The main Element of Modulation input and output signal:

(i) Modulating Signal

(ii) Modulated Signal

(iii) Carrier Signal

We Know That,

ec= Ec cos wCt

Here,

ec= Carrier voltage

Ec= Carrier Amplitude

Wc= 2Пfc ( Angular Velocity at carrier frequency fc)

es= Es cos wst

here,

es= Carrier voltage

Es= Carrier Amplitude

Ws= 2Пfs

Modulation Factor= m,

Es= mEc

So, Amplitude of AM wave

= Ec+es

= Ec+Es cos wst

= Ec(1+cos wst)

Current Voltage of AM Wave,

= Amplitude X Cos wct

= Ec(1+cos wst) X cos wct

= Ec cos wct+ Ec cos wct cos wst

= Ec cos wct + mEc/2{2 cos wct cos wst}

= Ec cos wct + mEc/2 { cos (wc+ws)t+cos (wc-ws)t }

= Ec cos wct + mEc/2 cos (wc+ws)t + mEc/2 cos (wc-ws)t

So,

c = Ec cos 2Пfct+ mEc/2 cos 2П (fc+fs)t+ mEc/2 cos 22П (fc-fs)t