Question

For an amplitude modulated wave , the maximum amplitude is found to be 10 V while has minimum amplitude is found to ve 2 V . Determine the modulation index , `mu`.
What would be the value of m if the minimum amplitude is zero volt ?

Answer 1

Given , maximum amplitude `A_("max") = 10V`
Minimum amplitude `A_("min") = 2 V`
Let `A_(c)` and `A_(m)` be amplitudes of carrier wave and signal wave
`A_("max") = A_(c) + A_(m) = 10 ` _____ (1)
and `A_("min") = A_(c) - A_(m) = 2 ` _______ (2)
Adding the equation (1) & (2) we get `2 A_(c) = 6V , A_(m) = 10 - 6 = 4 V `
Modulation index `mu = (A_(m))/(A_(c)) = (4)/(6) = (2)/(3)`
When the minimum amplitude is zero , then i.e., `A_("min") = 0`
`A_(c) + A_(m) = 10 " "` _____(3)
`A_(c) - A_m = 0 " " ` ______(4)
By solving (3) & (4) we get `2 A_(m) = 10 , A_(m) = 5 , A_(c) = 5`
Modulation index `mu = (A_(m))/(A_(c)) = (5)/(5) = 1`