Theory : Let `m(t)=A_(m) sin omega_(m)t " and "c(t) = A_c sin omega_(c) (t)`, where m(t) is a message signal and c(t) is the carrier wave. On modulation, the resultant wave becomes `x(t) = A_(m) sin omega_(m) t+A_c sin omega_(c)t` (Theorem of superposition of waves). The combined wave is applied to a non linear device called square law device which produces the output `y(t)= Bx(t)+Cx^2(t)` where B and C are constants. On simplification we get,
`y(t) = [BA_(m)sin omega_(m)t - ((CA_(m)^2)/(2) cos2 omega_(m)t + (CA_(c)^2)/(2) cos2 omega_(c)t)] + [(C )/(2) A_(m)^2 +(C )/(2) A_(c)^2]`
`+[BA+(c)sin omega_(c)t + CA_(m)A_(c) cos (omega_(c) - omega_(m)) t - CA_(m)A_(c) cos (omega_(c)+ omega_(m))t]`
If signal y(t) is passed through the band pass filter centred at `omega_c` , it rejects the sine terms of `omega_(m),2omega_(m) " and " 2omega_(c)` (I term ) and the DC terms (II term). The output of the band pass filter consists of only `omega_(c),omega_(c)+omega_(m) " and "omega_(c) - omega_(m)`. This output is the mdolulated carrier wave (III term) which is further amplified before transmitting.
