Amplitude Modulation

Amplitude Modulation

In amplitude modulation (AM), the amplitude of the carrier wave is varied in proportion to the instantaneous value of the message signal, while the carrier's frequency stays fixed.

Taking a carrier $c(t) = A_c\sin(\omega_c t)$ and a message/modulating signal $m(t) = A_m\sin(\omega_m t)$ (with $\omega_m = 2\pi f_m$), the amplitude-modulated signal is:

which can be rewritten as:

where $\mu = A_m/A_c$ is the modulation index, kept at or below 1 in practice to avoid distortion of the transmitted signal.

Using the identity $\sin A\sin B = \tfrac{1}{2}[\cos(A-B) - \cos(A+B)]$, Eq. 15.4 expands to:

$c_m(t) = A_c\sin(\omega_c t) + \frac{\mu A_c}{2}\cos\left[(\omega_c-\omega_m)t\right] - \frac{\mu A_c}{2}\cos\left[(\omega_c+\omega_m)t\right] \quad \text{(Eq. 15.5)}$ …