控制环路资料大全(UNITRODE研讨会资料)2

APPENDIXBBODEPLOTSTheBodeplotisamethodofdisplayingcomplexvaluesofcircuitgain(orimpedance).ThegainmagnitudeindBisplottedvs.logfrequency.Thephaseangleisplottedseparatelyagainstthesamelogfrequencyscale.Bodeplotsareanexcellentvehiclefordesigningswitchingpowersupplyclosedloopsystems.Theyprovidegoodvisibilityintothegain/phasecharacteristicsofthevariousloopelements.CalculationoftheoverallloopismadesimplybyaddinggainindBandphaseindegrees.Theprocessisfurthersimplifiedbyusingstraightlineapproximationsoftheactualcurves.calledasymptotes.Calculationsarethenmadeonlyatthefrequencieswheretheasymptoteschangedirection.Bode'stheoremforsimplesystems,whichincludesmostswitchingpowersupplies:Thephaseangleofthegainatanyfrequencyisdependentupontherateofchangeofgainmagnitudevs.frequency.Asinglepole(simpleRClowpassfilter)hasagainslopeof-20dB/decadeaboveitscornerfrequencyandhasacorresponding-90degreephaseshift.FIRSTwmFll.,TERS(RCorI.R)20Singlepoleorsinglezerofirstorderfiltersallhaveagainslopeof20dB/decade0abovethecornerfrequency.ThephaseshiftasymptotesGAINhaveaslopeof45°/decade.(dB)extending1decadeeachside-20ofthecornerfrequencyforatotal90°phaseshift(seeFigure8-1).-40Maximumerrorbetweenexactvalues{curvedlines)andthestraightlineapproximationsare:O.l111plOIlpClIpGain-3dBPhase-5.7°Figure8-128-1UNITRODECORPORATION.5FORBESROAD.LEXINGTON,MA02173.TEL.[phone].TWX(710)326-6509.TELEX95-1064LowPass-Sine:lePole:Fie:ureB-l1.F(s)=l+s/11JpIIIp=l/RCorL/R,s=jIllGain:-20dB/decadeslope.Phase:-900totallag~i~g1eZ~HasthesamegainandphasecharacteristicasthesinglepoleshowninFigureII-l.exceptgainincreaseswithfrequency.Gainandphaseslopesareboth1ositive.F(s)=l+s/wz,Wz=l/RCorL/RGain:+20dB/decadeslope.Phase:+900totalleadlli&h!-Half-PlaneZero.Referstoitslocationonthecomplexs-plane.TheRHPzerohasthesamepositivegainslopeastheconventional(left-half-plane)zero,butthephaseslopeisnegative,likeasinglepole.TheRHPzeroholdstheloopgainupwhileaddingadditionalphaselag,makingitvirtuallyimpossibletoprovidecompensationaboveitscornerfrequency.Fortunately,theright-half-planezeroisencounteredonlyinboostandflybackregulatorsoperatedincontinuousinductorcurrentmode.F(s)=l-s/IlJzGain:+20dE/decadeslope.Phase:-900totallagSECNDOODERFll,1ERS(ResonantLC)LowPass-2Pole:Fi2ure8-2Thesecondorder2poleresonantLCfiltercharacteristicofFigureB-2hasa-40dB/decadeslopeingainmagnitudeabovethecorner(resonant)frequencyandatotalphaselagof18degrees,thesameastwosinglepolefirstorderfiltersincascade.Herethesimilaritiesend.ThegaincharacteristichasapeakwhichvarieswiththeQoftheresonantcircuit,asshowninFigureB-3.Thisisoflittleimportanceunlesstheresonantfrequencyisclosetotheloopgaincrossoverfrequency,whenitcouldeliminatethegainmarginandcauseinstability.Thephasecharacteristicslopeis-45degrees/decadewithaQof0.5.AthighervaluesofQ.FigureB-4showsthephaseslopebecomesmuchmorerapid.makingcompensationbymeansoffirstorderzerosmoredifficult.Gain:-40dB/decadeslopeGainpeakatwo:20logQPhase:-180°totallag1Phaseasymptoteintercepts:w/K.Kw.K=S2Q1F(s)=1+(s/wo)/Q+(s/wo)21whereWo==m-.Q=woL/Rs.28-2UNITRODECORPORATION.5FORBESROAD.LEXINGTON,MA02173.TEL[phone].TWX(710)326-6509.TELEX95-1064Effectiveseriesresistance20RsdeterminesQ.Rsincludes:capacitorESR:Rc'inductor:RL'rectifierdynamic:Rd,leakageinductanceeffective0resistance:Ri'andloadGAINresistance:Ro'transformed(dB)intoitsequivalentseriesR.(L/C=ZoZ).-20Qseldomreachesmorethan4or5.Atfullload.lowRotransformsintohighRs.Atlightloads.diodeRdlimitsQ.-400PHASEFigureB-20Qa+10-450=2PHASE0-90GAIN(dB)II\-135,--20-1800.20.40.81'020.20.40.81..1..024~FigureB-3FigureB-428-3UNITRODECORPORATION.5FORBESROAD.LEXINGTON,MA02173.TEL.[phone]WX(710)326-6509.TELEX95-1064