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FourAna.II - L303.9.V5 Drexel University Electrical and...

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L303.9.V5 9-1 Drexel University Electrical and Computer Engineering Dept. Electrical Engineering Laboratory III, ECEL 303 E. L. Gerber FOURIER ANALYSIS and THIRD_ORDER FILTER DESIGN and ANALYSIS Object The object of this experiment is to become familiar with some properties of the Butterworth third-order filter. Then you will design a filter and observe the effect that the filter has on the frequency content of a periodic signal passing through it. Both computer simulation and real circuits will be examined. Theory Consider the third-order low pass filter below. The transfer function of an ideal third-order Butterworth filter (see the Appendix Eqs. 5 and 10) is written in terms of the corner frequency, C = 2 π f c , rad/sec., and its magnitude is, H ( s ) = C 3 s 3 + 2 Cs 2 + 2 C 2 s + C 3 abs [ H ( f )] = 1 1 + ( f / f c ) 6 Third-Order Filter #2. We can determine the output, v o (t), of this filter with a unit square wave input, as we did last week. We can calculate the output voltage at each of the harmonic frequencies of the Fourier series of the input. The solution to this system is much more complicated than the first-order filter that we did last week. So we can use Maple to solve the third-order transfer function H 3 (s) of this filter. Maple can then be used to solve for the output terms as was done in the first-order circuit earlier. Use the magnitude expression H(f) to solve for the values of H at the first ten non-zero terms. In order to obtain the output waveform from these terms
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L303.9.V5 9-2 you must sum the various terms with the appropriate phase and frequency. This can be accomplished in Maple by combining (sum) the magnitude of the transfer function with the Fourier series terms including the phase of the transfer function. That is, at each frequency
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