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TheTL431intheControlofSwitchingPowerSuppliesAgendaFeedbackgeneralitiesTheTL431inacompensatorSmall-signalanalysisofthereturnchainAtype1implementationwiththeTL431Atype2implementationwiththeTL431Atype3implementationwiththeTL431DesignexamplesConclusionAgendaFeedbackgeneralitiesTheTL431inacompensatorSmall-signalanalysisofthereturnchainAtype1implementationwiththeTL431Atype2implementationwiththeTL431Atype3implementationwiththeTL431DesignexamplesConclusionWhatisaRegulatedPowerSupply?VoutispermanentlycomparedtoareferencevoltageVref.ThereferencevoltageVrefispreciseandstableovertemperature.Theerror,,isamplifiedandsenttothecontrolinput.Thepowerstagereactstoreduceεasmuchasitcan.refoutVVεα=−+-+-VinVoutRupperRlowerErroramplifier-GVrefModulator-GPWMdPowerstage-HVpα+-+-VinVoutRupperRlowerErroramplifier-GVrefModulator-GPWMdPowerstage-HVpαControlvariableHowisRegulationPerformed?Textbooksonlydescribeopampsincompensators…outVerrVThemarketrealityisdifferent:theTL431rules!TL431optocouplererrVoutVI’mthelaw!HowdoweStabilizeaConverter?WeneedahighgainatdcforalowstaticerrorWewantasufficientlyhighcrossoverfrequencyforresponsespeed¾ShapethecompensatorG(s)tobuildphaseandgainmargins!ϕm=92°101001k10k100k1Meg-180°0°-0dB()Ts()Ts∠GM=67dB-88°()67TsdB=−fc=6.5kHzHowMuchPhaseMargintoChose?025507510002.557.51076°Qϕm5.00u15.0u25.0u35.0u45.0u200m600m1.001.401.80Q=0.1Q=0.5Q=0.707Q=1Q=5Fastresponseandnoovershoot!Q0.5overdampingQ=0.5criticaldampingQ0.5underdampingAsymptoticallystableQ=0.5aQfactorof0.5(criticalresponse)impliesaϕmof76°a45°ϕmcorrespondstoaQof1.2:oscillatoryresponse!phasemargindependsontheneededresponse:fast,noovershoot…goodpracticeistoshootfor60°andmakesureϕmalways45°WhichCrossoverFrequencytoSelect?crossoverfrequencyselectiondependsonseveralfactors:switchingfrequency:theoreticallimitis¾inpractice,staybelow1/5ofFswfornoiseconcernsoutputripple:ifripplepollutesfeedback,«tailchasing»canoccur.¾crossoverfrequencyrolloffismandatory,e.g.inPFCcircuitspresenceofaRight-HalfPlaneZero(RHPZ):¾youcannotcrossoverbeyond30%ofthelowestRHPZpositionoutputundershootspecification:¾selectcrossoverfrequencybasedonundershootspecs2swF2outpcoutIVfCπΔ≈Vout(t)WhatCompensatorTypesdoweNeed?Therearebasically3compensatortypes:¾type1,1poleattheorigin,nophaseboost¾type2,1poleattheorigin,1zero,1pole.Phaseboostupto90°¾type3,1poleattheorigin,1zeropair,1polepair.Boostupto180°101001k10k100k()Gs∠()Gs270−°boost1251020501002005001k()270Gs∠=−°()Gs101001k10k100k()Gs∠()Gs270−°boostType1Type2Type3AgendaFeedbackgeneralitiesTheTL431inacompensatorSmall-signalanalysisofthereturnchainAtype1implementationwiththeTL431Atype2implementationwiththeTL431Atype3implementationwiththeTL431DesignexamplesConclusionTheTL431ProgrammableZenerTheTL431isthemostpopularchoiceinnowadaysdesignsItassociatesanopen-collectoropampandareferencevoltageTheinternalcircuitryisself-suppliedfromthecathodecurrentWhentheRnodeexceeds2.5V,itsinkscurrentfromitscathode2.5VKARTL431AKARRAKTheTL431isashuntregulatorTheTL431ProgrammableZenerTheTL431lendsitselfverywelltooptocouplercontrollowerR1RLEDRbiasRoutVFBVddV2C1CTL431outV1ILEDI1Imin2.5VV=1fVV≈1biasbiasVIR=biasRRLEDmustleaveenoughheadroomovertheTL431:upperlimit!LEDRFastlaneSlowlanedcrepresentationpullupRTheTL431ProgrammableZenerThisLEDresistorisadesignlimitingfactorinlowoutputvoltages:431,min,maxmin,minCTRCTRoutfTLLEDpullupddCEsatbiaspullupVVVRRVVIR−−≤−+WhenthecapacitorC1isashort-circuit,RLEDfixesthefastlanegain()outVsLEDRpullupRddV1IcI0Vinac()FBVs1()CTRFBpullupVsRI=−⋅⋅1()outLEDVsIR=()CTR()pullupFBoutLEDRVsVsR=−Thisresistorplaysaroleindctoo!lowerR1RTheTL431–theStaticGainLimitLetusassumethefollowingdesign:,max512.520k0.34.80.310.320LEDRmk−−≤××−+××431,min,min512.54.83001CTR0.320outfTLddCEsatbiaspullupVVVVVVVVVmVImARk========Ω,max857LEDR≤Ω020CTR0.37170.857pullupLEDRGordBR≈IndesignswhereRLEDfixesthegain,G0cannotbebelow17dBYoucannot“amplify”bylessthan17dBTheTL431–theStaticGainLimitYoumustidentifytheareaswherecompensationispossible101001k10k100k18040.0-180-90.0090.0-40.0-20.0020.0dB°()argHs()Hs-17dB500500cfHzokNotokRequires17dBormoreRequireslessthan17dBofgainTL431–InjectingBiasCurrentATL431mustbebiasedabove1mAtoguarantyitsparametersIfnot,itsopen-loopsuffers–a10-dBdifferencecanbeobserved!Ibias=1.3mAIbias=300µA10-dBdifferenceEasysolutionIbiasRbias111biasRkm==ΩAgendaFeedbackgeneralitiesTheTL431inacompensatorSmall-signalanalysisofthereturnchainAtype1implementationwiththeTL431Atype2implementationwiththeTL431Atype3implementationwiththeTL431DesignexamplesConclusionTL431–Small-SignalAnalysisTheTL431isanopen-collectoropampwithareferencevoltageNeglectingtheLEDdynamicresistance,wehave:LEDRlowerR1R()outVs1C1I()opVs()()()1outopLEDVsVsIsR−=()()()1111opoutoutupperuppersCVsVsVsRsRC=−=−≈0()()11111outLEDupperIsVsRsRC⎡⎤=+⎢⎥⎢⎥⎣⎦Weknowthat:1()CTRFBpullupVsRI=−⋅⋅()()11CTR1pullupupperFBoutLEDupperRsRCVsVsRsRC⎡⎤+=−⎢⎥⎢⎥⎣⎦TL431–Small-SignalAnalysisInthepreviousequationwehave:9astaticgain9a0-dBoriginpolefrequency9azeroWearemissingapolefo