20105ee102_1_hw4 - 1 EE102 Systems and Signals Fall Quarter...

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Unformatted text preview: 1 EE102 Systems and Signals Fall Quarter 2010 Jin Hyung Lee Homework #4 Due: Wednesday, October 27, 2010 at 5 PM. 1. Suppose that f ( t ) is a periodic signal with period T , and that f ( t ) has a Fourier series. If τ is a real number, show that f ( t- τ ) can be expressed as a Fourier series identical to that for f ( t ) except for the multiplication by a complex constant, which you must find. 2. Switching amplifiers are a very efficient way to generate a time-varying output voltage from a fixed supply voltage. They are particularly useful in high-power applications. The basic idea is that an output voltage a is generated by rapidly switching between zero and the supply voltage A . The output is then lowpass filtered to remove the harmonics generated by the switching operation. For our purposes we can consider the lowpass filter as an integrator over many switching cycles, so the output voltage is the average value of the switching waveform.. Varying the switching rate varies the output voltage. In this problem we will only consider the case where the desired output voltage is constant. We can analyze this system with the Fourier series. If the output pulses are spaced by T , the waveform the amplifier generates immediately before the lowpass filter is T 2 T- 2 T- T t α T A The duty cycle of the switching amplifier is α , and the width of the pulses is αT . When α = 1 , the amplifier is constantly on and produces its maximum output A ....
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This note was uploaded on 04/20/2011 for the course EE 102 taught by Professor Levan during the Fall '08 term at UCLA.

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20105ee102_1_hw4 - 1 EE102 Systems and Signals Fall Quarter...

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