Ecel303_lab9se_Final - TITLE Fourier Analysis and Filter Design NAME Seher Ahmad PARTNER Palak Chandra TA Elaine Garbarine SECTION ECEL 303-061

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Unformatted text preview: TITLE: Fourier Analysis and Filter Design NAME: Seher Ahmad PARTNER: Palak Chandra TA: Elaine Garbarine SECTION: ECEL 303-061 DATE PERFORMED: 06/01/2007 DATE DUE: 06/08/2006 DATE RECEIVED Drexel University Electrical and Computer Engineering Dept. Electrical Engineering Laboratory III, ECEL-303 FOURIER ANALYSIS AND FILTER DESIGN OBJECT The object of the experiment was to become familiar with the Fourier series representation of a periodic wave and the effect the number of terms has on accuracy of the Fourier series. This was done by calculating the Fourier series of a periodic square wave followed by the design of a 3 rd order Butterworth filter and the effect it has on the periodic signal. Real and computer simulations were performed to gain an in-depth understanding. CIRCUIT DIAGRAMS Circuit Diagrams & Figures Fig. 1. Effect of an ideal low-pass filter Seher Ahmad and Palak Chandra, June 1 st , 2007 Fig. 2. Low-pass RC filter Seher Ahmad and Palak Chandra, June 1 st , 2007 DATA and CALCULATIONS HAND CALCULATIONS Calculation of Resistance and Capacitance for a Butterworth Filter R 1 = (0.75) * ω c * L = (0.75) * 2 πf c * L = (0.75)* (6.28)*(900Hz)*(100mH) = 423.9 Ω (1) C 1 = (0.5) /( R 1 * ω c ) = (0.5) /( R 1 * 2 πf c ) = (0.5)/ (423.9 Ω*6.28*900 Hz) = 208.6 nF (2) C 2 = (1.5) /( R 1 * ω c ) = (1.5) /( R 1 * 2 πf c ) = (1.5)/ (423.9 Ω *6.28*900) = 626.07 nF (3) THEORETICAL/CALCULATEDVALUE MEASURED/ACTUAL VALUE R 1 (in Ω) 423.9 446.5 C 1 (in nF) 208.6 209.5 C 2 (in nF) 626.07 685.7 (476.3 and 209.4 connected in parallel) L (in mH) 100 (assumed) 97.2 Table 1: Values of circuit elements for the 3 rd order Butterworth Filter Obtained by Seher Ahmad and Palak Chandra on 06/01/2007 Calculation of the expression for Transfer Function and its absolute value H(s) = (C^3)/ [s^3 + 2Cs + 2C^2s+ C^3] = (5652)^3/[s^3 + 2*(5652)s ^2 + 2*(5652)^2s + (5652)^3] (4) Abs (H(f)) = 1/[square root(1+(f/fc)^6)] = 1/[square root( (1+f/900)^6)] (5) Calculation of slope From Labview Data, slope = (-43.98 –(-6.67))/(1 dec) = -37.21 dB/dec (6) From PSpice data, slope = (-61.2-(-9.58))dB/(1 dec) = -51.62 dB/dec (7) From Maple plot (slope was obtained by drawing it on the graph), slope ,...
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This note was uploaded on 12/02/2011 for the course ECEL 353 taught by Professor Gerber during the Spring '11 term at Hanoi University of Technology.

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Ecel303_lab9se_Final - TITLE Fourier Analysis and Filter Design NAME Seher Ahmad PARTNER Palak Chandra TA Elaine Garbarine SECTION ECEL 303-061

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