# Amplitude Modulation

**Amplitude Modulation**

Amplitude modulation can naturally enter into many physical phenomena. More important perhaps is the deliberate (artificial) use of amplitude modulation to facilitate data transmission and signal conditioning. Let us first examine the related mathematics.

Amplitude modulation is achieved by multiplying the data signal (modulating signal) x (t) by a high frequency (periodic) carrier signal xc(t). Hence, amplitude-modulated signal xa (t) is given by

**xa (t)****=x (t) xc (t)**

Note that the carrier could be any periodic signal such as harmonic (sinusoidal), square wave, or triangular.

The main requirement is that the fundamental frequency of the carrier signal (carrier frequency) fc be significantly large (say, by a factor of 5 or 10) than the highest frequency of interest (bandwidth) of the data signal.

Analysis can be simplified by assuming a sinusoidal carrier frequency; thus,

**xc (t)****=ac cos2pƒct (4.65)**