Question

In amplitude modulation, the modulation index should be:

• A. Less than 0.5
• B. Equal to 1
• C. Greater than 1
• D. Between 0 and 1

Hint:

Over-modulation (\( m>1 \)) causes envelope distortion in AM signals — always keep \( m \leq 1 \).

Answer 1

The Correct Option is D

Step 1: Look at the AM wave envelope. 
In amplitude modulation, the information signal changes the height (envelope) of the carrier wave. For proper reception, this envelope must clearly follow the shape of the message signal.

Step 2: Condition for a valid envelope.
Mathematically, the AM signal is written as:
\[ s(t) = A_c \big(1 + m \cos \omega_m t\big)\cos \omega_c t \]
To keep the envelope always positive (no crossing or inversion), the term \[ 1 + m \cos \omega_m t \ge 0 \]
must hold for all values of time.

Step 3: Finding the allowed range of \( m \).
Since the maximum value of \( \cos \omega_m t \) is 1 and the minimum is −1:
\[ 1 - m \ge 0 \]
\[ m \le 1 \]
Also, modulation requires a positive value of \( m \), so:
\[ 0 < m \le 1 \]

Step 4: Eliminating incorrect options.
(A) Less than 0.5 → Not compulsory, modulation can be stronger.
(B) Equal to 1 → Valid, but not the full condition.
(C) Greater than 1 → Envelope crosses zero, causing distortion.
(D) Between 0 and 1 → Satisfies all conditions for distortionless AM.

Final Conclusion:
For a clean and undistorted AM signal, the modulation index must lie between 0 and 1.