A Comparative Study of Carrier-Frequency Modulation Techniques for Conducted EMI

Abstract—A rigorous mathematical analysis and a comparative study of carrier-frequency modulation (CFM) techniques for the conducted electromagnetic interference (EMI) suppression in pulsewidth-modulated converters is presented. CFM techniques dither the

618IEEETRANSACTIONSONINDUSTRIALELECTRONICS,VOL.49,NO.3,JUNE2002

AComparativeStudyofCarrier-FrequencyModulationTechniquesforConductedEMISuppressioninPWMConverters

K.K.Tse,AssociateMember,IEEE,HenryShu-HungChung,Member,IEEE,S.Y.RonHui,SeniorMember,IEEE,

andH.C.So,Member,IEEE

lossandradiatedEMI[2].Bysmoothingtheswitchingtransientsandreducingtheringingproblems,radiatedEMIemissioncanbelessened.Althoughthosetechniquesareparticularlyeffectiveforreducinghigh-frequencyemissions,theyareunsuitableforsuppressingswitching-frequency-relatedemissions(i.e.,conductedEMI).Apartfromusingpassivenoisefiltersandshieldsinthecircuit,anotherapproachofEMIsuppressionisbasedonmodulatingaparameter,suchastheswitchingfrequency,pulsewidth,orpulseposition,ofthepulsewidth-modulated(PWM)signalsthatapplytotheswitchingdeviceseitherinaperiodic[3]orrandommanner[4]–[8].Theparameterisditheredwithsmallamplitudesaroundthenominalvalue,sothattheharmonicpowerisredistributedoverthespectrumofconcern.Amongallpossibleparameters,modulatingthefrequency,namely,thecarrier-frequencymodulation(CFM),isaveryeffectivesolutionbecausetheswitchingfrequencyisnotfixedataconstantvalueand,thus,thespectralcomponentattheoriginalswitchingfrequencywillbediminishedintheinputandoutputspectra.

Asreportedin[3],periodicCFM(PCFM)canreducetheconductedEMIwithasuitableselectionofthemodulatingfrequency.ThismethodintroducessidebandsattheoriginaldiscretefrequencycomponentsinthestandardPWMschemewithmuchsmallermagnitude.Sofar,effectsoftheresolutionfilterbandwidthintheEMCanalyzeronthediscrepanciesbetweentheoreticalandmeasuredspectrahavenotbeenaddressed.Moreover,asdiscussedin[3],Carson’sruleisinapplicableforstudyinghigh-frequencybehaviors,duetotheoverlapofthesidebandharmonicsofdifferentswitchingfrequencyharmonics.Inthispaper,rigorousmathematicalanalysisofthespectrawillbegiven.

Fortherandomswitchingschemes,randomCFM(RCFM)withfixeddutycycleisthebestoptionbecause:1)alldiscreteharmonicscanbesignificantlyreduced;2)theharmonicpowercanbespreadoverasacontinuousnoisespectrumofsmallmag-nitude;and3)thelow-frequencyharmonicinjectionisminimal[6].

ThispaperpresentsacomparativestudyofusingPCFMandRCFMontheconductedEMIsuppressioninPWMconverters.Issuesaddressedincludetheoperationalpropertiesandtheinputandoutputpowerspectraldensitiesoftheconverterswiththetwomodulationtechniques.Inparticular,theircharacteristicsinlow-andhigh-frequencyharmonicpowerredistributionaredepicted.TheeffectsoftheresolutionfilterbandwidthintheEMCanalyzerontheconductedEMImeasurementwillbeem-phasized.Thevalidityoftheanalysesisverifiedexperimentallywithadc/dcbuckconverter.

Abstract—Arigorousmathematicalanalysisandacomparativestudyofcarrier-frequencymodulation(CFM)techniquesfortheconductedelectromagneticinterference(EMI)suppressioninpulsewidth-modulatedconvertersispresented.CFMtechniquesdithertheswitchingperiodwithasmallamplitudevariationaroundthenominalvalue,sothattheharmonicpowerisredis-tributedoverthespectrumofconcern.Twotypesofditheringsignals,includingtheperiodicandrandomsignals,areinves-tigatedinthispaper.Theoperationalcharacteristicsaswellastheinputandoutputpowerspectraoftheconverterswiththetwomodulatingsignalsarecompared.Inparticular,theircharacteristicsinthelow-andhigh-frequencyharmonicpowerredistributionwillbedepicted.ItisshownthatrandomCFM(RCFM)givesamoreeffectivewaytodispersetheharmonicsaroundtheswitchingfrequencythantheperiodicCFM(PCFM)withthesamefrequencydeviation.However,RCFMintroduceshigherlow-frequencyharmonicsthanthePCFMattheconverteroutput.Furthermore,effectsoftheresolutionfilterbandwidthintheelectromagneticcompatibilityanalyzeronconductedEMImeasurementisdiscussed.Thevalidityoftheanalysesiscon-firmedexperimentallybyusingadc/dcbuckconverteroperatingincontinuousconductionmode.

IndexTerms—DC–DCpowerconversion,powerelectronics,pulsewidthmodulation,randomswitchingtechniques,switchingcircuits.

I.INTRODUCTION

STHEelectromagneticspectrumbecomescrowded,manycountrieshaveimposedelectromagneticcompat-ibility(EMC)regulationsthatmustbemetbeforeelectronicproductscanbesoldlegally.Themostdirectwayofsolvingelectromagneticinterference(EMI)problemsistoreducetheemissionfromthenoisesource[1].

EMIisaseriousprobleminpowerelectronicscircuitsbe-causeoftheirfastswitchingcharacteristics.Extensiveresearchhasbeenconductedondevelopingvarioussoft-switchingtechniquesfordifferentapplicationstoreducebothswitching

A

ManuscriptreceivedOctober2,2000;revisedNovember26,2001.AbstractpublishedontheInternetMarch7,2002.ThisworkwassupportedbytheRe-searchGrantsCounciloftheHongKongSpecialAdministrativeRegion,China,underCERGProject9040266.TheworkofK.K.TsewassupportedbyTheCroucherFoundationFellowship.

K.K.TsewaswiththeDepartmentofElectronicEngineering,CityUniversityofHongKong,Kowloon,HongKong.HeisnowwithJohnsonElectric,HongKong.

H.S.-H.Chung,S.Y.R.Hui,andH.C.SoarewiththeDepartmentofElectronicEngineering,CityUniversityofHongKong,Kowloon,HongKong(e-mail:eeshc@cityu.edu.hk).

PublisherItemIdentifierS0278-0046(02)04926-2.

0278-0046/02$17.00©2002IEEE

Abstract—A rigorous mathematical analysis and a comparative study of carrier-frequency modulation (CFM) techniques for the conducted electromagnetic interference (EMI) suppression in pulsewidth-modulated converters is presented. CFM techniques dither the

TSEetal.:CARRIER-FREQUENCYMODULATIONTECHNIQUES

Fig.1.TypicalPWMfunction.

II.PCFMANDRCFM

Fig.1showsatypicalPWM

functionandtheswitching

periodhastwodiscretelevels

(namely,

canbe

expressedbyaFourierseries

[9]

thhar-monic,

respectively.

ismod-ulatedbyacosinusoidalfunctionof

amplitudeandfre-

quency

of

the

istheratioofthepeakinstantaneousfrequencydevia-tiontothefrequencyofthemodulatingsignal,namely,themod-ulationindexin[3]and[11].Itisdefined

as

619

is

the

(8)

NumericalvaluesoftheBesselfunctionswithrespect

to

uptothetenthorderaretabulatedinTableI.Thefollowingtwopropertiesarealso

noted:

(9a)

and

Abstract—A rigorous mathematical analysis and a comparative study of carrier-frequency modulation (CFM) techniques for the conducted electromagnetic interference (EMI) suppression in pulsewidth-modulated converters is presented. CFM techniques dither the

620IEEETRANSACTIONSONINDUSTRIALELECTRONICS,VOL.49,NO.3,JUNE2002

TABLEI

NUMERICALVALUESOFTHEFIRSTTENORDERJ

S

nnnn

nn

nnnnnnnn

n

n

nnn

nnn

nnnn

n

nn

Abstract—A rigorous mathematical analysis and a comparative study of carrier-frequency modulation (CFM) techniques for the conducted electromagnetic interference (EMI) suppression in pulsewidth-modulated converters is presented. CFM techniques dither the

TSEetal.:CARRIER-FREQUENCYMODULATIONTECHNIQUES

Fig.3.RelationshipsofjJagainstn .

TABLEII

COMPONENTVALUESANDSPECIFICATIONSOFTHEBUCKC

ONVERTER

Fig.4.Theoreticalinputcurrentpowerspectrumwith =0.

Theabovepropertiesareillustratedwithanexampleofabuckconverter.ItsspecificationsaretabulatedinTableII.Thevalues

of

equalszero(i.e.,standardPWMscheme).It

containsdiscreteharmonicsatthemultiplesoftheswitchingfre-quencyonly.Figs.5and6showthepowerspectra

with

,

and,respectively,undertwotestingconditions.Thefirsttestingconditionis

that

kHz,

(i.e,

621

kHz,

andHz,

respectively.TheresultsaresimilartothoseinFig.5.Theyindi-catethatharmonicsuppressionishighlydependentonthevalue

of

iskeptconstant[6].Insteadofusingpowerspectrum,PSDisconsideredintheanalysis[5].The

PSD

,isofuniformdistributionwiththeexpectedvalue

of

istherandomnesslevel.

Thisschemespreadsthediscreteharmonicsoverthefre-quencyspectrum.

As

islargerthan

acertainvalue,suchas0.15in[6].Moreover,low-frequencyharmoniccomponentsincrease

as

60dB(denoted

by

)

andis15.

That

is,

Abstract—A rigorous mathematical analysis and a comparative study of carrier-frequency modulation (CFM) techniques for the conducted electromagnetic interference (EMI) suppression in pulsewidth-modulated converters is presented. CFM techniques dither the

622IEEETRANSACTIONSONINDUSTRIALELECTRONICS,VOL.49,NO.3,JUNE

2002

(a)

(b)

(c)

Fig.5.Theoreticalpowerspectraoftheinputcurrentwithf =16.

=6kHzand =2.(b)1f

=48kHzand

modelthefilterattenuation.Thefilterresponse

functionByusingthepropertyin(9b),thetotalpowerof

the

(19)

mated

by

where

dB,

anddB.

Hence,themeasuredpower

at

thatfalls

withincanbeapproxi-

issmall.Thiscanbeachievedbyeither

reducing

or

increasing

willbesmallandthe

magnitudeofthesidefrequencieswillincrease.

If(20)

where

.

Abstract—A rigorous mathematical analysis and a comparative study of carrier-frequency modulation (CFM) techniques for the conducted electromagnetic interference (EMI) suppression in pulsewidth-modulated converters is presented. CFM techniques dither the

TSEetal.:CARRIER-FREQUENCYMODULATIONTECHNIQUES

623

(a)

(b)

(c)

Fig.6.Theoreticalpowerspectraoftheinputcurrentwith1f =16

.

=6kHzand =2.(b)f

=750Hzand

).

Increasingcaneffectively

dispersethelow-orderharmonics.However,withthe

sameand

different

Fig.7.Modelofthetriangle-likefilterresponseintheEMCanalyzer.

smaller

.Themeasuredspectrumisunabletodif-ferentiatetheeffectiveness

of

issufficientlylarge,thePSDofthemeasuredPWM

waveformisuniformlydistributed.Themeasuredspectrumwill

increases.increase

as

Abstract—A rigorous mathematical analysis and a comparative study of carrier-frequency modulation (CFM) techniques for the conducted electromagnetic interference (EMI) suppression in pulsewidth-modulated converters is presented. CFM techniques dither the

624IEEETRANSACTIONSONINDUSTRIALELECTRONICS,VOL.49,NO.3,JUNE2002

TABLEIII

INTERACTIONOFTHEnTHHARMONICIN

S

fkHzand =2.(b)

fno

fffnnkHzand

nuffrnnn

=61

f

=9

Abstract—A rigorous mathematical analysis and a comparative study of carrier-frequency modulation (CFM) techniques for the conducted electromagnetic interference (EMI) suppression in pulsewidth-modulated converters is presented. CFM techniques dither the

TSEetal.:CARRIER-FREQUENCYMODULATIONTECHNIQUES

(a)

(b)

parisonofthepredictedpowerspectrawithBW

=12kHz.(a)f=1:5kHzand =8

.

Fig.10.ImplementationoftherampVCO.

Low-frequencynoisewillinherentlyintroduce

when

isbasedontheharmonicspreading

effectsandthelow-frequencynoiseinjection.

III.EXPERIMENTALVERIFICATIONSANDCOMPARISONSThesameconverter,astabulatedinTableII,isinvestigated.CFMisachievedbyusingtherampvoltage-controlledoscillator(VCO)showninFig.10.Byintegratingthesignalthatcombines

amodulating

signal

(whichiseitherperiodicorrandom)

and

625

(a)

(b)

Fig.11.MeasuredpowerspectrumoftheinputcurrentwithPCFM(10dB/div).(a)f=6kHz,and =2.(b)f

=24kHz,and =8.

areferencedc

voltage

,atriangularwaveformisgenerated.Thepeak

valueoftheoutputisdefined

as

(27)

where

equals.Thetheoretical

andmeasuredresultsareshowninFig.12.

ComparingFig.11withFig.12,bothPCFMandRCFMgivesimilarprofilesinthemeasuredspectra,especiallyinthehigh-frequencyrange.However,forthelow-frequencyharmonics,

Abstract—A rigorous mathematical analysis and a comparative study of carrier-frequency modulation (CFM) techniques for the conducted electromagnetic interference (EMI) suppression in pulsewidth-modulated converters is presented. CFM techniques dither the

626IEEETRANSACTIONSONINDUSTRIALELECTRONICS,VOL.49,NO.3,JUNE

2002

(a)

(b)

Fig.12.

PowerspectraoftheinputcurrentwithRCFMandBW

=200Hz.(a):RCFM,<=0:5.(b):RCFM,<=0:2.(c):

RCFM,<=0:1.(d):PCFM.

theperformanceofthetwoschemesaredifferent.Thetheoret-icalspectraofthediodevoltagewiththetwoschemesareshowninFig.13.Basically,RCFMgiveshigherlow-frequencyhar-monicsthanthePCFM.Noharmonicswillbegeneratedbeyondthesidebandofthefirst-order-switchingharmonicinPCFM[Fig.13(d)].Fig.14showstheoutputvoltageoftheconverterunderthetwoschemes.ItcanbeobservedthattheRCFMintro-duceshigherlow-frequencyvariationthanthePCFM,thuscon-firmingthetheoreticalprediction.Althoughlow-frequencyhar-monicsintheRCFMcanbereducedwitha

smaller

Abstract—A rigorous mathematical analysis and a comparative study of carrier-frequency modulation (CFM) techniques for the conducted electromagnetic interference (EMI) suppression in pulsewidth-modulated converters is presented. CFM techniques dither the

TSEetal.:CARRIER-FREQUENCYMODULATIONTECHNIQUESbeendeveloped.Inaddition,duetothefinitebandwidthoftheresolutionfilterinEMCanalyzers,discrepanciesbetweenthetheoreticalandexperimentalresultshavebeenexplained.SelectionsofthemodulationfrequencyandthefrequencydeviationinPCFMhavebeendiscussed.Finally,theoreticalpredictionsareconfirmedbyexperimentalresultsofabuckconverteroperatingincontinuousconductionmode.

REFERENCES

[1]M.D.Heerema,“Designingforelectromagneticcompatibility,”inProc.

Hewlett-PackardSeminar,1996,pp.1–29.

[2]H.Chung,S.Y.R.Hui,andK.K.Tse,“Reductionofpowerconverter

EMIemissionusingsoft-switchingtechnique,”pat.,vol.40,pp.282–287,Aug.1998.

[3]F.LinandD.Y.Chen,“ReductionofpowersupplyEMIemissionby

switchingfrequencymodulation,”IEEETrans.PowerElectron.,vol.9,pp.132–137,Jan.1994.

[4]T.G.HabetlerandD.M.Divan,“Acousticnoisereductioninsinusoidal

PWMdrivesusingarandomlymodulatedcarrier,”IEEETrans.PowerElectron.,vol.6,pp.356–363,July1991.

[5]A.M.Stankovic,G.C.Verghese,andD.J.Perreault,“Analysisandsyn-thesisofrandomisedmodulationschemesforpowerconverters,”IEEETrans.PowerElectron.,vol.10,pp.680–693,Nov.1995.

[6]K.K.Tse,H.Chung,S.Y.R.Hui,andH.C.So,“Acomparativeinvesti-gationontheuseofrandommodulationschemesfordc/dcconverters,”IEEETrans.Ind.Electron.,vol.47,pp.245–252,Apr.2000.

[7]D.StoneandB.Chambers,“Theeffectsofcarrierfrequencymodulation

ofPWMwaveformsonconductedEMCproblemsinswitchedmodepowersupplies,”EPEJ.,vol.5,no.3/4,pp.32–37,Jan.1996.

[8]M.Bech,F.Blaabjerg,andJ.Pederson,“Randommodulationtechniques

withfixedswitchingfrequencyforthree-phasepowerconverters,”IEEETrans.PowerElectron.,vol.15,pp.753–761,July2000.

[9]C.R.WylieandL.C.Barrett,AdvancedEngineeringMathe-matics.NewYork:McGraw-Hill,1995.

[10]A.B.Carlson,CommunicationSystems:AnIntroductiontoSignaland

NoiseinElectricalCommunication.NewYork:McGraw-Hill,1986.[11]G.Kennedy,ElectronicCommunicationSystems.NewYork:Mc-Graw-Hill,1985.

[12]R.A.Witte,SpectrumandNetworkMeasurements.EnglewoodCliffs,

NJ:Prentice-Hall,1991.

[13]HP8590EMSeriesUser’sGuide,HewlettPackardCo.,PaloAlto,CA,

1995.

K.K.Tse(M’00)receivedtheB.Eng.(Hons.)degreeinelectricalengineeringfromTheHongKongPoly-technicUniversity,HongKong,andthePh.D.degreefromCityUniversityofHongKong,HongKong,in1995and2000,respectively.

HeservedasaLecturerattheHongKongInstituteofVocationalEducation(TsingYi)(formerlyTech-nicalCollege)in1998.From1999to2001,hewasaResearchFellowintheElectronicEngineeringDe-partment,CityUniversityofHongKong.SinceJune2001,hehasbeenwithJohnsonElectric,HongKong,

whereheiscurrentlyaTechnicalSpecialistintheR&Darea.Hehasauthoredmorethan20publishedtechnicalpapersintheareasofhisresearchinterests,whichincludenewnumericalmodelmethodsandcomputer-aidedsimulationtechniques,EMIreductionusingrandomswitchingschemesfordc–dccon-verters,andnewmaximumpowertrackingtechniquesforPVcells.

Dr.TsereceivedtheFirstPrizein1998intheIEEEPostgraduateStudentPaperContest,HongKongSection,andtheThirdPrizeinthe1999Region10IEEEPostgraduateStudentPaperContest.HewasarecipientofTheCroucherFoundationFellowshipin2000.InDecember2000,hereceivedtheSilverAwardintheYoungInventorCompetition,jointlyorganizedbytheFarEasternEconomicReviewandHewlettPackard

Company.

627

HenryShu-HungChung(S’92–M’95)receivedtheB.Eng.(withfirstclasshonors)degreeinelectricalengineeringandthePh.D.degreefromTheHongKongPolytechnicUniversity,HongKong,in1991and1994,respectively.

Since1995,hehasbeenwithCityUniversityofHongKong,HongKong,whereheiscurrentlyanAssociateProfessorintheDepartmentofElectronicEngineering.Hisresearchinterestsincludetime-andfrequency-domainanalysisofpowerelectroniccir-cuits,switched-capacitor-basedconverters,random-switchingtechniques,digitalaudioamplifiers,soft-switchingconverters,andelectronicballastdesign.Hehasauthoredfourresearchbookchaptersandmorethan130technicalpapers,including65refereedjournalpapersinthecurrentre-searcharea,andistheholderoftwoU.S.patents.

Dr.ChungiscurrentlytheIEEEStudentBranchCounseloratCityUniversityofHongKongandwasTrackChairoftheTechnicalCommitteeonPowerElec-tronicsCircuitsandPowerSystemsoftheIEEECircuitsandSystemsSocietyin1997–1998.HeispresentlyanAssociateEditoroftheIEEETRANSACTIONSONCIRCUITSANDSYSTEMSI.HewasawardedtheGrandAppliedResearchEx-cellenceAwardin2001fromCityUniversityofHong

Kong.

S.Y.RonHui(SM’94)wasborninHongKongin1961.HereceivedtheB.Sc.(Hons.)degreein1984fromtheUniversityofBirmingham,Birmingham,U.K.,andtheD.I.C.andPh.D.degreein1987fromImperialCollegeofScienceandTechnology,UniversityofLondon,London,U.K.

HewasaLecturerinpowerelectronicsattheUniversityofNottingham,Nottingham,U.K.,in1987–1990.In1990,hetookupalectureshipattheUniversityofTechnology,Sydney,Australia,wherehebecameaSeniorLecturerin1991.Hejoined

theUniversityofSydneyin1993andwaspromotedtoReaderofElectricalEngineeringandDirectorofthePowerElectronicsandDrivesResearchGroupin1996.HeiscurrentlyaChairProfessorofElectronicEngineeringandanAssociateDeanoftheFacultyofScienceandEngineeringatCityUniversityofHongKong,HongKong.Hehasauthoredmorethan150publishedtechnicalpapers,includingmorethan80refereedjournalpublications.Hisresearchinterestsincludeallaspectsofpowerelectronics.

Prof.HuireceivedtheTeachingExcellenceAwardin1999andtheGrandAp-pliedResearchExcellenceAwardin2001fromCityUniversityofHongKong.HehasbeenappointedanHonoraryProfessorbytheUniversityofSydneysince

2000.

H.C.SowasborninHongKong.HereceivedtheB.Eng.degreefromCityUniversityofHongKong,HongKong,andthePh.D.degreefromChineseUni-versityofHongKong,HongKong,in1990and1995,respectively,bothinelectronicengineering.

From1990to1991,hewasanElectronicEngineerintheResearchandDevelopmentDivision,EverexSystemsEngineeringLtd.HewasthenaPost-Doc-toralFellowatChineseUniversityofHongKongforoneyear.From1996to1999,hewasaResearchAs-sistantProfessorintheDepartmentofElectronicEn-gineering,CityUniversityofHongKong.Currently,heisanAssistantProfessorintheDepartmentofComputerEngineeringandInformationTechnology,CityUniversityofHongKong.Hisresearchinterestsincludeadaptivefiltertheory,detectionandestimation,wavelettransform,andsignalprocessingforcommu-nicationsandmultimeda.

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