GATE 2016 EC – Question 33
The amplitude of a sinusoidal carrier is modulated by a single sinusoid to obtain the amplitude modulated signal $s(t) = 5\cos 1600\pi t + 20\cos 1800\pi t + 5\cos 2000\pi t$. The value of the modulation index is ___________
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Correct answer: 0.49 to 0.51
Explanation
The carrier is the middle term, $20\cos 1800\pi t$, and the other two terms are the sidebands at $\pm 100$ Hz, each of amplitude 5. Each sideband has amplitude $\frac{\mu A_c}{2}$, so $\frac{\mu \times 20}{2} = 5$ and $\mu = 0.5$.