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Unformatted text preview: PHYS3360/AEP3630 Electronic Circuits, Spring 2011, HW3 Solutions 1 AC Circuits Solutions 1. a. Choose any convenient value for and perform integration of one period. , = 2 ¡ (1 − ( − 1) ), ¡ > 0, , = 0, ¡ = 0. Units of , are volts. Note: all even harmonics are 0. This is true for any half-wave (odd) symmetric shape, e.g. a shape for which each half-cycle is the mirror image of the next half-cycle. b. through d. The new Fourier coefficients corresponding to the output are given by ¢ , = , ¡ / 1 + ¡ / . Here = 2 /1ms = 6.28 kHz is the fundamental angular frequency, and = 1/0.1ms = 10 kHz is the corner frequency of the high-pass filter. The corresponding plots are shown above. It is seen that with ¡ = 19 the most salient features of the shapes (both input and output) are being reproduced with truncated Fourier series. There are some artifacts, such as ringing and overshoot (undershoot) near abrupt steps. The latter is known as Gibbs phenomenon, which (undershoot) near abrupt steps....
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This note was uploaded on 06/10/2011 for the course AEP 3630 taught by Professor Bozarov during the Spring '08 term at Cornell University (Engineering School).
- Spring '08