GATE 2021 EE – Question 58
The waveform shown in solid line is obtained by clipping a full-wave rectified sinusoid (shown dashed). The ratio of the RMS value of the full-wave rectified waveform to the RMS value of the clipped waveform is ________. (Round off to 2 decimal places.)
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Correct answer: 1.20 to 1.23
Explanation
The waveform follows $V_m\sin\omega t$ until $\frac\pi4$, is clipped at $0.707V_m$ from $\frac\pi4$ to $\frac{3\pi}4$, and then follows the sine again. Its mean square is $\frac1\pi\left[2V_m^2\left(\frac\pi8-\frac14\right)+0.5V_m^2\cdot\frac\pi2\right]=0.341V_m^2$, so the RMS value is $0.584V_m$. The full-wave rectified RMS value is $0.707V_m$, so the ratio is $\frac{0.707}{0.584}=1.21$.