LLC 电路基本原理分析及公式推导

Simplified Analysis and Design of Series-resonant LLC Half-bridge ConvertersMLD GROUPINDUSTRIAL & POWER CONVERSION DIVISIONOff-line SMPS BU Application LabI&PC Div. - Off-line SMPS Appl. LabPresentation Outline•LLC series-resonant Half-bridge: operation and significant waveforms•Simplified model (FHA approach)•300W design exampleI&PC Div. - Off-line SMPS Appl. LabSeries-resonant LLC Half-Bridge Topology and featuresQ1CrLsVinQ2 LpLLC tank circuit Preferably integrated into a singlemagnetic structure3 reactive elements, 2 resonant frequencies1f r12⋅π⋅Ls⋅Crf>fr1r2Center-tapped output with full-wave rectification(low voltage and high current)VoutVoutSingle-ended output withbridge rectifiication(high voltage and low current)Multiresonant LLCtank circuitVariable frequency controlFixed50%duty cycle for Q1&Q2Deadtime between LGandHGtoallow MOSFET’s ZVS@turnonfsw≈fr,sinusoidal waveforms:lowturnofflosses,low EMIEqual voltage&current stressforsecondary rectifiers;ZCS,then norecovery lossesNooutputchoke;cost savingIntegrated magnetics:both L’scanbe realized with thetransformer.Highefficiency:>96%achievablefr212⋅π⋅(Ls+Lp)⋅CrI&PC Div. - Off-line SMPS Appl. LabLLC Resonant Half-bridgeWaveforms at resonance (f sw = f r1)Dead-timeGate-drivesignalsHB mid-pointVoltageResonant capvoltage Tank circuit current is sinusoidal Magnetizing current is triangularTransformercurrentsDiodevoltagesOutput currentCCM operationDiodecurrentsI&PC Div. - Off-line SMPS Appl. LabSwitching details at resonance (f sw = f r1)Dead-time Gate-drivesignalsZVS !HB mid-pointVoltageResonant capvoltageTank circuit current >0Magnetizing current Transformer currentsV(D1)<0Diodevoltages I(D1)=0 ZCS !DiodecurrentsI&PC Div. - Off-line SMPS Appl. LabOperating Sequence at resonance (Phase 1/6) 1/6Q Q Q1 ONQ2 OFFQ1 OFFQ2 ONQ1Coss1VinLsCr n:1:1D1CoutCoss2VoutLpQ2D2Q1is OFF,Q2is OND1is OFF,D2is ON;V(D1)=2VoutLp is dynamically shorted:V(Lp)=nVout.Cr resonates with Ls,f r1appearsOutputenergy comes from Cr andLsPhase ends when Q2is switched offI&PC Div. - Off-line SMPS Appl. LabOperating Sequence at resonance (Phase 2/6) 2/6Q1 OFF Q2 ON Q1 ONQ2 OFFQ1 OFFQ2 ONQ1Coss1VinLsCr n:1:1D1CoutCoss2VoutLpQ2D2Q1andQ2areOFF(deadtime)D1andD2areOFF;V(D1)=V(D2)=0;transformer’s secondary is openI(Ls+Lp)charges C OSS2anddischargesC OSS1,until V(C OSS2)=Vin;Q1’sbodydiodes tarts conducting,energy goes backto VinI(D2)is exactly zeroatQ2switch offPhase ends when Q1is switched onI&PC Div. - Off-line SMPS Appl. LabOperating Sequence at resonance (Phase 3/6) 3/6Q1 OFF Q2 ON Q1 ONQ2 OFFQ1 OFFQ2 ONQ1Coss1VinLsCr n:1:1D1CoutCoss2VoutLpQ2D2Q1is ON,Q2is OFFD1is ON,D2is OFF;V(D2)=2VoutLp isdynamicallyshorted:V(Lp)=nVout.CrresonateswithLs,f r1appearsI(Ls)flows throughQ1’sR DS(on)backtoVin(Q1is workinginthe3rd quadrant)Phase ends when I(Ls)=0I&PC Div. - Off-line SMPS Appl. LabOperating Sequence at resonance (Phase 4/6)4/6Q1 OFF Q2 ONQ1 OFFQ2 ONQ1Coss1VinLsCr n:1:1D1CoutCoss2VoutLpQ2D2Q1is ON,Q2is OFFD1is ON,D2is OFF;V(D2)=2VoutLp isdynamicallyshorted:V(Lp)=nVout.CrresonateswithLs,f r1appearsI(Ls)flows throughQ1’sR DS(on)from Vinto groundEnergy is taken from Vin andgoes to VoutPhase ends when Q1is switched offI&PC Div. - Off-line SMPS Appl. LabOperating Sequence at resonance (Phase 5/6)5/6Q1 OFF Q2 ON Q1 ONQ2 OFFQ1 OFFQ2 ONQ1Coss1VinLsCr n:1:1D1CoutCoss2VoutLpQ2D2Q1andQ2areOFF(deadtime)D1andD2areOFF;V(D1)=VD(2)=0;transformer’s secondary is openI(Ls+Lp)charges C OSS1anddischargesC OSS2,until V(C OSS2)=0;Q2’sbodydiodestarts conductingI(D1)is exactly zeroatQ1switch offPhase ends when Q2is switched onI&PC Div. - Off-line SMPS Appl. LabOperating Sequence at resonance (Phase 6/6)6/6Q1 OFF Q2 ON Q1 ONQ2 OFFQ1 OFFQ2 ONQ1Coss1VinLsCr n:1:1D1CoutCoss2VoutLpQ2D2Q1is OFF,Q2is OND1is OFF,D2is ONLp isdynamicallyshorted:V(Lp)=nVout.CrresonateswithLs,fr1appearsI(Ls)flows throughQ2’sR DS(on)(Q2isworkinginthe3rd quadrant)Outputenergy comes from Cr andLsPhase ends when I(Ls)=0,Phase1starts I&PC Div. - Off-line SMPS Appl. LabWaveforms above resonance (f sw > f r1)Dead-timeGate-drivesignalsHB mid-pointVoltageResonant capvoltage Tank circuit current Magnetizing current is triangularTransformercurrentsSinusoid @ f=f r1 ~ Linear portionDiodevoltagesOutput currentCCM operationDiodecurrentsI&PC Div. - Off-line SMPS Appl. LabLLC Resonant Half-bridgeSwitching details above resonance (f sw > f r1)Dead-time Gate-drivesignalsZVS !HB mid-pointVoltageResonant capvoltage Tank circuit current >0 Slope ~ -(Vc-n·Vout)/LsMagnetizing currentTransformercurrentsV(D1)<0Diodevoltages ZCS ! Output currentI(D1)=0DiodecurrentsI&PC Div. - Off-line SMPS Appl. LabLLC Resonant Half-bridgeOperating Sequence above resonance (Phase 1/6) 1/6Q Q Q1 ONQ2 OFFQ1 OFFQ2 ONQ1Coss1VinLsCr n:1:1D1CoutCoss2VoutLpQ2D2Q1is OFF,Q2is OND1is OFF,D2is ON;V(D1)=2VoutLp is dynamically shorted:V(Lp)=nVout.Cr resonates with Ls,f r1appearsOutputenergy comes from Cr andLsPhase ends when Q2is switched off I&PC Div. - Off-line SMPS Appl. LabLLC Resonant Half-bridgeOperating Sequence above resonance (Phase 2/6) 2/6Q1 OFF Q2 ON Q1 ONQ2 OFFQ1 OFFQ2 ONQ1Coss1VinLsCr n:1:1D1CoutCoss2VoutLpQ2D2Q1andQ2areOFF(deadtime)D1andD2areOFF;V(D1)=V(D2)=0;transformer’s secondary is openI(Ls+Lp)charges C OSS2anddischargesC OSS1,until V(C OSS2)=Vin;Q1’sbodydiodes tarts conducting,energy goes backto VinV(D2)reverses as I(D2)goes to zeroPhase ends when Q1is switched onI&PC Div. - Off-line SMPS Appl. LabOperating Sequence above resonance (Phase 3/6)3/6Q1 OFF Q2 ON 1 ON2 OFFQ1 OFFQ2 ONQ1Coss1VinLsCr n:1:1D1CoutCoss2VoutLpQ2D2Q1is ON,Q2is OFFD1is ON,D2is OFF;V(D2)=2VoutLp isdynamicallyshorted:V(Lp)=nVout.CrresonateswithLs,f r1appearsI(Ls)flows throughQ1’sR DS(on)backtoVin(Q1is workinginthe3rd quadrant)Phase ends when I(Ls)=0I&PC Div. - Off-line SMPS Appl. LabOperating Sequence above resonance (Phase 4/6)4/6Q1 OFF Q2 ON QQQ1 OFFQ2 ONQ1Coss1VinLsCr n:1:1D1CoutCoss2VoutLpQ2D2Q1is ON,Q2is OFFD1is ON,D2is OFF;V(D2)=2VoutLp isdynamicallyshorted:V(Lp)=nVout.CrresonateswithLs,f r1appearsI(Ls)flows throughQ1’sR DS(on)from Vinto groundEnergy is taken from Vin andgoes to VoutPhase ends when Q1is switched off I&PC Div. - Off-line SMPS Appl. LabOperating Sequence above resonance (Phase 5/6)5/6Q1 OFF Q2 ON Q1 ONQ2 OFFQ1 OFFQ2 ONQ1Coss1VinLsCr n:1:1D1CoutCoss2VoutLpQ2D2Q1andQ2areOFF(deadtime)D1andD2areOFF;V(D1)=VD(2)=0;transformer’s secondary is openI(Ls+Lp)charges C OSS1anddischargesC OSS2,until V(C OSS2)=0;Q2’sbodydiodestarts conductingOutputenergy comes from CoutPhase ends when Q2is switched onI&PC Div. - Off-line SMPS Appl. LabOperating Sequence above resonance (Phase 6/6)6/6Q1 OFF Q2 ON Q1 ONQ2 OFFQ1 OFFQ2 ONQ1Coss1VinLsCr n:1:1D1CoutCoss2VoutLpQ2D2Q1is OFF,Q2is OND1is OFF,D2is ONLp isdynamicallyshorted:V(Lp)=nVout.CrresonateswithLs,fr1appearsI(Ls)flows throughQ2’sR DS(on)(Q2isworkinginthe3rd quadrant)Outputenergy comes from Cr andLsPhase ends when I(Ls)=0,Phase1starts I&PC Div. - Off-line SMPS Appl. LabWaveforms below resonance (f sw < f r1)Dead-timeGate-drivesignalsHB mid-pointVoltageResonant capvoltage Tank circuit current Magnetizing currentSinusoid @ f=f r2TransformercurrentsSinusoid @ f=f r2Diodevoltages Output currentDCM operationDiodecurrentsI&PC Div. - Off-line SMPS Appl. LabLLC Resonant Half-bridgeSwitching details below resonance (f sw < f r1)Dead-time Gate-drivesignalsZVS !HB mid-pointVoltage Resonant cap voltageTank circuitcurrent = Magnetizing current >0 Portion of sinusoid @ f=f r2TransformercurrentsV(D1)<0DiodevoltagesZCS ! Output currentI(D1)=0DiodecurrentsI&PC Div. - Off-line SMPS Appl. LabOperating Sequence below resonance (Phase 1/8) 1/8Q1 ON Q2 OFF Q1 OFFQ2 ONQ1Coss1VinLsCr n:1:1D1CoutCoss2VoutLpQ2D2Q1is OFF,Q2is OND1is OFF,D2is ON;V(D1)=2VoutLp is dynamically shorted:V(Lp)=nVout.Cr resonates with Ls,f r1appearsOutputenergy comes from Cr andLsPhase ends when I(D2)=0Operating Sequence below resonance (Phase 2/8) 2/8Q1 OFF Q2 ON Q1 ONQ2 OFFQ1 OFFQ2 ONQ1Coss1VinLsCr n:1:1D1CoutCoss2VoutLpQ2D2Q2is ON,Q1is OFFD1andD2areOFF;V(D1)=V(D2)=0;transformer’s secondary is openCr resonates with Ls+Lp,f r2appearsOutputenergy comes from CoutPhase ends when Q2is switched offOperating Sequence below resonance (Phase 3/8) 3/8Q1 OFF Q2 ON Q1 ONQ2 OFFQ1 OFFQ2 ONQ1Coss1VinLsCr n:1:1D1CoutCoss2VoutLpQ2D2Q1andQ2areOFF(deadtime)D1andD2areOFF;V(D1)=V(D2)=0;transformer’s secondary is openI(Ls+Lp)charges C OSS2anddischargesC OSS1,until V(C OSS2)=Vin;Q1’sbodydiodes tarts conducting,energy goes backto VinPhase ends when Q1is switched onI&PC Div. - Off-line SMPS Appl. LabOperating Sequence below resonance (Phase 4/8) 4/8Q1 OFF Q2 ON Q1 ONQ2 OFFQ1 OFFQ2 ONQ1Coss1VinLsCr n:1:1D1CoutCoss2VoutLpQ2D2Q1is ON,Q2is OFFD1is ON,D2is OFF;V(D2)=2VoutLp isdynamicallyshorted:V(Lp)=nVout.CrresonateswithLs,f r1appearsI(Ls)flows throughQ1’sR DS(on)backtoVin(Q1is workinginthe3rd quadrant)Energy is recirculating into VinPhase ends when I(Ls)=0Operating Sequence below resonance (Phase 5/8) 5/8Q1 OFF Q2 ON Q1 OFFQ2 ONQ1Coss1VinLsCr n:1:1D1CoutCoss2VoutLpQ2D2Q1is ON,Q2is OFFD1is ON,D2is OFF;V(D2)=2VoutLp isdynamicallyshorted:V(Lp)=nVout.CrresonateswithLs,f r1appearsI(Ls)flows throughQ1’sR DS(on)from Vinto groundEnergy is taken from Vin andgoes to VoutPhase ends when I(D1)=0Operating Sequence below resonance (Phase 6/8)6/8Q1 OFF Q2 ON Q1 ONQ2 OFFQ1 OFFQ2 ONQ1Coss1VinLsCr n:1:1D1CoutCoss2VoutLpQ2D2Q1is ON,Q2is OFFD1andD2areOFF;V(D1)=V(D2)=0;transformer’s secondary is openCr resonates with Ls+Lp,f r2appearsOutputenergy comes from CoutPhase ends when Q1is switched offOperating Sequence below resonance (Phase 7/8)7/8Q1 OFF Q2 ON Q1 ONQ2 OFFQ1 OFFQ2 ONQ1Coss1VinLsCr n:1:1D1CoutCoss2VoutLpQ2D2Q1andQ2areOFF(deadtime)D1andD2areOFF;V(D1)=VD(2)=0;transformer’s secondary is openI(Ls+Lp)charges C OSS1anddischargesC OSS2,until V(C OSS2)=0,then Q2’sbodydiode starts conductingOutputenergy comes from CoutI&PC Div. - Off-line SMPS Appl. LabOperating Sequence below resonance (Phase 8/8)8/8Q1 OFF Q2 ON Q1 ONQ2 OFFQ1 OFFQ2 ONQ1Coss1VinLsCr n:1:1D1CoutCoss2VoutLpQ2D2Q1is OFF,Q2is OND1is OFF,D2is ONLp isdynamicallyshorted:V(Lp)=nVout.CrresonateswithLs,fr1appearsI(Ls)flows throughQ2’sR DS(on)(Q2isworkinginthe3rd quadrant)Outputenergy comes from Cr andLsPhase ends when I(Ls)=0,Phase1startsI&PC Div. - Off-line SMPS Appl. LabCapacitive mode (f sw ~ f r2): why it must be avoidedCapacitivemodeis encountered when f sw gets close to f r2Although incapacitivemodeZCScanbe achieved,however ZVSis lost,which causes:Hardswitching ofQ1&Q2:highswitching losses atturnonandvery highcapacitivelosses atturn offBodydiode ofQ1&Q2is reverserecovered:highcurrent spikes atturnon,additionalpowerdissipation;MOSFETswill easily blow up.Highlevel ofgenerated EMILarge andenergetic negativevoltage spikes intheHBmidpoint that may causethecontrolICto failAdditionally,feedbackloop sign could change from negativeto positive:Incapacitivemodetheenergy vs.frequency relationship is reversed Converteroperatingfrequencywouldrunawaytowardsitsminimum(ifMOSFETshavenotblownupalready!)I&PC Div. - Off-line SMPS Appl. LabWaveforms in capacitive mode (f sw ~ f r2)Dead-timeGate-drivesignalsHB mid-pointVoltageResonant capvoltage Tank circuit current is piecewise sinusoidal Magnetizing currentSinusoid @ f=f r2Transformercurrents Sinusoid @ f=f r1DiodevoltagesOutput currentDiodecurrentsI&PC Div. - Off-line SMPS Appl. LabSwitching details in capacitive mode (f sw ~ f r2)Gate-drivesignalsHARD SWITCHING !Very high voltage on Cr!HB mid-pointVoltage Resonant cap voltageMagnetizing currentTank circuit current is <0Transformer currentsCurrent is flowing in Q1’s body diode Q1’s body diode is recoveredDiodevoltagesOutput currentDiodecurrents I&PC Div. - Off-line SMPS Appl. LabApproximate analysis with FHA approach: BasicsBASICPRINCIPLES Input sourceC SN (ControlledSwitch Network)Resonant tankIdealtransformerUncontrolledrectifierLow-passfilterLoadCSNprovides asquare wave voltage atafrequency fsw,deadtimes are neglectedResonant tank responds primarily to its fundamental component,then: Tank waveforms areapproximated by their fundamental components Uncontrolled rectifier+lowpass filter’s effect is incorporated into theload.VinQ1Q2Cr Lsa:1Cout RLpVoutVinVin2Q1 ONQ2 OFF 0Q1 OFFQ2 ON2πVinNote:Cr is both resonant anddc blocking capacitorIts ac voltage is superimposed onadc componentequal to Vin/2(duty cyle is50%for both Q1andQ2) I&PC Div. - Off-line SMPS Appl. LabLLC Resonant Half-bridgeEquivalent model with FHA approachTheactualcircuitturnsintoanequivalentlinearcircuitwheretheacresonanttankis excitedbyaneffectivesinusoidalinputsourceanddrivesaneffectiveresistiveload. Standardacanalysiscanbeusedtosolvethecircuit Functions ofinterest:InputImpedance Z in (j ω)andForward TransferFunction M(j ω).It is possible to showthat thecomplete conversion ratioVout/Vin is:controlled switchrectifier withM (j ω)low-pass filterdc outputiiIS Routvac resonant tankRVout RRe8 = aR 2 Re2πdc inputIinvSZin (jω)⇒Vin2v S=Vin⋅sin(2π⋅fs⋅t)πVoutVin=M(jω) 2 2 1I=i cos(ϕ)=v Rein S Zs SππIout=2πa iRi ThisresultisvalidforanyresonanttopologyI&PC Div. - Off-line SMPS Appl. LabLLC Resonant Half-bridge Transformer model (I)Physical model All-Primary-Side equivalent model used for LLC analysisL1 Ideal Transformer L L2aLn:1:1 Sec. leakageinductanceLs Ideal Transformera:1:1Prim. leakage inductance LµSec. leakageinductanceLpMagnetizing inductance LL2bResults from theanalysis ofthemagnetic structure(reluctance modelappraach)nis theactual primarytosecondary turnratioL models themagnetizing flux linking all windings L L1models theprimary flux not linked to secondary L L2a andL L2b modelthesecondary flux not linked to primary;symmetrical windings:L L2a=L L2b APSequivalent model:terminalequations arethe same,internal parameters aredifferentais not theactual primarytosecondary turnratioLs is theprimary inductance measured with all secondaries shorted outLp is thedifference between theprimaryinductance measured with secondaries openandLsNOTE:L L1+L=Ls+Lp=L1primary winding inductance I&PC Div. - Off-line SMPS Appl. Lab。