Question

Derive the expression of amplitude modulated wave, where carrier wave is c(t)=acsin wct and message signal is m(t)=amsinwmt

Answer 1

when the modulation is done by combining the amplitude of high frequency carrier wave with the amplitude of low frequency message wave, then it is known as amplitude modulation.

carrier wave , C(t) = Ac sinωct

message wave = M(t)=Amsinωmt

Hence the amplitude of the carrier wave is mixed with message signal.

CM(t) = (Ac + Am sinωmt) sinωct

=> CM(t) = Ac(1 + (Am/Ac) sinωmt) sinωct

Let,

Am/AC = μ

Where,

μ = Modulation index

CM(t) = Ac(1 + μ sinωmt) sinωct

=>  CM(t) = Ac sinωct + μAcsinωmt . sinωct

=>  CM(t) = Ac sinωct + (μ Ac)/2  cos(ωc - ωm)t - (μ AC)/ 2 cos(ωc + ωm)t

which is the required expression of amplitude modulated wave.