Question

A modulating signal is a square wave, as shown in the figure If the carrier wave is given as $c ( t )=2 \sin (8 \pi t)$ volts, the modulation index is:

• A. $\frac{1}{3}$
• B. 1
• C. $\frac{1}{2}$
• D. $\frac{1}{4}$

Answer 1

The Correct Option is C

The modulation index of an amplitude modulated wave is defined as the ratio of the amplitude of the modulating signal to the amplitude of the carrier wave. It can be expressed as:

\(m = \frac{A_m}{A_c}\)

where:

• \(A_m\) is the amplitude of the modulating signal.
• \(A_c\) is the amplitude of the carrier wave.

Given that the modulating signal is a square wave with an amplitude of 1 volt (as shown in the figure), and the carrier wave is given by:

\(c(t) = 2 \sin(8 \pi t)\) volts

The amplitude of the carrier wave, \(A_c\), is 2 volts.

Therefore, the modulation index \(m\) can be calculated as follows:

\(m = \frac{A_m}{A_c} = \frac{1}{2}\)

Therefore, the modulation index is \(\frac{1}{2}\).