Question

Why does Amplitude Modulation have sideband frequencies? Shouldn't the carrier wave have only one frequency?

Answer 1

Amplitude Modulation (AM) is a modulation technique used in communication systems to encode information onto a carrier wave. In AM, the carrier wave's amplitude is varied in proportion to the message signal, such as an audio signal. The modulation process results in the creation of sideband frequencies, which are additional frequencies present alongside the original carrier frequency.

The presence of sideband frequencies in AM can be explained by understanding the modulation process. When the message signal is applied to modulate the carrier wave's amplitude, it causes the carrier wave's amplitude to vary. This variation in amplitude leads to the creation of new frequencies around the carrier frequency. The sidebands occur at frequencies above and below the carrier frequency and are symmetrically spaced.

The generation of sidebands can be understood through mathematical analysis. When a carrier wave with frequency $f_c$ and an audio signal with frequency components $f_m$ is used to modulate the amplitude, the resulting modulated waveform can be expressed as:

$A(t)=[1+k_{a}m(t)]\cos (2\pi f_{c}t)$

Where:

• $A(t)$ represents the modulated waveform
• $k_a$ is the amplitude sensitivity constant (related to modulation index)
• $m(t)$ is the message signal (audio signal)
• $f_c$ is the carrier frequency
• $t$ represents time

Using trigonometric identities, we can expand the expression:

A(t)=cos⁡(2πfct)+kam(t)cos⁡(2πfct)A(t) = cos(2pi f_c t) + k_a m(t) cos(2pi f_c t)A(t)=cos(2πf<span style="top: -2.55em; margin-left: -0.10