Question

The maximum and minimum amplitude of an amplitude modulated wave is \(16\,\mathrm{V}\) and \(8\,\mathrm{V}\) respectively. The modulation index for this amplitude modulated wave is \(x \times 10^{-2}\). The value of \(x\) is __________.

Hint:

Use \(m=\dfrac{A_{max}-A_{min}}{A_{max}+A_{min}}\) for an AM wave.

Answer 1

Correct Answer: 33

For an amplitude modulated wave, \(A_{max}=A_c(1+m)\) and \(A_{min}=A_c(1-m)\).
Hence \(m=\dfrac{A_{max}-A_{min}}{A_{max}+A_{min}}\).
\(m=\dfrac{16-8}{16+8}=\dfrac{8}{24}=\dfrac{1}{3}\approx 0.333=33.3\times10^{-2}\).
Nearest integer: \(x=33\).
Answer: 33