Consider sinusoidal modulation in an AM system. Assuming no over-modulation, the modulation index (𝜇) when the maximum and minimum values of the envelope, respectively, are 3 V and 1 V is ________.

Question

Question

This question was previously asked in

UPPSC AE Electrical 2019 Official Paper II (Held on 13 Dec 2020)

Answer 1

Concept:

A single tone modulated signal is given as:

F5 S.B 20.8.20 Pallavi D 7

Maximum envelope Amax : Ac (1+μ)

Minimum envelope Amin : Ac (1-μ)

\(\frac{{{A_{max}}}}{{{A_{min}}}} = \frac{{1 + μ}}{{1 - μ}}\)

The above can be written as:

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

Calculation:

Given: Amax = 3 V and Amin = 1 V

The modulation index will be:

\(μ = \frac{{{3} - 1}}{{3 + 1}}\)

μ = 0.5