电流模式变换器的建模-分析和补偿

50%1.0150%23450%1PWM231BUCK42.150%50%2ILVeILID0.52AD0.52B)mm(II12O1Δ-=Δ(1)2C-m)mmmm(II12O1++Δ-=Δ(2)221mm-(3)1BUCKm2(Vo/L)*RsLVTRAOS(4)50%2.223nTInRLCab1/212m-m2RLC42.352BUCK2.3.11/2fs56VOIL5IL=Dm1T-Dm2T4VC=Dm1T+Dm2T56Ve=VC+2DmT656VCIL/Vem2mmmmVI2121eL++-=ΔΔ(7)Dm1T=-(1-D)m2T(8)212mmmD--=97)m/m1(D211VI2eL+-=ΔΔ(10)IL2T4/ILf=1/2fS2eLm/m1D21/4vi+-π=11CAf=1/2fs=22m/m1D21CTA4+-π122.3.212f=1/2fsAmax=CT4m/m1D2122π+-(13)Amax7f=1/2fsm=050%m=-1/2m21Amaxmm=-m2m2.48m=-1/2m29m=-1/2m212.510mm2m=-1/2m23.01BUCK3.111BUCKDL)D1(VDL)VV(IOOIL---=•(14)RVCIVOLO-=•(15)VI+VIVO+VOD+DIL+IL2LDVLVLIDIIOLLΔ+Δ-Δ=Δ•(16)CRVCIVOLOΔ-Δ=Δ•(17)Ve6L2TRV)D1(mDTVRISOeSL---=18OOSSeLV)D1(L2T)L2VRm(DTRVIΔ---Δ-Δ=Δ19191617ΔD)L2VRm(LTVI)L2VRm(L2)D1(VV)L2VRm(LTRVeVVLDIOSILOS2IOOSSIIL-Δ---Δ--ΔΔ=Δ+•20CRVCIVOLOΔ-Δ=Δ•2111B3.211BRXLmRXCRXLm=0LRXmL2VROSLRCmm=L2VROS6m2LVROSm=2m21-RX2.41212VBUCK120HzBUCKVO=12VVI=25VL=200uHC=300uFRS=0.5RL=1~122m21-m(-6.4dB)RL=11312ΔVO/ΔVe0dBm2m21m-=6dB/12dB/1804.0ICUC1846UC1846IC14ABUC18464aR1/R2bR2CT14CU-97APPLICATIONNOTEMODELLING,ANALYSISANDCOMPENSATIONOFTHECURRENT-MODECONVERTERAbstractAscurrent-modeconversionincreasesinpopularity,severalpeculiaritiesassociatedwithfixed-frequency,peak-currentdetectingschemeshavesurfacedTheseincludeinstabilityabove50%dutycycle,atendencytowardssubharmonicoscillation,non-idealloopresponse,andanincreasedsensitivitytonoise.Thispaperwillattempttoshowthattheperformanceofanycurrent-modeconvertercanbeimprovedandatthesametimealloftheaboveproblemsreducedoreliminatedbyaddingafixedamountof“slopecompensation”tothesensedcurrentwaveform.1.0INTRODUCTIONTherecentintroductionofintegratedcontrolcircuitsdesignedspecificallyforcurrentmodecontrolhasledtoadramaticupswingintheapplicationofthistechniquetonewdesigns.Althoughtheadvantagesofcurrent-modecontroloverconventionalvoltage-modecontrolhasbeenamplydemonstrated(l-5),therestillexistseveraldrawbackstoafixedfrequencypeak-sensingcurrentmodeconverter.Theyare(1)openloopinstabilityabove50%dutycycle,(2)lessthanidealloopresponsecausedbypeakinsteadofaverageinductorcurrentsensing,(3)tendencytowardssubharmonicoscillation,and(4)noisesensitivity,particularlywheninductorripplecurrentissmall.Althoughthebenefitsofcurrentmodecontrolwill,inmostcases,farout-weightthesedrawbacks,asimplesolutiondoesappeartobeavailable.Ithasbeenshownbyanumberofauthorsthataddingslopecompensationtothecurrentwaveform(Figure1)willstabilizeasystemabove50%dutycycle.Ifoneistolookfurther,itbecomesapparentthatthissamecompensationtechniquecanbeusedtominimizemanyofthedrawbacksstatedabove.Infact,itwillbeshownthatanypracticalconverterwillnearlyalwaysperformbetterwithsomeslopecompensationaddedtothecurrentwaveform.Thesimplicityofaddingslopecompensation-usuallyasingleresistor-addstoitsattractiveness.However,thisintroducesanewproblem-thatofanalyzingandpredictingconverterperformance.SmallsignalACmodelsforbothcurrentandvoltage-modePWM’shavebeenextensivelydevelopedintheliterature.However,theslopecompensatedor“dualcontrol”converterpossessespropertiesofbothwithanequivalentcircuitdifferentfromyetcontainingelementsofeach.Althoughthishasbeenaddressedinpartbyseveralauthors(l,2),therestillexistsaneedforasimplecircuitmodelthatcanprovidebothqualitativeandquantitativeresultsforthepowersupplydesigner.FIGURE1-ACURRENT-MODECONTROLLEDBUCKREGULATORWITHSLOPECOMPENSATION.3-43APPLICATIONNOTEU-97Thefirstobjectiveofthispaperistofamiliarizethereaderwiththepeculiaritiesofapeak-currentcontrolconverterandatthesametimedemonstratetheabilityofslopecompensationtoreduceoreliminatemanyproblemareas.Thisisdoneinsection2.Second,insection3,acircuitmodelforaslopecompensatedbuckconverterincontinuousconductionwillbedevelopedusingthestate-spaceaveragingtechniqueoutlinedin(1).Thiswillprovidetheanalyticalbasisforsection4wherethepracticalimplementationofslopecompensationisdiscussed.2.1OPENLOOPINSTABILITYAnunconditionalinstabilityoftheinnercurrentloopexistsforanyfixedfrequencycurrent-modeconverteroperatingabove50%dutycycle-regardlessofthestateofthevoltagefeedbackloop.Whilesometopologies(mostnotablytwotransistorforwardconverters)cannotoperateabove50%dutycycle,manyotherswouldsufferseriousinputlimitationsifgreaterdutycyclecouldnotbeachieved.Byinjectingasmallamountofslopecompensationintotheinnerloop,stabilitywillresultforallvaluesofdutycycle.Followingisabriefreviewofthistechnique.A.)DUTYCYCLE0.5B.)DUTYCYCLE0.5COMPENSATINGSLOPEC.)DUTYCYCLE0.5WITHSLOPECOMPENSATIONFIGURE2-DEMONSTRATIONOFOPENLOOPINSTABILITYINACURRENT-MODECONVERTER.Figure2depictstheinductorcurrentwaveform,IL,ofacurrent-modeconverterbeingcontrolledbyanerrorvoltageV,.ByperturbingthecurrentILbyanamountAI,itmaybeseengraphicallythatAIwilldecreasewithtimeforD0.5(Figure2A),andincreasewithtimeforD0.5(Figure2B).MathematicallythiscanbestatedasCarryingthisastepfurther,wecanintroducealinearrampofslope-masshowninFigure2C.Notethatthisslopemayeitherbeaddedtothecurrentwaveform,orsubtractedfromtheerrorvoltage.ThisthengivesSolvingformat100%dutycyclegivesm-‘/zm2(3)Therefore,toguaranteecurrentloopstability,theslopeoft