charger control loop

ApplicationReportSLUA371–September2006Closed-LoopCompensationDesignofaSynchronousSwitchingChargerUsingbq2472x/3xLingyinZhao........................................................................................................PMPPortablePowerABSTRACTDesignoftheloopcompensatorisoneofthekeychallengesinthecircuitdesignofaswitchingcharger.Thisapplicationreportpresentstheinternalcontrolloopoperationofthebq2472x/3xaswellastheexternalcompensatordesignguideline.Themodelingofthenonlinearbehaviorofaswitchingchargerisbasedonthestatespaceaveragemodel.Adesignexamplebasedonpracticalspecificationsisdemonstrated.Contents1Buck-TypeChargerPowerStageSmall-SignalModel........................................22bq2472x/3xControl-LoopModelandCompensationDesign.................................63DesignExample....................................................................................94Reference..........................................................................................19ListofFigures1ThePowerStageofaBuck-TypeCharger.....................................................22Three-TerminalModelofaPWMSwitchinCCM..............................................23Control-to-OutputSmall-SignalModelinCCM.................................................34Three-TerminalModelofaPWMSwitchinDCM..............................................45Control-to-OutputSmall-SignalModelinDCM.................................................56PWMandErrorAmplifiersBlockofbq2472x/3x................................................67SimplifiedControl-LoopBlockDiagram..........................................................78ATypicalBodePlotoftheConverterControl-to-OutputGainUnderCCMConditions...89ATypeIIICompensator...........................................................................810BodePlotofaTypicalTypeIIICompensator...................................................811Control-to-Output-VoltageTransferFunction..................................................1012Control-to-Charge-CurrentTransferFunction.................................................1113Control-to-Input-CurrentTransferFunction....................................................1214TransferFunctionofGvd,theCompensatorandtheEntireVoltageLoopGain..........1315Single-CellLi-IonBatteryEquivalentCircuitModel(18560).................................1416Output-VoltageLoopGainTV(CCM)...........................................................1517Charge-CurrentLoopGainTis(CCM)..........................................................1618Input-CurrentLoopGainTii(CCM)..............................................................1719Output-VoltageLoopGainTV(DCM)...........................................................1820Input-CurrentLoopGainTii(DCM).............................................................19SLUA371–September2006Closed-LoopCompensationDesignofaSynchronousSwitchingChargerUsingbq2472x/3x1SubmitDocumentationFeedback(CCM)Small-SignalModelQ1Q2cap(a)aPWMSwitchacp1D1IdC^(b)Small-SignalModelVapDˆdBuck-TypeChargerPowerStageSmall-SignalModelAtypicalstageofasynchronousbuck-typeswitchingbatterychargerisshowninFigure1.Figure1.ThePowerStageofaBuck-TypeChargerThesmall-signalmodelisobtainedfromtherelationshipsamongtheperturbationinaverageterminalquantitiesatagivendcoperatingpoint.Themodelisdifferentundercontinuousconductionmode(CCM)anddiscontinuousconductionmode(DCM).Theaveragevaluesoftheswitchnetworkterminalwaveformscanbedeterminedintermsoftheconverterstatevariablesandtheconverterindependentinputs.ThebasicassumptionismadethatthenaturaltimeconstantsoftheconverternetworkaremuchlongerthantheswitchingperiodTs.Thisassumptioncoincideswiththerequirementforsmallswitchingripple.Theresultingaveragedmodelpredictsthelow-frequencybehaviorofthesystem,whileneglectingthehigh-frequencyswitchingharmonics[1].Thethree-terminalmodelforaPWMswitchnetworkinCCMisillustratedinFigure2.Figure2.Three-TerminalModelofaPWMSwitchinCCMToperformtheCCMsmall-signalanalysis,thePWMswitchinthebuckconverterissubstitutedwiththethree-terminalmodelinCCMandVinisshorted,asshowninFigure3.2Closed-LoopCompensationDesignofaSynchronousSwitchingChargerUsingbq2472x/3xSLUA371–September2006SubmitDocumentationFeedback(s)VodVin
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