Switch-Mode Power Converters This page intentionally left blank Switch-Mode Power Converters Design and Analysis Keng C. Wu Amsterdam • Boston • Heidelberg • London • New York • Oxford Paris • San Diego • San Francisco • Singapore • Sydney • Tokyo ElsevierAcademicPress 30CorporateDrive,Suite400,Burlington,MA01803,USA 525BStreet,Suite1900,SanDiego,California92101-4495,USA 84Theobald’sRoad,LondonWC1X8RR,UK Thisbookisprintedonacid-freepaper. Copyright(cid:1)2006,ElsevierInc.Allrightsreserved. Nopartofthispublicationmaybereproducedortransmittedinanyformorbyany means,electronicormechanical,includingphotocopy,recording,oranyinformation storageandretrievalsystem,withoutpermissioninwritingfromthepublisher. 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TK7872.C8W8532006 621.31’7–dc22 2005014319 BritishLibraryCataloguinginPublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary ForinformationonallAcademicPresspublicationsvisitourWebsiteat www.academicpress.com PrintedintheUnitedStatesofAmerica 05 06 07 08 09 9 8 7 6 5 4 3 2 1 To My wife, Shwu My daughter, Stephanie My mother, Tai This page intentionally left blank Table of Contents Preface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii 1. IsolatedStep-Down(Buck)Converter 1 1.1. CCMOpen-LoopOutputandDutyCycle Determination. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2. DCMOpen-LoopOutputandDutyCycle Determination. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3. CCMtoDCMTransition,CriticalInductance. . . . . . . . . . 6 1.4. GainFormulaforNonidealOperationalAmplifiers . . . . . . 7 1.5. FeedbackunderVoltage-ModeControl. . . . . . . . . . . . . . . 9 1.6. Voltage-ModeCCMClosedLoop . . . . . . . . . . . . . . . . . . 11 1.7. Voltage-ModeDCMClosedLoop . . . . . . . . . . . . . . . . . . 13 1.8. Voltage-ModeCCMSmall-SignalStability . . . . . . . . . . . . 14 1.9. Current-ModeControl. . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.10. CCMCurrent-ModeControlinaClosed-Loop SteadyState . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.11. CCMCurrent-ModeControlSmall-SignalStability. . . . . . . 24 1.12. OutputCapacitorSizeandAcceleratedSteady-State Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1.13. ACompleteExample . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 1.14. StateTransitionTechnique . . . . . . . . . . . . . . . . . . . . . . . 45 2. Push–PullConverterwithCurrent-ModeControlandSlope Compensation 49 2.1. PowerStageofaCenter-TappedPush–PullConverter. . . . . 50 2.2. DiscontinuousConduction-ModeOperation . . . . . . . . . . . 51 2.3. ContinuousConduction-ModeOperation . . . . . . . . . . . . . 61 3. NonisolatedForwardConverterwithAverageCurrent-Mode Control 67 3.1. AverageCurrentFeedback . . . . . . . . . . . . . . . . . . . . . . . 67 3.2. DutyCycleDetermination . . . . . . . . . . . . . . . . . . . . . . . 71 vii viii CONTENTS 3.3. Steady-StateClosedLoop . . . . . . . . . . . . . . . . . . . . . . . . 72 3.4. Closed-LoopRegulationandOutputSensitivity. . . . . . . . . . 73 3.5. Small-SignalLoopGainandStability. . . . . . . . . . . . . . . . . 74 3.6. Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 3.7. StateTransitionTechnique. . . . . . . . . . . . . . . . . . . . . . . . 76 4. Phase-ShiftedFull-BridgeConverter 83 4.1. Power-StageOperation . . . . . . . . . . . . . . . . . . . . . . . . . . 84 4.2. CurrentDoubler. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 4.3. Steady-StateDutyCycle. . . . . . . . . . . . . . . . . . . . . . . . . . 86 4.4. Steady-StateOutputWaveforms . . . . . . . . . . . . . . . . . . . . 87 4.5. Steady-StateOutputWaveformsExample. . . . . . . . . . . . . . 93 5. Current-FedPush–PullConverters 95 5.1. OverlappingContinuous-ConductionMode . . . . . . . . . . . . 97 5.2. OverlappingContinuousConduction,SteadyState. . . . . . . . 101 5.3. OverlappingContinuousConduction,Example . . . . . . . . . . 105 5.4. NonoverlappingContinuous-ConductionMode. . . . . . . . . . 105 5.5. LoadCurrentSharingandParallelOperation . . . . . . . . . . . 108 5.6. ACSmall-SignalStudiesUsingState-SpaceAveraging . . . . . 113 5.7. State-TransitionTechnique. . . . . . . . . . . . . . . . . . . . . . . . 116 6. IsolatedFlybackConverters 119 6.1. DCMDuty-CycleDetermination,AnotherApproach. . . . . . 120 6.2. CCMDuty-CycleDetermination. . . . . . . . . . . . . . . . . . . . 121 6.3. CriticalInductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 6.4. Voltage-ModeDCMClosedLoop. . . . . . . . . . . . . . . . . . . 123 6.5. Voltage-ModeDCMSmall-SignalStability. . . . . . . . . . . . . 124 6.6. Voltage-ModeCCMClosedLoop. . . . . . . . . . . . . . . . . . . 125 6.7. Voltage-ModeCCMSmall-SignalStability . . . . . . . . . . . . . 126 6.8. PeakCurrent-ModeDCMClosedLoop. . . . . . . . . . . . . . . 126 6.9. PeakCurrent-ModeDCMSmall-SignalStability. . . . . . . . . 128 6.10. PeakCurrent-ModeCCMClosedLoop . . . . . . . . . . . . . . . 129 6.11. PeakCurrent-ModeCCMSmall-SignalStability . . . . . . . . . 130 6.12. OutputCapacitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 6.13. AcceleratedSteady-StateOutput . . . . . . . . . . . . . . . . . . . . 133 6.14. ACompleteDCMExample . . . . . . . . . . . . . . . . . . . . . . . 136 7. NonisolatedBoostConverter 149 7.1. Duty-CycleDetermination . . . . . . . . . . . . . . . . . . . . . . . . 149 7.2. CriticalInductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 CONTENTS ix 7.3. PeakCurrent-ModeClosed-LoopSteadyState inCCM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 7.4. PeakCurrent-ModeSmall-SignalStabilityinCCM. . . . . . 152 7.5. PeakCurrent-ModeClosed-LoopSteadyStateinDCM . . 153 7.6. PeakCurrent-ModeSmall-SignalStabilityinDCM . . . . . 154 7.7. DCMOutputCapacitorSize . . . . . . . . . . . . . . . . . . . . . 155 7.8. CCMOutputCapacitorSize . . . . . . . . . . . . . . . . . . . . . 156 8. Quasi-ResonantConverters 157 8.1. HowDoesItWork?. . . . . . . . . . . . . . . . . . . . . . . . . . . 158 8.2. MathematicalAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . 159 8.3. Steady-StateClosedLoopandStability. . . . . . . . . . . . . . 165 8.4. DesignIssues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 8.5. ExampleandDilemma . . . . . . . . . . . . . . . . . . . . . . . . . 168 9. Class-EResonantConverter 171 9.1. StartingStatesoftheSteadyState . . . . . . . . . . . . . . . . . 175 9.2. Time-DomainSteady-StateSolutions . . . . . . . . . . . . . . . 182 9.3. Closed-LoopDCAnalysis. . . . . . . . . . . . . . . . . . . . . . . 184 9.4. Closed-LoopACAnalysis. . . . . . . . . . . . . . . . . . . . . . . 187 9.5. TypeIIAmplifier. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 9.6. Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 9.7. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 10. AC–DCPower-FactorCorrectionSupplies 203 10.1. FundamentalDefinition . . . . . . . . . . . . . . . . . . . . . . . . 204 10.2. Single-PhaseSingle-StageNonisolatedBoostPFC. . . . . . . 206 10.3. OutputCapacitorSize. . . . . . . . . . . . . . . . . . . . . . . . . . 207 10.4. DCMBoostInductorSelection . . . . . . . . . . . . . . . . . . . 210 10.5. CCMBoostInductorSelection . . . . . . . . . . . . . . . . . . . 214 10.6. High-PowerPFCandLoadSharing . . . . . . . . . . . . . . . . 217 10.7. SurgeProtection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 10.8. LoadShort-CircuitProtection . . . . . . . . . . . . . . . . . . . . 222 10.9. Three-PhasePFC . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 11. ErrorAmplifiers 237 11.1. AmplifierCategory. . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 11.2. InnatePhaseoftheControlLoop . . . . . . . . . . . . . . . . . 242 11.3. TypeIIAmplifierImplementation . . . . . . . . . . . . . . . . . 243 11.4. TypeIIIAmplifierImplementation . . . . . . . . . . . . . . . . 245 11.5. ExampleforTypeIIAmplifierImplementation . . . . . . . . 247 x CONTENTS 12. SupportingCircuits 249 12.1. BipolarSwitchDrivers . . . . . . . . . . . . . . . . . . . . . . . . . 249 12.2. MOSFETSwitchDrivers . . . . . . . . . . . . . . . . . . . . . . . 255 12.3. DissipativeSnubber . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 12.4. LosslessSnubber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 12.5. IsolatedFeedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 12.6. SoftStart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 12.7. Negative-ChargePump. . . . . . . . . . . . . . . . . . . . . . . . . 264 12.8. Single-PhaseFull-WaveRectifierwithRCFilter. . . . . . . . 267 12.9. Duty-CycleClamping. . . . . . . . . . . . . . . . . . . . . . . . . . 273 13. State-SpaceAveragingandtheCukConverter 279 13.1. State-SpaceAveraging . . . . . . . . . . . . . . . . . . . . . . . . . 279 13.2. GeneralProcedure. . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 13.3. Example:CukConverter. . . . . . . . . . . . . . . . . . . . . . . . 282 14. Simulation 291 14.1. DynamicEquationsforaForwardConverterwith Voltage-ModeControl . . . . . . . . . . . . . . . . . . . . . . . . . 292 14.2. Turn-onForwardConverterwithVoltage-Mode Control. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298 14.3. Steady-StateForwardConverterwithVoltage-Mode Control. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298 14.4. SteadyState,ZoomedIn. . . . . . . . . . . . . . . . . . . . . . . . 298 14.5. Load-TransientForwardConverterwith Voltage-ModeControl . . . . . . . . . . . . . . . . . . . . . . . . . 303 14.6. DynamicEquationsforaForwardConverterwith PeakCurrent-ModeControl . . . . . . . . . . . . . . . . . . . . . 306 14.7. Simulation,ForwardConverterwithPeakCurrent-Mode Control. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310 14.8. StateTransitionTechnique:AcceleratedSteadyState . . . . 313 15. PowerQualityandIntegrity 327 15.1. ToleranceofComponents,Devices,andOperating Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 15.2. DCOutputRegulationandWorstCaseAnalysis . . . . . . . 330 15.3. SupplyOutputRippleandNoise . . . . . . . . . . . . . . . . . . 332 15.4. SupplyOutputTransientResponses . . . . . . . . . . . . . . . . 333 15.5. TheConceptsofFrequencyandHarmonicContent . . . . . 335 15.6. Control-LoopBandwidth . . . . . . . . . . . . . . . . . . . . . . . 339 15.7. StepResponseTest . . . . . . . . . . . . . . . . . . . . . . . . . . . 342