(第四章模拟调制系统.ppt

Bandpass communication system Cn=AcJn(β) The Bessel function Jn(β) can not be evaluated in analytic form,but it is well-known numerically. We have G(f): G(f)= Σcnδ(f-nfm)= Σ AcJn(β) δ(f-nfm) The G(f)’s distribution depends greatly on β. Conclusion:the bandwidth of the angle modulated signal will depends on β and fm.In general,that will be infinite. In fact , it can be shown that 98% of the total power is contained in the bandwidth: Carson’s Rule BT=2(β+1)B where β is phase or frequency modulation index. So we can estimate the bandwidth of an angle modulated signal by Carson’s Rule with sufficient precision. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Narrowband angle modulation when θ(t) is restricted to a small value, │θ(t)│<0.2rad, the complex envelope g(t)= Ace jθ(t) may be approximated by a Taylor’s series where only the first two terms are used. g(t)=Ac[1+j θ(t)] So we have the narrowband angle modulated signal: s(t)=Accosωct -Acθ(t) sinωct we see that the narrowband angle modulation can be considered an AM-type. Discrete carrier term Sideband power Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Diagram of the narrowband Angle modulation system: Spectrum of NBFM S(f)=Ac/2{[δ(f-fc)+δ(f+fc)]+j[Θ(f-fc)-Θ(f+fc)]} Θ(f)=F[θ(t)]=DpM(f) for PM and (Df/j2πf)M(f) for FM Integrator gain=Df Σ Local oscillator -90o + - m(t) s(t) NBFM Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Wideband frequency modulation Theorem:for WBFM signaling,where s(t)= Accos [ωct+Df-∞∫tm(t)dt] βf =(Df/2πB)max[m(t)]>>1 and B is the bandwidth of m(t).The normalized PSD of the WBFM signal is approximated by: Where fm(*) is the PSD of the modulating signal m(t). Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pt