Lecture5模拟角度调制Lecture5†角度调制的基本概念†窄带角度调制†单频正弦的宽带调频模拟角度调制†调频信号的调制与解调FrequencyModulation非线性调制非线性调制‡相位调制(PhaseModulation,PM)‡频率调制(FrequencyModulation,FM)♦载波C(t)=Acos(ωt+Φ)c♦瞬时角频率偏移Δω=KFMf(t)♦瞬时相位偏移ΔΦ=KPMf(t)♦瞬时角频率ω=ωc+KFMf(t)♦瞬时相位Φ(t)=KPMf(t)+Φ0KFM—频偏常数KPM—相移常数♦S(t)=Acos[ωt+K∫f(t)dt]♦SPM(t)=Acos[ωct+KPMf(t)]FMcFM非线性调制非线性调制‡简谐振荡S(t)=A0cos[θ(t)]‡间接调相dθ(t)‡瞬时角频率f(t)SPM(t)ω(t)=微分调频dtt‡瞬时相位角θ(t)=∫0ω(τ)dτ‡间接调频dθ(t)d[ωct+KPMf(t)]df(t)ω(t)===ωc+KPMdtdtdtf(t)SFM(t)积分调相ttθ(t)=∫0ω(τ)dτ=ωct+KFM∫0f(τ)dτtS(t)=Acos[]θ(t)=Acos[]ωct+KFM∫0f(τ)dτ1单频角度调制单频角度调制‡调制信号‡调频信号tf(t)=AcosωtS()tA=+cos⎡ωtKAcosωτdτ⎤mmFM⎣⎢cFMm∫0m⎦⎥‡调相信号=+Atcos⎣⎦⎡⎤ωβcFMmsinωtS(t)=Acos[ωt+KAcosωt]PMcPMmm⎡⎤Δω=+Atcosωωmaxsint=Acos[]ωct+βPMcosωmt⎢⎥cm⎣⎦ωm‡调相指数‡调频指数βPM=KPMAmβFMFMmm=⋅KA//ωωω=Δmaxmf(t)f(t)ttLecture5模拟角度调制角度调制的基本概念ω(t)ω(t)††窄带角度调制tt†单频正弦的宽带调频†调频信号的调制与解调SPM(t)SFM(t)tt(a)(b)(a)调相信号波形(b)调频信号波形窄带角调制窄带调频信号时域表达StA()=+cos⎡⎤ωtKftdt()FM⎣⎦cFM∫=−AtKcosωωcos⎡f(tdt)⎤⎡⎤AsintsinKf(tdt)πcFM⎣∫∫⎦⎣⎦cFMΔΦmax=KftFM()<<∫max6∵窄带调制π∴sin⎡⎤Kf(tdt)≈Kf(tdt)ΔΦ=Kft()<<⎣⎦FM∫∫FMmaxPMmax6cos⎡⎤Kftdt()≈1⎣⎦FM∫S()tA≈−cosωtAK⎡⎤f()tdtsinωtNBFMc⎣⎦FM∫c2窄带调频信号频域表达与AM信号的比较∞单频调制ωf(t)无直流分量F(0)=∫−∞f(τ)dτ=0‡f(t)=AmcosmtF(ω)F(ω)‡SNBFM(t)≈Acosωct−[AKFM∫f(t)dt]sinωctF[]∫f(t)dt=+πF(0)δ(ω)=jωjω1=Acosωct−AAmKFMsinωmtsinωctωm1⎡F(ω−ωc)F(ω+ωc)⎤F{}[]∫f(t)dtsinωct=⎢−⎥AAK2jj(ω−ω)j(ω+ω)mFM⎣cc⎦=Acosωct−[]cos(ωc−ωm)t−cos(ωc+ωm)t2ωmSANBFM()ωπδωωδωω=−++⎣⎦⎡⎤(c)(c)A‡S(t)=A(1+mcosωt)cosωtAMAmcAKFM⎡⎤FF()()ωω−+ccωω+−⎢⎥2ωω−+ωωAm⎣⎦cc=Acosωt+[]cos(ω−ω)t+cos(ω+ω)tc2cmcmF(ω)与AM信号的比较ω‡载波+两个边带：-ωmωm♦单频—载频ωSAM(ω)c♦上边频ωc+ωm下边频ωωω♦c-m-ωC-ωmωC-ωC+ωmωC-ωmωCωC+ωm‡BNBFM=BAM=2fmSNBFM(ω)‡标准AM中，f(t)改变载波的幅度；-ωC+ωmωC-ωmω窄带FM改变的是载波的频率。-ωC-ωmωCωCωC+ωm与AM信号的比较窄带调相‡时域StAPM()=+cos⎣⎦⎡⎤ωctKftPM()=−AtKftAtKftcosωωcPMcPMcos⎣⎡()⎦⎣⎦⎤⎡⎤sinsin()≈−AtAKfttcosωωcPMc()sin‡频域SANBFM()ωπδωωδωω=−++⎣⎦⎡⎤(c)(c)jAK+−−+PM⎡FF()()ωωωω⎤2⎣cc⎦3Lecture5模拟角度调制单频调制时