Amplitude Modulation - Practice Questions & MCQ

Amplitude Modulation

The process of changing the amplitude of a carrier wave in accordance with the amplitude of the audio frequency (AF) signal is known as amplitude modulation (AM). Carrier wave remains unchanged in AM frequency. The amplitude of a modulated wave is varied in accordance with the amplitude of modulating wave.

 Modulation index: The ratio of change of amplitude of carrier wave to the amplitude of original carrier wave is called the modulation factor or degree of modulation or modulation index (m).

$
\mu_a=\frac{\text { Change in amplitude of carrier wave }}{\text { Amplitude of original carrier wave }}=\frac{E_m}{E_c}
$

where

$
\mu_a=\frac{E_m}{E_c}=\frac{E_{\max }-E_{\min }}{E_{\max }+E_{\min }}
$

If a carrier wave is modulated by several sine waves the total modulated index m is given by-

$
m_t=\sqrt{m_1^2+m_2^2+m_3^2+\ldots \ldots}
$

Voluage equation for AM wave:
Suppose voltage equations for carrier wave and modulating wave are $e_c=E_c \cos \omega_c t$ and

$
e_m=E_m \sin \omega_m t=m E_c \sin \omega_m t
$

where,

• $e_c=$ Instantaneous voltage of carrier wave,
• $\mathrm{E}_{\mathrm{C}}=$ Amplitude of carrier wave,
• $\omega_c=2 \pi f_c=$ Angular velocity at the carrier frequency í
• $e_m=$ The instantaneous voltage of modulating.
• $E_m=$ The amplitude of modulating wave,
• $\omega_m=2 \pi f_m=$ Angular velocity of modulating frequency ' f

The voltage equation for $A M$ wave is

$
\begin{aligned}
e & =E \sin \omega_c t=\left(E_c+e_m\right) \sin \omega_c t=\left(E_c+e_m \sin \omega_m t\right) \sin \omega_c t \\
& =E_c \sin \omega_c t+\frac{m_a E_c}{2} \cos \left(\omega_c-\omega_m\right) t-\frac{m_a E_c}{2} \cos \left(\omega_c+\omega_m\right) t
\end{aligned}
$

The above AM wave indicated that the AM wave is equivalent to the summation of three sinusoidal waves, one having amplitude ' $E$ ' and the other two having amplitude $\frac{m_o E_c}{2}$.

Sideband frequencies: The AM wave contains three frequencies, $f_c,\left(f_c+f_m\right)$ and $\left(f_c-f_m\right) . f_c$ is called carrier frequency, $\left(f_c+f_m\right)$ and $\left(f_c-f_m\right)$ are called sideband frequencies.
$\left(f_c+f_m\right):$ Upper sideband (USB) frequency
$\left(f_c-f_m\right):$ Lower sideband (LSB) frequency
In general sideband frequencies are close to the carrier frequency.
Bandwidth: The two sidebands lie on either side of the carrier frequency at equal frequency interval $\mathrm{f}_{\mathrm{m}}$.

So, bandwidth $=\left(f_c+f_m\right)-\left(f_c-f_m\right)=2 f_m$