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Solved Problems-5

Determine the Fourier series of voltage response obtained at the output of a half-wave rectifier shown in the figure. Plot the discrete spectrum of the waveform.
Description: Description: 4789.png
Here, time period T = 0.4 second;
f = Description: Description: 4795.png
ω = Description: Description: 4801.png
The function, v(t) = Description: Description: 4811.png
= 0; 0.1 ≤ t ≤ 0.3
Description: Description: 4817.png
If the period extending from t = –0.1 to t = 0.3 is taken, it will result in fewer equations and hence, fewer integrals.
∴ Description: Description: 4823.pngDescription: Description: 4831.png
= 0; 0.1 ≤ t ≤ 0.3
∴ Description: Description: 4837.png
∴ Description: Description: 4846.pngn  1
Description: Description: 4852.png
Description: Description: 4865.png
Description: Description: 4871.pngn ≠1
For, a =1, Description: Description: 4879.png

Similarly, bn = 0 for any value of n, and the Fourier series thus contains no sine terms.
∴ Description: Description: 4885.png

Description: Description: 4907.png

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