Question

An audio signal of amplitude one half the carrier amplitude is used in amplitude modulation. Calculate the modulation index?
A) $0.5$
B) $0.6$
C) $0.7$
D) $0.8$

Answer 1

The frequency of the signal that is used for communications is very feeble to transfer to very long distances. When this signal is transferred to a very large distance, the signal loses its strength and dies out. Hence, it is required for a mechanism to transfer the small frequency signal to larger distances. This can be done by the process of modulation.

Complete step by step answer:
The modulation is defined as the process of varying one or more properties of a wave called the carrier signal, with another wave known as modulating signal, which contains the information required to be transmitted.
This means that either the amplitude or the frequency of a bigger signal known as the carrier signal is varied so as to match that of the modulating signal and transmitted. This modulated signal is demodulated at the receiving end to perceive the signal.
There are three kinds of modulation based on the quantity of the carrier signal varied for transferring the signal.
1. Amplitude Modulation
2. Phase Modulation
3. Frequency Modulation
The modulation index is a term used to indicate the level of modulation achieved. In amplitude modulation, the modulation index is the ratio of the amplitude of the modulating signal to the ratio of the amplitude of the carrier signal.
If ${A_m}$ is the amplitude of modulating signal and ${A_c}$ is the amplitude of the carrier signal, the modulation index, M is given by –
$\Rightarrow M = \dfrac{{{A_m}}}{{{A_c}}}$
Given that the amplitude of the modulating audio signal is half of that of the amplitude of carrier signal, we have –
$\Rightarrow \dfrac{{{A_m}}}{{{A_c}}} = \dfrac{1}{2} = 0.5$
Hence, modulation index, $M = \dfrac{{{A_m}}}{{{A_c}}} = 0.5$.

Hence, the correct option is Option A.

Note: The modulation techniques mentioned here, are only applicable for analog signals, which are continuous in nature. For discrete signals, also called, digital signals, the modulation techniques used are different. Some of the techniques are –
1. Amplitude Shift Keying
2. Frequency Shift Keying
3. Phase Shift Keying