Question

An amplitude modulated signal is [A + 0.5 A cos ω_m t] cos ω_c t where ω_m and ω_c are respectively, modulating and carrier frequencies. The power efficiency is    
1. 11.11%
2. 0.25%
3. 4.32%
4. 50%

Answer 1

Correct Answer - Option 1 : 11.11%

Concept:

The standard equation of AM is

\(y\left( t \right) = {A_c}\cos 2\pi {f_c}t(1 + μ \cos 2\pi {f_m}t)\)     -----(1)

The modulation efficiency of the AM signal is given as:

\(η = \frac{{{μ ^2}}}{{2 + {μ ^2}}} \times 100\)

Where, μ = Modulation index.

For under modulation : μ < 1

For critical modulation : μ = 1

For over modulation : μ > 1

Calculation:

Given:

[A + 0.5Acosωmt]cosωct 

Compare it with equation (1)

μ = 0.5

The modulation efficiency of the AM signal is given as:

\(η = \frac{{{0.5^2}}}{{2 + {0.5^2}}} \times 100\)

η = 11.11%