Overmodulation & Distortion in AM

Overmodulation in AM and How It Causes Distortion

1. AM Signal Equation

s(t) = A_c [1 + μ m(t)] cos(2π f_c t)

• A_c = carrier amplitude
• m(t) = normalized modulating signal (|m(t)| ≤ 1)
• μ = modulation index

2. Modulation Index

μ = A_m / A_c

- Normal AM: 0 < μ ≤ 1 → no distortion
- Overmodulation: μ > 1 → distortion occurs

3. Envelope and Overmodulation

A(t) = A_c [1 + μ m(t)]

- For undistorted AM: 1 + μ m(t) ≥ 0 at all times
- If μ > 1: 1 + μ m(t) < 0 at negative peaks → carrier flips

Example:

Let m(t) = cos(2π f_m t), A_c = 1 V, μ = 1.2
Minimum envelope: A_min = A_c [1 - 1.2] = -0.2 V

Negative amplitude → envelope crosses zero → 180° phase flip

4. Mathematical Consequence

-A_c cos(θ) = A_c cos(θ + π)

This phase reversal is what causes distortion in the demodulated signal.

5. Instantaneous AM Signal

s(t) = A_c [1 + μ cos(2π f_m t)] cos(2π f_c t)

• μ ≤ 1 → envelope detector works correctly
• μ > 1 → envelope < 0 at some t → distortion

6. Summary Equations

Envelope: A(t) = A_c (1 + μ m(t))
Overmodulation condition: μ |m(t)| > 1

Effect: A(t) < 0 → carrier flips phase → distortion

Summary

• Overmodulation occurs when μ > 1
• Negative envelope values flip carrier phase
• Envelope detector cannot follow negative peaks → distortion
• AM distortion is directly linked to the modulation index exceeding 1