()Spicetweaking(OKforsmallchanges),()RevisitabovecalculationsandimproveassumtionsandequationsEgfactorintheexpectederrorfromthedominantpoleapproximationAnadvantageofthepresentedmethodologyisthatmost,ifnotalldiscrepancieserrorscanbetrackeddownbycomparingtheSpicecomponentvalues(gm,gmID,Cdb,fromop)withthoseusedintheoptimizationroutineCloseinspectionoftheopvaluesbelowrevealsthatmostsmallsignalparameterscalculatedaboveagreewithSpicetowithinsubcktxxxxxxelement:ma:mb:ma:mb:md:mcmodel:pch:pch:nch:nch:nch:nchregionSaturatiSaturatiSaturatiSaturatiSaturatiSaturatiiduuuuuuibsibdvgsmmvdsvbsmmvthmmmmmmvdsatmmmmmmvodmmmmmmbetammmmumgameffmmmmmmgmmmmmuugdsuuuuuugmbuummuucdtotffffffcgtotffffffcstotffffffcbtotffffffcgsffffffcgdffffaasubcktxxxxxxelement:mb:ma:md:mc:mb:mamodel:nch:nch:pch:pch:pch:pchregionSaturatiSaturatiSaturatiSaturatiSaturatiSaturatiiduuuuuuibsibdvgsmmmmvdsmmmmvbsvthmmmmmmvdsatmmmmmmvodmmmmmmbetammmmmmgameffmmmmmmgmmmummmgdsuuuuuugmbuuummmcdtotffffffcgtotffffffcstotffffffcbtotffffffcgsffffff

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两级OTA的设计举例_688504330

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