# Power of A Single-Tone Amplitude Modulated (AM) Signal

Communication
May 22, 2020

## Power of A Single-Tone Amplitude Modulated (AM) Signal

### Mathematical Expressions

Let us consider that a carrier signal A cosω_{c}t is amplitude-modulated by a single-tone modulating signal

x(t) = V_{m}cosω_{m}t.

Then the unmodulated or carrier power is :

P_{c} = mean square value of A cosω_{c}t

The sideband power is given by :

We know that the total modulated power P_{t }is the sum of P_{c} and P_{s}. Therefore ,

But,

Hence,

But,

Therefore,