an FM modulator has ouput s(t) = A Cos[ (2*pi*fc*t)+beta*sin(2*pi*fm*t)] a- for

Question

                                an FM modulator has ouput                             

                                s(t) = A Cos[ (2*pi*fc*t)+beta*sin(2*pi*fm*t)]                             

                                 a- for this modulator a 1-v signal produces a deviation of 20Khz determine the amplitude and phase spectra of s(t) for the modulating signal m(t) = 1.5 cos(2*pi*6*10^4*t) when fc>>fm                             

                                b- find the bandwidth of the modulated signal using carson's rule.                             

                                It would be great if I can get detailed solutions.                             

Explanation / Answer

a-) amplitude = %u221A5 + 1

phase modulation= %u03B8i (t)=2%u03C0 fct+kpm(t)

b-)bandwidth= 2x(peak deviation + highest modulating frequency)
hence, the bandwidth= around 44 Khz

hope this helps

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