Amplitude Modulation

Let carrier wave be represented by the equation
vc=Vccos(ωct) ----- (1)
Let Modulating Signal be represented by the equation
vm=Vmcos(ωmt) ----- (2)

After Amplitude Modulation Amplitude of the carrier varies according to the instantaneous value of modulating signal. The total Amplitude of the Modulated carrier is given as

VAM = Vc+Vmcos(ωmt)

The Expression for AM Wave is

vAM = VAMcos(ωct)
=(Vc+Vmcos(ωmt))cos(ωct)
=Vccos(ωct)+Vmcos(ωmt)cos(ωct)
=Vc(cos(ωct)+macos(ωmt)cos(ωct)) , ( Since Vm/Vc = ma)



Now use the formula

CosA.CosB =	1	[Cos(A+B)+Cos(A-B)]
	2

vAM = Vc(cos(ωct)+	ma	[cos(ωmt+ωct)+cos(ωmt-ωct)]
	2

=Vccos(ωct)+	maVc	cos2π(fm+fc)t+	maVc	cos2π(fm-fc)t
	2		2