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Unformatted text preview: iscussion #7 Example Problem his problem illustrates how Fourier series are helpful tools for analyzing electronic ircuits. ften in electronic circuits we need sinusoids of various frequencies ut we may already have circuitry in the system that generates a clock signal an we avoid having to build a sinusoidal oscillator by exploiting the clock signal? ) ( t x t he box labeled oscillator in the figure below produces this signal. ssume that the output impedance of the oscillator is very low so that the rest of the ircuit doesnt load it (recall our previous discussions of loading). ssume that the resistor is 800 , the capacitor is 1 F, and the inductor is 250 H Lets imagine that our job is to design circuitry to convert a square wave into a sinusoid of 10000 Hz. Suppose we have a square wave oscillator that generates the following signal with a period of 100 s: (a) Find the Fourier Series for the square wave signal x ( t ) that gets applied to the input of the RLC circuit. (b) Find the frequency response H ( ) of the RLC circuit and use a computer to plot  H ( f ) vs. f 0 (with f in Hz) (c) Find the FS spectrum at the output of the circuit and verify that it represents approximately a 10000 Hz sinusoid (d) Find the total harmonic distortion of our resultant sinusoid. Total Harmonic Distortion (THD) is used in practice to measure the quality of a sinewave generator (a perfect one has 0% THD). THD is also used measure the quality of a linear system (e.g., an audio amplifier): you put a sinusoid in and should get a sinusoid of the same frequency out but if the system is nonlinear youll get power at other...
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This note was uploaded on 02/29/2012 for the course EECE 301 taught by Professor Fowler during the Fall '08 term at Binghamton University.
 Fall '08
 FOWLER
 Frequency

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