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March1999MixedSignalProductsApplicationReportSLVA059IMPORTANTNOTICETexasInstrumentsanditssubsidiaries(TI)reservetherighttomakechangestotheirproductsortodiscontinueanyproductorservicewithoutnotice,andadvisecustomerstoobtainthelatestversionofrelevantinformationtoverify,beforeplacingorders,thatinformationbeingreliedoniscurrentandcomplete.Allproductsaresoldsubjecttothetermsandconditionsofsalesuppliedatthetimeoforderacknowledgement,includingthosepertainingtowarranty,patentinfringement,andlimitationofliability.TIwarrantsperformanceofitssemiconductorproductstothespecificationsapplicableatthetimeofsaleinaccordancewithTI’sstandardwarranty.TestingandotherqualitycontroltechniquesareutilizedtotheextentTIdeemsnecessarytosupportthiswarranty.Specifictestingofallparametersofeachdeviceisnotnecessarilyperformed,exceptthosemandatedbygovernmentrequirements.CERTAINAPPLICATIONSUSINGSEMICONDUCTORPRODUCTSMAYINVOLVEPOTENTIALRISKSOFDEATH,PERSONALINJURY,ORSEVEREPROPERTYORENVIRONMENTALDAMAGE(“CRITICALAPPLICATIONS”).TISEMICONDUCTORPRODUCTSARENOTDESIGNED,AUTHORIZED,ORWARRANTEDTOBESUITABLEFORUSEINLIFE-SUPPORTDEVICESORSYSTEMSOROTHERCRITICALAPPLICATIONS.INCLUSIONOFTIPRODUCTSINSUCHAPPLICATIONSISUNDERSTOODTOBEFULLYATTHECUSTOMER’SRISK.Inordertominimizerisksassociatedwiththecustomer’sapplications,adequatedesignandoperatingsafeguardsmustbeprovidedbythecustomertominimizeinherentorproceduralhazards.TIassumesnoliabilityforapplicationsassistanceorcustomerproductdesign.TIdoesnotwarrantorrepresentthatanylicense,eitherexpressorimplied,isgrantedunderanypatentright,copyright,maskworkright,orotherintellectualpropertyrightofTIcoveringorrelatingtoanycombination,machine,orprocessinwhichsuchsemiconductorproductsorservicesmightbeorareused.TI’spublicationofinformationregardinganythirdparty’sproductsorservicesdoesnotconstituteTI’sapproval,warrantyorendorsementthereof.Copyright1999,TexasInstrumentsIncorporatediiiUnderstandingBuck-BoostPowerStagesinSwitchmodePowerSuppliesContents1Introduction1...................................................................................2Buck-BoostStageSteady-StateAnalysis3........................................................2.1Buck-BoostSteady-StateContinuousConductionModeAnalysis3...............................2.2Buck-BoostSteady-StateDiscontinuousConductionModeAnalysis8.............................2.3CriticalInductance12.......................................................................3Buck-BoostPowerStageSmallSignalModeling13................................................3.1Buck-BoostContinuousConductionModeSmall-SignalAnalysis14..............................3.2Buck-BoostDiscontinuousConductionModeSmall-SignalAnalysis17............................4VariationsoftheBuck-BoostPowerStage22......................................................4.1FlybackPowerStage22.....................................................................5ComponentSelection25.........................................................................5.1OutputCapacitance25......................................................................5.2OutputInductance26.......................................................................5.3PowerSwitch27...........................................................................5.4OutputDiode28............................................................................6Summary30.....................................................................................7References32...................................................................................FiguresivSLVA059ListofFigures1Buck-BoostPowerStageSchematic2................................................................2Buck-BoostPowerStageStates4...................................................................3ContinuousModeBuck-BoostPowerStageWaveforms5...............................................4BoundaryBetweenContinuousandDiscontinuousMode9..............................................5DiscontinuousCurrentMode9......................................................................6DiscontinuousModeBuck-BoostConverterWaveforms11..............................................7PowerSupplyControlLoopComponents13..........................................................8Buck-BoostPowerStageGainvsDutyCycle14.......................................................9DCandSmallSignalCCMPWMSwitchModel15.....................................................10CCMBuck-BoostPowerStageModel15............................................................11DCMPWMSwitchModel19.......................................................................12DCMBuck-BoostConverterModel19...............................................................13SmallSignalDCMBuck-BoostPowerStageModel21.................................................14FlybackPowerStageSchematic23.................................................................15DiscontinuousModeFlybackWaveforms23.............................................