Practical

Computer

Analysisof

SwitchMode

PowerSupplies

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Practical

Computer

Analysisof

SwitchMode

PowerSupplies

Copyrighi2005byTaylor&FrancisGroup.LLC

Practical

Computer

Analysisof

SwitchMode

PowerSupplies

JOHNNYC.BENNER

Taylor&Francis

tJTaylorFrancisGroup

BocaRatonLondonNewYorkSingapore

ACRCtitle,partoftheTaylor&Francisimprint,amemberofthe

Taylor&FrancisGroup,theacademicdivisionofT&FInformaplc.

Copyright2005byTaylor&FrancisGroup,LLC

Publishedin2005by

CRCPress

Taylor&FrancisGroup

6000BrokenSoundParkwayNW.Suite300

BocaRaton,FL33487-2742

?2005byTaylor&FrancisGroup,LLC

CRCPressisanimprintofTaylor&FrancisGroup

NoclaimtooriginalU.S.Governmentworks

PrintedintheUnitedStatesofAmericaonacid-freepaper

10987654321

InternationalStandardBookNumber-10:0-8247-5387-9(Hardcover)

InternationalStandardBookNumber-13:978-0-8247-5387-0(Hardcover)

LibraryofCongressCardNumber2005050581

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quotedwithpermission,andsourcesareindicated.Awidevarietyofreferencesarelisted.Reasonableefforts

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Bennett,JohnnyC.

Practicalcomputeranalysisofswitchmodepowersupplies/JohnnyC.Bennett,

p.cm.

Includesbibliographicalreferencesandindex.

ISBN0-8247-5387-9

1.Switchingpowersupplies-Computersimulation.I.Utle.

TK7881.I5.B462005

621.31'7-dc222005050581

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Copyrighi2005byTaylor&FrancisGroup.LLC

Preface

Formanyyearspriortothe1970s,engineersdesignedandbuiltswitchmode

powersupplies(SMPSs)usingmethodsbasedlargelyonintuitiveandexper-

imentallyderivedtechniques.Ingeneral,thesepowersupplieswereableto

achievetheirprimarygoalofhigh-efficiencypowerconversion;unfortu-

nately,duetothelackofadequatetheoreticalanalysistechniques,manyof

thesepowersuppliesonlymarginallymettheirdesiredperformancerequire-

ments.Inmanycases,theywereconsideredtobeunreliable.Althoughthey

appearedtobeverysimpleinconcept,theseswitchingregulatorsexhibited

phenomenathatwerenotunderstoodandcertainlycouldnotbeanalyzed.

Thingsbegantoimprove,however;intheearly1970s,whenDr.R.D.Mid-

dlebrookandhisgroupofstudentsattheCaliforniaInstituteofTechnology

developedthepowerfulcircuit-averagingtechniques,thusopeningthedoor

fortheapplicationofconventionallinearcircuitanalysismethods.Withthese

toolsbroughttobear,themanysubtlecomplexitiesoftheconceptually"simple”

switchingregulatorweresoonunderstood,allowingengineerstodesign

SMPSswithimprovedperformanceandhigherreliability.Atthispoint,the

powerelectronicsfieldbegantoexpandrapidlyasbettercomponentswere

developed,powerconversiontechnologyadvancementsweremade,and

sophisticatedcomputer-aideddesignandanalysismethodswereutilized.

Havingbeeninthepowerelectronicsfieldformanyyears,Ihavehadthe

goodfortunetobeinvolvedwiththedesignandanalysisofmanydifferent

typesofpowersupplies.Hereinthisbook,oneofmygoalsistoprovidethe

readerwithagoodunderstandingoftheessentialrequirementsforanalyzing

theswitchingregulatedpowersupplyperformancecharacteristics.Another

goalistofurtherdemonstratethepowerofthecircuit-averagingtechniqueby

usingcomputercircuitsimulationprogramstoprovidethedesiredperformance

analyses.Atthispoint,Iwouldliketoreferencetheveryimportantworkof

Dr.VincentBello,who,inhisseminalpaper;9pointedthewaytousingthe

SPICE-basedcomputercircuitsimulatortoperformlinearsmallsignalanalysis

andnonlinearlargesignaltransientperformanceanalysisaswell.Thesimula-

tiontechniquespresentedinthisbookarebasedalmostentirelyonDr.Bello's

approach.Therehavebeenseveraltheoreticalandpracticalcontributorstothe

advancementofthecircuit-averagingtechniquesovertheyearsandIhopethat

theinformationpresentedherecanhelptofurthertheseadvancements.

?Chapter1isarefresherofthebasicsofSMPSfundamentalsand

circuit-averagingmodeling.Thismayalsobeaprimerforthenew-

comer,butitisrecommendedthatthebeginnerreadthereferenced

workstoobtainamorecompleteunderstanding.

Copyrighi2005byTaylor&FrancisGroup.LLC

?Chapter2providesinformationonthegeneralanalysisrequirements

ofapowersupply.Thisisdeemednecessarybecauseitisequally

importanttoknowwhatquestionstoaskasitistoprovidethe

answers.

?Chapter3givesinformationonhowtodevelopthegeneraltypesof

SMPSmodelsanddemonstratestheanalysisapproachusinga

SPICE-basedcircuitsimulator.

?Chapter4looks,inapracticalwayatmostofthebasicfirst-order

typesofanalysisgenerallyassociatedwithSMPSperformance.

?Chapter5providesmorepracticalanddetailedinformationon

developinganSMPSandSMPScomponentmodels.

?InChapter6,threepowersuppliesareanalyzedinpracticaldetail.

Intheseexamples,emphasisisplacedonusingthecircuit-averaging

macromodeloftheintegratedcircuitPWMcontroller.Thisisfeltto

simplifyandexpeditetheanalysisofaparticulardesignthatuses

thesecommerciallyavailablecontrollers.Ascircuitsandsystems

becomelargerandmorecomplex,themacromodelapproachwill

continuetoincreaseinimportanceinalmostallareasofelectronic

circuitanalysis.ThePWMmacromodelingeffortpresentedherewill

hopefullyleadtothefuturedevelopmentofmanymoresuchmac-

romodelsforcommerciallyavailablePWMcontrollers,ashasbeen

thecasewithmacromodelsfortransistors,opamps,etc.

?AppendixAdealswiththeoptimaldesignofSMPSinputfilters.

Thisisincludedheresimplybecauseofthefundamentalimportance

ofthissubjecttoanypowersupply.

?AppendixBprovidesthefirst-orderapproachusedindeveloping

themacromodelfortwocommerciallyavailablePWMcontrollers.

Aswasstatedearlier;thisisonlyafirststepandhopefullywilllead

totheadvancementandfurtherdevelopmentofthesemacros.

Althoughtheyareveryimportantaspectsofanyswitchmodepower

supply;theanalysesofactualswitchingcircuitspersearenotspecifically

addressedinthisbook.Forourpurposes,theseswitchingcircuitsarecon-

sideredtobeintherealmofconventionalelectroniccircuittransientanalysis

andnotimplicitlyrelatedtotheperformanceofanSMPS.Theremaybe

exceptionstothis,ofcourse.

Iwouldliketoexpressmythanksandappreciationtoallthewonderful

peoplewithwhomIhaveworkedovertheyearswhohavesharedtheir

invaluableknowledgeandexperiences.Iwouldalsoliketoexpresslythank

Col.WilliamT.McLymanoftheJetPropulsionLaboratoryforhisencour-

agementandforbeinginstrumentalinproducingthisbook.

JohnnyC.Bennett

Copyrighi2005byTaylor&FrancisGroup.LLC

Author

JohnnyC.BennettisanativeofthestateofLouisianaandisagraduateof

LouisianaTechUniversity.HereceivedhisBSEEin1964andhasworkedas

anelectronicsengineeroverthepast40yearsspecializinginanalogand

powerelectronicscircuitdesign.Hehasworkedformanyofthetoptech-

nologicalcompaniesbothasanemployeeandasaconsultant.Johnny's

hobbiesarereading,music,genealogy,andtraveling.Hecurrentlyresides

inthecityofSouthLakeTahoe,California,andisthefatheroftwoadultsons.

Copyrighi2005byTaylor&FrancisGroup.LLC

Contents

1ReviewofSwitchModePowerSupplyFundamentals

1.1BasicTopologies

1.1.1BuckConverter—ContinuousMode

1.1.2BuckConverter—DiscontinuousMode

1.1.3BoostConverter—ContinuousMode

1.1.4BoostConverter—DiscontinuousMode

1.1.5Buck-BoostConverter—ContinuousMode

1.1.6Buck-BoostConverter—DiscontinuousMode

1.2BasicControlMethods

1.2.1FrequencyofOperationFactors(FOFs)

1.2.2VoltageModeControl

1.2.3CurrentModeControl

1.2.4FeedbackandFeedforwardControlAdditions

1.3Conclusion

2SMPSAnalysisRequirements

2.1DCRequirements

2.1.1OutputRegulation

2.1.2CrossRegulationwithMultipleOutputs

2.1.3Efficiency

2.1.4MiscellaneousRangeandThresholdConsiderations

2.2ACRequirements

2.2.1ACControlLoopStabilityMargins

2.2.2InputFilterStabilityMargins

2.2.3SourceandLoadStabilityMargins

2.2.4ElectromagneticCompatibility

2.3TransientRequirements

2.3.1LoadTransients

2.3.2LineTransients

2.3.3Power-UpandPower-DownTransients

2.3.4EnergyStorageforLineDropouts

2.4Summary

3FundamentalSwitchModeConverter

ModelDevelopment

3.1BuckandBoostConverterContinuousMode

LargeSignalModels

Copyrighi2005byTaylor&FrancisGroup.LLC

3.2BuckandBoostConverterDiscontinuousMode

LargeSignalModels

3.3BuckandBoostContinuousandDiscontinuous

ModeUnifiedModels

3.4Buck-Boost(Flyback)ConverterContinuous

ModeLargeSignalModel

3.5Buck-Boost(Flyback)ConverterDiscontinuous

ModeLargeSignalModel

3.6Buck-BoostContinuousandDiscontinuous

ModeUnifiedModel

3.7CukConverterContinuousMode

LargeSignalModel

3.8CukConverterDiscontinuousModeLargeSignalModel

3.9CukConverterContinuousandDiscontinuous

ModeUnifiedModel

3.10BoostConverterModelAnalysisExample

3.11Summary

4AnalyzingtheFundamentalSMPSModel

4.1BuckConverterSMPSAnalysis(VoltageMode)

4.1.1VoltageModeConverterModelSetup

4.1.2OpenLoopAnalysis(Continuousand

DiscontinuousModes)

ForwardTransferFunction

OutputImpedance(VoltageMode)

ControltoOutput(VoltageMode)

4.1.3SMPSClosedLoopAnalysis(Continuous

andDiscontinuousModes)

ACLoopGain(VoltageMode)

SMPSOutputImpedance(VoltageMode)

4.13.3SMPSLineRegulation(VoltageMode)

SMPSFeedforwardAnalysis

4.1.4SMPSCombinedFeedbackandFeedforward

Analysis(LineRegulation)

4.2BuckConverterSMPSAnalysis(CurrentMode)

4.2.1CurrentModeConverterModelSetup

4.2.2OpenVoltageLoopACAnalysis(Continuousand

DiscontinuousModes)

OpenVoltageLoopACOutputImpedance

(CurrentMode)

OpenVoltageLoopForwardTransfer

Function(CurrentMode)

ControltoOutputAnalysis(CurrentMode)

InnerInductorCurrentControlLoopGain

Copyrighi2005byTaylor&FrancisGroup.LLC

4.2.3SMPSClosedLoopAnalysis(CurrentMode)

4.2.3.1SMPSOutputImpedance(CurrentMode)

4.23.2SMPSLineRegulation(CurrentMode)

4.3Summary

5SMPSComponentModels

5.1ComponentModelDevelopment

5.1.1Real-WorldCapacitorMacro.

5.1.2Real-WorldInductorMacro

5.1.3SMPSDiodeMacro

5.1.4IntegratedCircuitControllers

5.2ParasiticResistanceEffects

5.3PeripheralCircuitAdditions

5.3.1InputFilter

5.3.2InrushCurrentLimiter

5.3.3UndervoltageLockoutandSoftStartCircuits

5.3.4PowerFactorCorrectionCircuits

5.3.5MultipleOutputs

5.3.6PostregulatedOutputCircuits

5.3.7SynchronousRectifierCircuits

5.3.8EnergyStorageSystems

5.4Summary

6AnalyzingtheAdvancedSMPSModel

6.1PulseWidthModulator(PWM)ControllerMacromodel

6.2PracticalFlybackSMPSAnalysis

6.2.1FlybackSMPSModelSetup

6.2.2FlybackSMPSLargeSignalPowerON/OFFAnalysis

6.2.3FlybackSMPSLargeSignalLoadandLine

TransientAnalysis

6.2.4FlybackSMPSCurrent-LimitingPerformance

6.2.5FlybackSMPSACStabilityAnalysis

6.2.6FlybackSMPSACLineRejectionAnalysis

6.3PracticalBuckSMPSAnalysiswithParasiticResistances

6.3.1PracticalBuckConverterModelDevelopment

withParasiticResistances

6.4Practical/zLoop-Opening,/TechniquesforACAnalysis

6.5BuckSMPSSoftStartand"Hiccup"CurrentLimitAnalysis

6.6Summary

AppendixADesignFundamentalsofSMPSInputFilters

A.lGeneralRequirements

A.2FundamentalSingle-StageLCSectionExamples

Copyrighi2005byTaylor&FrancisGroup.LLC

A.3ParallelDampedSingle-StageInputFilter

A.4SeriesDampedSingleStageInputFilter

A.5Two-StageInputFilterDesign

AppendixBPulseWidthModulatorController

Macromodeling

B.lUC1844Circuit-AveragingMacromodelDevelopment

B.2UC1825ACircuit-AveragingMacromodelDevelopment

References

Copyrighi2005byTaylor&FrancisGroup.LLC

1_____________

ReviewofSwitchModePowerSupply

Fundamentals

Aswitchmodepowersupply(SMPS)mayingeneralbedefinedasanytype

ofelectroniccircuitthatconvertsand/orregulatesvoltageorcurrentby

utilizingswitchingcircuitsandenergystorageelements(capacitorsand

inductors).Thesecircuitsareideallylosslesswith100%energytransfer.This

beginningchapterwillprovideareviewofthemostbasicpowerconverter

topologiesintheirsimplestformandanexplanationofalltheirvarious

modesofoperationandcontrol.

1.1BasicTopologies

Therearebasicallythreefundamentallydefinedswitchmodepowersupply

convertertopologies:thebuck,theboost,andthecombinedformgenerally

referredtoasthebuck-boostconverter.Eachoftheseconvertershasits

uniquepropertiesand,ingeneral,isappliedinacomplementarymannerto

eachoftheothers.Also,eachmayhavethecapabilityofoperatinginone

oftwofundamentalmodes:thecontinuousmodeorthediscontinuousmode.

Thesewillbediscussedindetailinthefollowingsections.

1.1.1BuckConverter—ContinuousMode

Asanimmediateinitiationtothefundamentals,consideranillustration

usingthesimplestexampleofall:theelementarybuckconverter.(Presum-

ably;thedefiningword"buck"isdeducedfromthefactthattheinputvoltage

isbucked,orattenuated,inamplitudeandaloweramplitudevoltageappears

attheoutput.)Figure1.1ashowsthecircuittopologyandFigure1.1bshows

thedefiningcurrentandvoltagewaveforms.Theswitchpositionsdanddf

representthefractionoftimethattheperiodicallytogglingswitchremains

ineachposition.(TheperioddTPisgenerallyreferredtoastheconverter

f

ONtimeandtheperioddTPiscalledtheconverterOFFtime.)Byassigning

aperioddurationofunity;itcanthenbeseenthatd+d'=1.Theswitching

period,dTP/occursatafrequencythatismuchgreaterthanthecut-off

Copyrighi2005byTaylor&FrancisGroup.LLC

iiNI■OUT

FIGURE1.1

Basicbuckconverter:a)topology;b)continuousmodewaveforms.

frequencyoftheLClow-passfilter;thus,itprovidestheaverageorDC

componentoftheswitchedor“chopped"inputvoltage,vIN/totheloadwith

anattenuatedanddesiredverylowACripplecomponent.Thelargesignal

nonlineartransferfunctionofthisconverterisindicatedinEquation1.1.

VOUT=也收(1.1)

Copyrighi2005byTaylor&FrancisGroup.LLC

1:N

d=D+d(DC+incrementalquantities)

v=MN+V|N

v=V0UT+v0UT

Na

f(s)Le

Buck￡

DD1L

Boost]]L

一

T-DT^D

BuckBoostDDL

1-DD（l-D）(l-D)2

FIGURE1.2

BasicSMPScontinuousconductionmodecanonicalmodel.

AsmallsignallinearmodeldevelopedbyMiddlebrookandCukb2that

hasachievedwideacceptanceisshowninFigure1.2.Thiscanonicalmodel

isapplicabletoallthreebasictopologiesoperatinginthecontinuousmode;

thedifferentcircuitcomponentparametersarenotedinthetableinthis

figure.Thedifferentfacetsofeachtopologywillbediscussedinthefollowing

correspondingsections.Thislinearizedmodelisusedtoallowallofthe

linearcircuitanalysistechniquesdevelopedovertheyearstobeapplied

whenanalyzingapowersupplyataparticularDCoperatingpoint.Note

thedependentvoltageandcurrentgenerators.Someimportantobservations

areimmediatelynoted.

First,whenafeedbackcontrolfromtheoutputisusedtocontrold,itis

immediatelyobviousthatthetwo-poleLCfilterpresentsa"sticky“ACstability

concernthatmustbedealtwith.Next,withanidealinputvoltagesource—that

is,withzerosourceimpedance—thedependentcurrentgeneratorisessentially

Copyrighi2005byTaylor&FrancisGroup.LLC

shortedandhasnoeffectontheoutputcontrol;thedependentvoltage

generatorprovidesoutputvoltagecontrolthroughthetwo-poleLCfilter.It

isthenrecognizedthatwhenreal-worldpowersourceswithfinitesource

impedancesareused,thecontrol,d,tooutput,v,willbeaffectedbythis

dependentcurrentgenerator.

1.1.2BuckConverter—DiscontinuousMode

Figure1.3ashowsamorerealisticrepresentationofthebuckconverterin

whichtheidealswitchisreplacedbythetransistorswitchandacatchdiode

combination.Whentheloadcurrent,iOLlTfisreducedtoavaluethatcauses

theaverageinductorcurrenttobelessthanone-halftheinductorripple

current,AzL,theinductorcurrentwantstoflownegativelythroughthe

inductor.However,withthetransistorswitcho仔andthecatchdiode

reversedbiased,thenegativeinductorcurrenthasnopathalongwhichto

flow.Atthispoint,nocurrentwillflowintheinductorfortheremainder

oftheconverterOFFtime.Withthisdiscontinuityintheinductorcurrent,

thismodeofoperationisgenerallyreferredtoasthediscontinuousmode.

(Sometimesthiszeroinductorcurrentconditionisreferredasz/theinductor

runningdry/')

Figure1.3bshowsthedefiningcurrentandvoltagewaveformswithobvi-

ousdifferencesnotedbetweenthoseofthecontinuousmodeinFigure1.1b.

TheconverterOFFtimeforthismodeofoperationisgenerallydesignated

inadifferentway.TheportionoftheOFFtimeduringwhichinductorcurrent

也〃

isstillflowingisdesignatedasanditisnowrecognizedthat+d2<1.

TheconventionforthiswasestablishedinCukandMiddlebrook3inthe

courseoftheirpioneeringworkinthedevelopmentofanalyticalpower

convertermodels.Thetransferfunctionforthediscontinuousmodeisnoted

inEquation1.2andisnotassimplearelationshipasthatofthecontinuous

mode.Itisnowafunctionofdfoutputloadcurrent,iOiJT/andtheratioofL/tp.

3,

Middlebrookdefinesa/"conductionparameter/k=2L/RtP/thatdenotes

theboundarybetweencontinuousanddiscontinuousmodes.Forthebuck

converter;k=D'atthisboundary.Thisrelationshipcanbederivedvery

easilyfromthewaveformsshowninFigure1.1bandFigure1.3b.

2

VOUT=VINI.r(1.2)

?+v1+z

where

,2L

卜=西(1.2a)

Copyrighi2005byTaylor&FrancisGroup.LLC

a)

b)

FIGURE1.3

Basicbuckconverter:a)topology;b)discontinuousmodewaveforms.

and

R三｝W(1.2.b)

【OUT

Copyrighi2005byTaylor&FrancisGroup.LLC

FIGURE1.4

Basicboostconverter:a)topology;b)continuousmodewaveforms.

1.1.3BoostConverter—ContinuousMode

ThesimpleboostconverterisshowninFigure1.4a;asitsnameimplies,it

stepsupor"boosts"theinputvoltagetoalevelhigherthanthatoftheinput

voltage.Thistopologyisconsideredthe"dual"orcomplementofthebuck

Copyrighi2005byTaylor&FrancisGroup,LLC

converter.SeeCukandMiddlebrook4formoredetailontheuniquerelation-

shipsbetweenallofthesefundamentalconvertertopologies.

ThedefiningvoltageandcurrentwaveformsareshowninFigure1.4b.

Oneoftheinterestingdualitiesnotedincomparingthecontinuousmode

boostandbuckconvertersisthattheinputcurrenttothebuckconverteris

pulsatingor"chopped,“asnotedinFigure1.1b;however,becauseofthe

inductorontheinputside,theinputcurrenttotheboostconverterisnon-

pulsatingorrelativelysmooth,asnotedinFigure1.4b.Conversely,the

outputcurrentoftheboostconverter;iD,whichisaveragedbytheoutput

filtercapacitor,ischopped,buttheoutputcurrentofthebuckconverter,zL,

issmoothasaresultoftheinductorontheoutputside.Thetransferfunction

ofthisconverterisindicatedinEquation1.3.

(1.3)

NoteinFigure1.2thattheboostconvertersmallsignalmodelisalittle

morecomplexthanthatofthebuckconverterinthattheequivalentoutput

filterinductor,Le,isnotsimplyLbutisactuallyafunctionoftheoperating

pointdutyratio,D.Alsonotethatthedependentvoltagesourcegenerator

hasaright-halfplane(RHP)zeroassociatedwithit.ThismakestheAC

stabilityproblemevenmoredifficult.

AbriefwordregardingthisRHPzeromightbemadehere.Thiszeroresults

because,whenthedutyratiochangeswithtime,theoutputvoltageactually

shiftsintheoppositedirectionduringthischangebecauseofthelagging

inductorcurrentchange.Whenthisconve