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Question
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 = Ec + Em ...(2)
The minimum amplitude of the modulated wave, b = Ec - Em ....(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))`.
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