#### Question

Short Note

**Answer the following question.**

If A and B represent the maximum and minimum amplitudes of an amplitude-modulated wave, write the expression for the modulation index in terms of A and B.

#### Solution

Modulation index for an AM wave for which the maximum amplitude is 'a' while the minimum amplitude id 'b'.

Modulation index,

`a_m = (E_m)/(E_c)` ...(1)

The maximum amplitude of the modulated wave, a = E_{c} + E_{m} ...(2)

The minimum amplitude of the modulated wave, b = E_{c} - E_{m} ....(3)

From the above equations,

`E_c = (a + b)/2 , E_m = (a - b)/2`

From Equation 1 we get,

Thus, the modulation index is `a_m = E_m/E_c = (((a - b))/2)/(((a + b))/2) = ((a - b))/((a + b))`.

Concept: Amplitude Modulation

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