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,