电压反馈-type-iii类电路补偿

1APPLICATIONNOTEDesignTypeIIICompensationNetworkForVoltageModeStep-downConvertersSkyworksSolutions,Inc.•Phone[781]376-3000•Fax[781]376-3100•[e-mail]••SkyworksProprietaryInformation•ProductsandProductInformationareSubjecttoChangeWithoutNotice.•September21,2012IntroductionThisapplicationnotedetailshowtocalculateatypeIIIcompensationnetworkandinvestigatestherelationshipbetweenphasemarginandloadtransientresponsefortheSkyworksfamilyofvoltagemodecontrolstep-downconverters.ThisfamilyincludestheAAT1184,AAT1185,AAT1189,AAT2687,AAT2688,andAAT2689.VoltagemodecontrolhasbecomeaverypopulartopologyforDCtoDCconverters,especiallywithlownoiseoutputsystemsincludingDSLandcablemodems,notebookcomputers,satelliteset-topboxes,andwirelessLANsystems.BackgroundInordertoreducetheDC-DCconverter’soutputvoltageripple,theequivalentseriesresistance(ESR)oftheoutputcapacitorneedstobereduced.Ceramicoutputcapacitorshaveaverysmallequivalentseriesresistance(ESR),lowcost,andsmallsize,makingthemtheidealoutputfiltersolutionforDC-to-DCconverters.However,theuseoflowESRceramiccapacitorssignificantlyaffectsthedesignoftheerroramplifierinthefeedbackloop.ThepowerstageconsistsofadoublepoleduetotheLCOUTfilterandanESRzero.TheESRzeroispushedfarawayfromthedoublepolefre-quencywhichresultsininadequatephasemarginatthecross-overfrequency.Therefore,typeIIIcompensationisusedtostabilizetheloopandoptimizetheoutputtransientresponsetodynamicloadchanges.VoltageModeControlLoopAsillustratedinFigure1,atypicalvoltagemodecontrolloophasthreemainstages:step-downpowerstage,compen-sationnetwork,andPWMmodulator.TheTypeIIIcompensationnetworkgeneratestwozerosandtwopoles.Thetwozerosareplacedfrom60%to150%ofdoublepolefrequencytocounterthe180°phaselagduetotheLCOUToutputfilter.ThetwopolesaresetattheswitchingfrequencyoftheconvertertonullifytheESRzeroandattenuatethehighfrequencynoise.RDCRC1C2R1COUTLRfbhRfblCffRffCOMPARATORErrorAmpRESRROUTVOUTVreffVINDriverRAMPPWMMODULATORCOMPCOMPENSATIONNETWORKSTEP-DOWNPOWERSTAGEFigure1:ClosedLoopStep-DownConverterwithTypeIIINetworkCompensation.2APPLICATIONNOTEDesignTypeIIICompensationNetworkForVoltageModeStep-downConvertersSkyworksSolutions,Inc.•Phone[781]376-3000•Fax[781]376-3100•[e-mail]••SkyworksProprietaryInformation•ProductsandProductInformationareSubjecttoChangeWithoutNotice.•September21,2012Step-DownPowerStageTransferFunctionThetransferfunctionofthepowerstageofthestep-downconvertercanbedeterminedbythevoltagedivision:Eq.1:VOUTVINZOUTZL+ZOUT=WhereZLandZOUTaretheinductorimpedanceandoutputimpedanceofthepowerstage.TheRDCRincludestheDCwindingresistance,theturn-onresistanceoftheMOSFET,andthetraceresistance.RESRistheequivalentseriesresis-toroftheoutputcapacitor.ZLandZOUTarecalculatedusingEquations2and3.Eq.2:1sCOUTs·COUT·RLOAD·RESR+RLOADs·COUT·(RLOAD+RESR)+1ZOUT=RLOAD//RESR+=Eq.3:ZL=s·L+RDCRWherethecomplexvariables=j·wand-1j=RDCRCOUTLRESRRLOADVOUTVINDriverSTEP-DOWNPOWERSTAGEZLZOUTFigure2:Step-DownConverterPowerStage.Thestep-downpowerstageopenloopgainisgivenbysubstitutingEquations2and3intoEquation1.Algebraicmanipulationyieldsthefollowingexpressionfortheopen-looptransferfunctionofthepowerstage:Eq.4:VOUTVINRLOAD·(s·COUT·RESR+1)s2·L·COUT·(RLOAD+RESR)+s{L+COUT·[RDCR(RLOAD+RESR)+RLOAD·RESR]}+RLOAD+RDCRGP==AtypicalBodeplotofthestep-downconverterpowerstageisillustratedinFigure3.Adoublepoleatthecut-offfre-quencycausesthegaintorolloffwitha-40dB/decadeslope(blue)andthephasetoexhibitaverysharpslopedown-wardfrom0degreeto-180degreephaselag(red).TheESRzeroisobservedataveryhighfrequencyduetotheceramicoutputcapacitor.3APPLICATIONNOTEDesignTypeIIICompensationNetworkForVoltageModeStep-downConvertersSkyworksSolutions,Inc.•Phone[781]376-3000•Fax[781]376-3100•[e-mail]••SkyworksProprietaryInformation•ProductsandProductInformationareSubjecttoChangeWithoutNotice.•September21,2012OutputDoublePoleatcut-offfrequencyESRzeroatveryhighfrequency-40dB/dec-20dB/decFrequency(Hz)Gain(dB)andPhase(degree)-180degreephaselagduetodoublepoleFigure3:TheBodePlotoftheOutputStage.ErrorAmplifierTransferFunctionCalculationTheerroramplifiertransferfunctionwithtypeIIIcompensationasshowninFigure4iscalculatedfromEquation5:Eq.5:VCOMPVOUTGE=1s·C21s·C1//R1+=1s·CffRfbh//Rff+C1R1C2RfbhRfblCffRffErrorAmpVREFVCOMPVOUTZ2Z1P2P1Figure4:ErrorAmplifierWithTypeIIICompensationNetwork.4APPLICATIONNOTEDesignTypeIIICompensationNetworkForVoltageModeStep-downConvertersSkyworksSolutions,Inc.•Phone[781]376-3000•Fax[781]376-3100•[e-mail]••SkyworksProprietaryInformation•ProductsandProductInformationareSubjecttoChangeWithoutNotice.•September21,2012Byalgebraicmanipulation,GEcanbeexplicitlyexpressedintermsofzerosandpolesinEquation6.Eq.6:Rfbh+RffRfbh·Rff·C2GE=1R1·C11(Rfbh+Rff)·Cff·s+s+·(C1+C2)R1·C1·C21Rff·Cffs·s+·s+Equation6givestwozeroesatfrequenciesFZ1andFZ2andtwopolesatfrequenciesFP1andFP2inthefollowingexpres-sions:12π·(Rfbh+Rff)·CffFZ1=12π·R1·C1FZ2=and1andFP2=12π·Rff·CffFP1=C1·C