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AngleModulation(parttwo)EE20422DepartmentofElectronicsandElectricalEngineeringXi’anJiaotong–LiverpoolUniversity
LectureSevenBroadbandFMBandwidthofFMwaves Carson’srule UniversalcurveGenerationofFMwavesDemodulationofFMsignals Frequencydiscriminator Phase-lockedloop
Broad-bandFM:Besselfunctionexpansion
FMspectrumpropertiesThespectrumoftheFMsignals(t)containsacarriercomponentandaninfinitesetofsidefrequencieslocatedsymmetricallyaboutthecarrierfrequency.Whenβ1,J0(β)≈1,J1(β)≈β/2,Jn(β)≈0(n2),henceFMiseffectivelycomposedofcarrierandasinglepairofside–frequencies.TheaveragepowerofFMis
FMspectrumpropertiesThespectrumoftheFMsignals(t)containsacarriercomponentandaninfinitesetofsidefrequencieslocatedsymmetricallyaboutthecarrierfrequency.-0.500.5105101520bJ0(b)J1(b)J2(b)J3(b)BesselfunctionsJn(b)ofdifferentordernJ4(b)
IllustrationofFMSignalSpectraConsiderfmfixed,thevariationofβresultsintwoextremesofbandwidthrepresentation.Whenβ1,B=2ΔfWhenβ1,B=2fm
Carson’sruleforbandwidthofFMsignalCarsondefinedasimpleeffectivebandwidthasafunctionofmodulationindexbandbandwidthfmofbasebandmessagebasedonthesimpleempiricalrelation:Whenβ1,thesidefrequenciesthatareseparatedfromthecarrierfrequencybytheamountgraterthanthefrequencydeviationaredecreasedrapidlytowardzero.Whenβ1,thebandwidthneededfornarrowbandFMis2fm,thesameasforAM.Howaboutβinbetweentwoextremes?Carson’srulegivesaslightunderestimateoftheactualbandwidthneededforanFMsignal
BT=2nmaxfm,wherenmaxisthelargestvaluethatsatisfieslJn(β)l0.01
ExampleInNorthAmericabroadcastFMradioemploysamaximumfrequencydeviationof75KHz,BroadcastFMuseacarrierfrequencybetween88MHzto108MHz,andprovidesabasebandbandwidth(fm)of15KHz.Howmuchisthemodulationindexβ?Considertherequiredbandwidth?
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