Question

A carrier signal of 2 MHz and peak voltage 30 V is being modulated by a signal of 30 kHz and and peak voltage 10 V. The modulation index is  
1. 0.33
2. 0.67
3. 1
4. 3

Answer 1

Correct Answer - Option 1 : 0.33

Content:

Modulation: The process of varying some characteristics such as amplitude, frequency, or phase of a carrier signal is varied in accordance with the instantaneous value of the low-frequency audio signal(or modulating signal) is known as Modulation. In other words, in modulation, we use a high-frequency carrier wave to carry audio signals(message) to large distances. Audio signals have low frequencies with a bandwidth of about 20 kHz only. Such low signals cannot be transmitted directly to large distances. That is why we need modulation of these audio signals. 

Modulation can be of various types such as amplitude modulation, frequency modulation, phase modulation, etc.

Amplitude Modulation: It is the process in which the amplitude of the carrier signal changes in accordance with the instantaneous amplitude of modulating wave. In this process, an amplitude proportional to the amplitude of modulating signal gets added to the message signal. Common features of AM signals are-

• The amplitude of the message signal varies with the frequency fm of modulating signal.
• The frequency of the modulated signal is equal to the frequency fc of the carrier signal.

 

Modulation Index: Modulation index or modulation depth is defined as the ratio of change in the amplitude of the carrier wave to the amplitude of the carrier wave. We know that in amplitude modulation amplitude A_m gets added to the amplitude A_c of the carrier wave. So the change in amplitude of carrier wave is A_m. So, the Modulation index is given by-

\(\mu= \dfrac{A_m}{A_c}\)

Calculation:

given A_m = 10 V

and A_c= 30 V

So, \(\mu=\dfrac{10}{30}\)

= 0.33

The correct answer is option (1)