GATE 2024 EC – Question 28
An amplitude modulator has output (in Volts)
$$s(t)=A\cos(400\pi t)+B\cos(360\pi t)+B\cos(440\pi t).$$
The carrier power normalized to $1\ \Omega$ resistance is 50 Watts. The ratio of the total sideband power to the total power is $1/9$. The value of $B$ (in Volts, rounded off to two decimal places) is ________.
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Show answer and explanation
Correct answer: 2.49 to 2.51
Explanation
Carrier power $A^2/2=50$, so $A=10$. The two sidebands together carry $2\times\frac{B^2}{2}=B^2$. The total power is $50+B^2$, so $\dfrac{B^2}{50+B^2}=\dfrac19$, i.e. $8B^2=50$ and $B=2.5$ V.