Question

# (a) How is amplitude modulation achieved ? (b) The frequencies of two side bands in an AM wave are 640 kHz and 660 kHz respectively. Find the frequencies of carrier and modulating signal. What is the bandwidth required for amplitude modulation ?

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Solution

## (a) Process to achieve AM: Here the modulating signal Am sin ωmt is added to the carrier signal Am sin ωmt to produce the signal x(t). This signal x(t)=Am sinωct is passed through a square law device which is a non- linear device which produces an output y(t)=Bx(t)+Cx2(t) Where B and C are constant, Thus, y(t)=BAmsin ωmt+BAcsin ωct +C[A2msin2 ωmt+A2csin2 ωct+2AmAcsinωmtsinωct]...(ii)=BAmsinωmt+BAcsinωct+CA2m2+C2A2c−CA2m2cos 2ωmt−CA2c2cos 2ωct+CAmAccos(ωc−ωm)t−CAmAccos(ωc+ωm)t...(iii) In equation (iii) , there is a dc term C/2(A2m+A2c) and sinusoids of frequencies ωm,2ωm,ωc,2ωc,ωc−ωm and ωc+ωm. As shown in the above figure , this signal is passed through a band pass filter which rejects dc, the sinusoids of frequencies ωm,2ωm,2ωc and retains the frequencies ωc,ωc−ωm and ωc+ωm. The output of the band pass filter is an AM wave. (b) Given : fc+fm=660 (i)fc+fm=640 (ii) Adding (i) and (ii), 2fc=1300fc=650khz Putting in (i), fm=660−650 fm=10khz Bandwidth = 2fm =2×10 = 20 kHz

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