112FREQUENCY MODULATION[CHAP.4is referred toasthe carrierswing. Thus, for amodulating signalwhich hasequal positive and negativepeaks,such as apure sine wave, thecarrierswing isequal to twotimes the frequency deviation.A/= frequency deviationCarrierswing =2 XfrequencydeviationIt canbe shown that theequation forthe frequency-modulated wavecanbe manipulated intoA/v =A sin 277fct + — cos2irfat(4.5)faHowever,since the mathematics involvedin developing this secondequation depends oncalculus, itwill notbe shown.Note thatin thisequation the cosine termisprecededby the termA///„. Thisquantityis calledthe modulationindex and is indicated as mf.Modulation index =ny(4.6)fawhereA/is the frequency deviation.TheFederal Communications Commission ofthe United Statesrequires that frequency modulation beusedasthemodulationtechnique forthe bandof frequenciesbetween 88MHz and 108MHz. This isknown astheFMbroadcast band.Frequency modulation is also mandated astherequired modulation technique forthe audioportion ofthetelevision broadcast band.TheFederal Communications Commission setsamaximumfrequency deviation of75 kHz for FMbroadcaststationsin the 88- to108-MHzband.A maximum frequency deviation of25kHz ispermitted forthe soundportion oftelevisionbroadcasts.4.1 PERCENT MODULATIONThe term“percentmodulation” asit is used in reference toFM refers tothe ratio of actual frequencydeviation tothe maximum allowable frequency deviation. Thus, 100%modulation corresponds to75 kHzforthe commercial FMbroadcast band and 25 kHz fortelevision.A/aclualPercentmodulation M =X100(4.7)A/n4.2SIDEBANDSAnalyzing afrequency-modulated waveresultsin finding thatunlike theamplitude-modulated wave,which has only twoside frequencies for eachmodulating frequency, the FMsignalhas aninfinite numberofside frequencies spaced/,, apart onboth sides ofthe resting frequency. See Fig. 4-2.Happily, however,mostoftheside frequencies do notcontain significant amountsof power.fc-3fafc-2fafc~fafc + fafc + 2fafc + 3faFig. 4-2