Question

In our daily life, modulation plays an important role. Discuss the amplitude modulation.

Answer 1

Modulation is the process of varying the properties of a periodic waveform (carrier signal) as per the modulating signal. There are different kinds of modulation like amplitude modulation, frequency modulation, etc. The carrier signal is of high frequency and provides many advantages to be transmitted as compared to transmitting modulating signal directly. Some major advantages are:

1. Low attenuation

2. Small size of antenna

3. Allowing multiplexing (sending multiple signals simultaneously)

4. Reducing interference between two different signals

In amplitude modulation, amplitude of carrier wave is varied according the modulating signal.

Equation for carrier signal is: $c\left(t\right)=A_c\sin \left({\omega }_{c}t\right)$

Modulated signal is given by: $y\left(t\right)=(1+x(t\left)\right)c\left(t\right)$ where $x\left(t\right)$ is the modulating signal.

$y\left(t\right)=A_c(1+x(t\left)\right)\cos \left({\omega }_{c}t\right)$

Let $x\left(t\right)=M\cos \left({\omega }_{m}t\right)$

Then, $y\left(t\right)=A_c(1+M\cos ({\omega }_{m}t\left)\right)\cos \left({\omega }_{c}t\right)$

$M$ is called modulation index and should be less than $1$ for proper transmission of signal.

Further, using trigonometry,

$y\left(t\right)=A_c\sin \left({\omega }_{c}t\right)+\frac{A_{c}M}{2}\left[\sin \right({\omega }_c+{\omega }_m)t+\sin ({\omega }_c-{\omega }_m\left)t\right]$

From above equation, modulated signal lies in the frequency range $({\omega }_c-{\omega }_m$, ${\omega }_c+{\omega }_m)$