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PowerSupplyElectronics
IntroductiontoPowerElectronics
H62PSE
WorkedExample1IntheconverterofFigure1,theinputvoltageVin=20V.TheoutputvoltageVo=12V.Calculatetheduty-ratiodAandthepulsewidthTup,iftheswitchingfrequencyfs=200kHz.Figure1.Buckconverter
WorkedExample1Solution:UsingEquationTherefore,asshownintheFigureWaveformsintheconverter
RealizingtheBi-PositionalSwitchinBuckConverter
Ifthecurrentwaveforminsteadystateinaninductorof50μHisasshowninFigure2,calculatetheinductorvoltagewaveformvL(t).WorkedExample2Figure2
WorkedExample2Solution:Duringthecurrentrise-timeThereforeDuringthecurrentfall-timeTherefore
WorkedExample2Inductorvoltagewaveform
CapacitoroperatinginthedcsteadystateAsimilaranalysisappliestoanycapacitorinaswitch-modeconvertercircuit.thecapacitorvoltageatatimetcanbeexpressedintermsofitsinitialvaluevC(0)as:(1)(2)
Inthedcsteadystate,thewaveformsofallcircuitvariablesmustrepeatwiththeswitchingfrequencytime-periodTs,resultinginthefollowingconclusionsThecapacitorvoltagewaveformrepeatswithTs,andthereforeIntegratingoveroneswitchingtime-periodTsinEquation(2)andusingEquation(3)showthatthecapacitorcurrentintegraloverTsiszero,whichleadstotheconclusionthattheaveragecapacitorcurrent,averagedoverTs,iszero:(3)Capacitoroperatinginthedcsteadystate
ThecapacitorcurrentiC,showninFigure3,isflowingthroughacapacitorof100μF.Calculatethepeak-peakrippleinthecapacitorvoltagewaveformduetothisripplecurrent.WorkedExample3Figure3
Solution:Forthegivencapacitorcurrentwaveform,thecapacitorvoltagewaveform,asshowninFigure4,isatitsminimumattimet1,priortowhichthecapacitorcurrenthasbeennegative.Thisvoltagewaveformreachesitspeakattimet2,beyondwhichthecurrentesnegative.Theha
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