Question

In AM modulation, a signal is modulated on a carrier wave such that maximum and minimum amplitude are found to be $6 V$ and $2 V$ respectively The modulation index is

• A. $100 \%$
• B. $80 \%$
• C. $60 \%$
• D. $50 \%$

Answer 1

The Correct Option is D

To solve this problem, we need to calculate the modulation index in amplitude modulation (AM). The modulation index \( m \) is given by the formula:

\(m = \frac{A_{\text{max}} - A_{\text{min}}}{A_{\text{max}} + A_{\text{min}}}\)

where:

• \(A_{\text{max}}\) is the maximum amplitude of the modulated signal.
• \(A_{\text{min}}\) is the minimum amplitude of the modulated signal.

Given:

• \(A_{\text{max}} = 6 \, \text{V}\)
• \(A_{\text{min}} = 2 \, \text{V}\)

Substituting these values into the modulation index formula, we get:

\(m = \frac{6 - 2}{6 + 2}\)

This simplifies to:

\(m = \frac{4}{8} = 0.5\)

To express the modulation index as a percentage, multiply by 100:

\(m \times 100 = 0.5 \times 100 = 50\%\)

Thus, the modulation index is 50%. The correct answer is $50 \%$.