# Consider sinusoidal modulation in an AM system. Assuming no over-modulation, the modulation index (μ) when the maximum and minimum values of the envel

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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 ________.

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Concept:

Amax = Ac(1 + μ)

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