3.1IntroductionAnalogmodulation:modulationofacarrierbyasourcebasebandanalogsignalCarrier:adeterministicperiodicwaveform－cosinusoidal where,A---amplitude

0---angularfrequency ofcarrier

0---initialphaseDefinition:Modulatingsignalm(t)－signalfromthesourceModulatedsignals(t)－signalafterbeingmodulatedModulator－thedeviceformodulation

Figure3.1.1ModulatorModulatorModulatedsignals(t)Modulatingsignalm(t)Chapter3Analogmodulationsystem1PurposeofmodulationFrequencyspectrummovement---foraccommodatingtherequirementofchanneltransmissionorforcombiningseveralsignalsformulti-channeltransmissionImprovementofanti-jammingabilityClassificationofanalogmodulation:Linearmodulation:AM,SSB,DSB,VSB,…Nonlinearmodulation(angularmodulation):FM,PM2(a)FrequencyspectraldensityofinputsignalS(f)f0f-f00M(f)f0(b)Frequencyspectraldensityofoutputsignal3.2Linearmodulation

3.2.0Basicconcept Assume:thecarrieris:c(t)=Acos0t=Acos2f0t modulatingsignalisaenergysignalm(t),itsspectrumisM(f)

carrier:c(t)

multiplicationresult:s(t)

filteroutput:s(t)

“”isusedtoexpressFouriertransform:

where,H(f)s(t)Modulatedsignals(t)Modulatingsignalm(t)Acos0t3

3.2.1AMBasicprinciples Let:m(t)=[1+m(t)]，|m(t)|1，

m(t)|max=m－modulationindex,thenwehavetheAMsignal s(t)=[1+m(t)]Acos0t， where,[1+m(t)]0,i.e.,theenvelopeofs(t)isnon-negative +1=

=m(t)101+m(t)101+m(t)4FrequencydensityContaindiscretecarriercomponentWhenm(t)iscosinusoidal,andm＝100％, sumofthetwosidebandpower＝halfofcarrierpowerFigure3.2.3Waveformandspectrumofmodulatedsignalm(t)s(t)M(f)C(f)c(t)A-Atfm-fmf0-f02fmS(f)2fm-f0f0ffftt5ReceptionofAMsignal:envelopedetectonPrinciple:Characteristics:assumetheinputvoltageiswhere istheinputnoisevoltageofthedetector

Theenvelopeofy(t):ForlargeS/N:RectifierLow-passfilterFigure3.2.4Envelopedetector6

Afterdetection(D.C.componenthasbeenfiltered): Signaltonoisepowerratioofoutputsignal:

∵signaltonoisepowerratiobeforedetectionequals ∴RatioofS/Nbeforeandafterdetection:

Sincem(t)1，obviouslytheaboveratior0/riislessthan1,i.e.,theS/Ndecreasedafterdetection.73.2.2DSBmodulationPrinciple:whenthemodulationsignalm(t)hasnoD.C.component,DSBsignalisobtained.Frequencyspectrum:thetwosidebandscontainidenticalinformation.M(f)f0f00-f0fS(f)(a)FrequencyspectraldensityofmodulatingsignalFigure3.2.5Spectrumofdouble-sidebandmodulationsignalUpper-sideband(b)FrequencyspectraldensityofmodulatedsignalUpper-sidebandLower-sideband8Demodulation:needlocal carrierLetreceivedDSBsignal be

localcarrierofreceiver be ProductoftheabovetwovoltagesisAfterlow-passfiltered,weobtainTheoutputsignalequalsm(t)/2,onlyifthelocalcarrierhasnofrequencyandphaseerror.Advantage&disadvantage:DSBsignalcansavetransmittingpower,butthereceivingcircuitwillberathercomplicated.Figure3.2.6BlockdiagramofDSBsignaldemodulatorBasebandsignalm(t)Receivedsignals(t)cos0tr(t)H(f)93.2.3SSBmodulationPrinciples:Twosidebandscontain identicalinformationOnlyonesidaband shouldbetransmittedToolowfrequencycomponentsinm(t)is notallowedDemodulation:localcarrier isneededSince,if

z(t)=x(t)y(t)，then,wehave

Z()=X()

Y()DuringdemodulationofSSBsignal,thecarriercos0tismultipliedwiththereceivedsignal;itisequivalenttoconvolutionofcarrierandsignalspectrainfrequencydomain.Figure3.2.7Frequencyspectrumofsingle-sidebandsignal(b) Upper-sidebandfiltercharacteristicandsignalfrequencyspectrumf00f-f00ff0-f0HH(f)HH(f)S(f)Upper-sidebandUpper-sideband(c) Lower-sidebandfiltercharacteristicandsignalfrequencyspectrum-f0f0fHL(f)S(f)Lower-sideband(a) SignalfrequencyspectrumbeforefilteringUpper-sidebandS(f)Upper-sidebandLower-sideband10Touseuppersidebandasexampleshowsdemodulatedsignalafterlow-passfiltering.

AdvantagesofSSB:smallertransmittingpowerandbandwidththanDSBsignal.Figure3.2.7Frequencyspectrumofsingle-sidebandsignal(b)Upper-sidebandfiltercharacteristicandsignalfrequencyspectrumf00f-f00ff0-f0HH(f)HH(f)S(f)Upper-sidebandUpper-sideband(c)Lower-sidebandfiltercharacteristicandsignalfrequencyspectrum-f0f0fHL(f)S(f)Lower-sideband(a)SignalfrequencyspectrumbeforefilteringUpper-sidebandS(f)Upper-sidebandLower-sideband113.2.4VSBmodulationAdvantagesofVSB:Duringdemodulation,nolocalcarrierisnecessary;modulatingsignalmaycontainverylowfrequencyandD.C.components.Principles:VSBisstilllinearmodulation.ThefrequencyspectrumofthemodulatedsignalisAssumethetransferfunctionofthefilterofmodulatorisH(f)，thenthefrequencyspectrumofthemodulatedsignalafterfilteringiss(t)Acos0tH(f)Demodulatedsignals(t)Modulatingsignalm(t)12Let’sfindtheconditionwhichshouldbesatisfiedbytransferfunctionH(f)inthefigure.Inthefigure,thereceivedsignalismultipliedbythelocalcarrier,andthefrequencyspectrumoftheresultantsignalr(t)is:Substitutingthefrequencyspectrumofthemodulatedsignalintotheaboveequation,thefrequencyspectrumofr(t)isobtainedas:

M(f+2f0)andM(f–2f0)intheaboveequationmaybefilteredoutbythelow-passfilter,hencethespectraldensityofthedemodulatedsignalfromfilteringis:Basebandsignalm(t)Receivedsignals(t)cos0tr(t)H(f)13

Fordistortionlesstransmission,require Since

Theaboveequationcanberewrittenas

TheaboveequationisaprerequistieforthefiltercharacteristictoproduceVSBsignal.14

Theaboveequationrequiresthatthecut-offcharacteristicofthefilteriscomplementarysymmetrywithrespecttothef0.H(f+f0)-(f0+fm)0000ffff0-f0f0+fm-2f02f0-2f02f0fm-fmfmfH(f)H(f-f0)H(f+f0)+H(f–f0)153.3Nonlinearmodulation

3.3.1BasicprinciplesConceptoffrequency:strictlyspeaking,onlythesinusoidalwavewithconstantamplitude,constantphase,andinfinitelengthhassinglefrequency.Acarrieraftermodulatednolongerhassinglefrequency.Conceptof“instantaneousfrequency”:letacarriercanbeexpressedaswhere,0---initialphaseofcarrier(t)=0t+0---instantaneousphaseofcarrier0=d(t)/dt---angularfrequencyofcarrierDefineinstantaneousfrequencyas:

Theaboveequationcanbewrittenas:16Definitionofangularmodulation: Ascanbeseenfromthefollowingequation,

(t)isthephaseofcarrier.Ifitvarieswithmodulatingsignalm(t)accordingtocertainmode,thenitiscalledangularmodulation.Definitionofphasemodulation:Ifphase(t)linearlyvarieswithm(t),i.e.,letthenitiscalledphasemodulation.Thus,theexpressionofthemodulatedsignalis Now,theinstantaneousfrequencyofthemodulatedcarrieris:Theaboveequationshowsthattheinstantaneousfrequencyinphasemodulationlinearlyvarieswiththederivativeofthemodulatingsignal.17Definitionoffrequencymodulation:Ifinstantaneousfrequencylinearlyvarieswiththemodulatingsignal,thenfrequencymodulationisobtained.Nowinstantaneousangularfrequencyis andinstantaneousphaseis Inthisway,theexpressionofthemodulatedsignalobtainedis: Ascanbeseenfromtheaboveequation,thephaseofthecarrierislinearlyvarieswiththeintegrationofmodulatingsignal.18Comparisonofphasemodulationandfrequencymodulation:Thecarrierphase(t)inphasemodulationlinearlyvarieswiththemodulatingsignalm(t),andthecarrierphase(t)infrequencymodulationlinearlyvarieswiththeintegralofthemodulatingsignalm(t).Ifm(t)isintegratedfirst,andthephaseofcarrierismodulated,thenfrequencymodulatedsignalisobtained.Similarly,ifm(t)isdifferentiatedfirst,andfrequencyofcarrierismodulated,thenphasemodulatedsignalisobtained.Itisimpossibletodistinguishthembymodulatedsignalwaveforms.19WaveformofangularmodulationIfm(t)linearlyvaries,thenthemodulatedsignalisfrequencymodulatedsignal.Ifm(t)varieswitht2,thenthemodulatedsignalisphasemodulatedsignal.i20 3.3.2Frequencyspectrumandbandwidthofmodulated signal

Assume：modulatingsignalm(t)isacosinusoidalwave:

Itisusedtomodulat