#### CHAPTER 15 COMMUNICATION SYSTEMS

Amplitude modulation

In amplitude modulation the amplitude of the carrier is varied in accordance with the information signal.

Let c(t) = Ac sin ωct represent carrier wave and m(t) = Am sin ωmt represent the message or the modulating signal where ωm = 2πfm is the angular frequency of the message signal.

The modulated signal cm (t) can be written as,

${\mathrm{C}}_{\mathrm{m}}\left(\mathrm{t}\right)=\left({\mathrm{A}}_{\mathrm{c}}+{\mathrm{A}}_{\mathrm{m}}\mathrm{sin}{\mathrm{\omega }}_{\mathrm{m}}\mathrm{t}\right)\mathrm{sin}{\mathrm{\omega }}_{\mathrm{c}}\mathrm{t}$

Where, μ = $\frac{{\mathrm{A}}_{\mathrm{m}}}{{\mathrm{A}}_{\mathrm{c}}}$ is the modulation index.

In practice, μ is kept ≤ 1 to avoid distortion.

Using the trigonometric relation,

We can write,

Here ωc – ωm and ωc + ωm are called the lower side and upper side frequencies, respectively.

The modulated signal consists of the carrier wave of frequency ωc plus two sinusoidal waves each with a frequency slightly different from ωc, known as side bands.

If the broadcast frequencies (carrier waves) are sufficiently spaced out so that sidebands do not overlap, different stations can operate without interfering with each other.