Question

If the maximum and minimum amplitudes of an amplitude modulated wave are 9 V and 3 V respectively, then the modulation index is

• A. 1/2
• B. 3
• C. 2
• D. 1/3

Hint:

Modulation index determines the quality of the signal. $\mu>1$ leads to distortion (over-modulation).

Answer 1

The Correct Option is A

Step 1: Formula for Modulation Index:
The modulation index ($\mu$ or $m$) is given by: \[ \mu = \frac{A_{max} - A_{min}}{A_{max} + A_{min}} \] where $A_{max}$ is maximum amplitude and $A_{min}$ is minimum amplitude.
Step 2: Substitution and Calculation:
Given $A_{max} = 9$ V and $A_{min} = 3$ V. \[ \mu = \frac{9 - 3}{9 + 3} \] \[ \mu = \frac{6}{12} \] \[ \mu = \frac{1}{2} \]
Step 3: Final Answer:
The modulation index is 1/2 (or 0.5).