# HW4_S - clear all close all define system b =[1,8 a =...

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DKL:3/2/10 HW 4 1/3 HW 4 ECE 3704 Due 3-4-10 When drawing Bode plots: 1. You must use semilog graph paper (See Scholar). 2. You must use a straight edge. 1. (10) Draw the straight line approximations of the magnitude and phase Bode plots for the transfer function Y ( s ) X ( s ) = sL R + sL = s s + R L , R L = 10 Solution Y ( s ) X ( s ) = sL R + sL = s s + 10 = ( s ) 1 10 1 s + 10 20log(0.1) = 20 dB

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DKL:3/2/10 HW 4 2/3 16.4.1 (a) (20) Draw the straight line approximations of the magnitude and phase Bode plots for the transfer function H ( s ) = ( s + 8) ( s + 0.5)( s 2 + 2.4 s + 4) (b) (5) Verify the approximations with MATLAB. Include plots. See Sec 16.4.3. Solution H ( s ) = ( s + 8) ( s + 0.5)( s 2 + 2.4 s + 4) = 8 (0.5)(4) s + 8 8 0.5 s + 0.5 4 s 2 + 2(.6)(2) s + 2 2 20log(0.4) = 12 !" ! # !" ! ! !" " !" ! !" # ! !"" ! \$" " \$" %&’()’*+,- &/012’+ 03 4/5*67)0’ 89:7 %:& 8&:;9’< # !" ! # !" ! ! !" " !" ! !" # ! ="" ! #"" ! !"" " %&’()’*+,- &/012’+ 0’5 8>/2’ 89:7 %:& 8&:;9’< #
DKL:3/2/10 HW 4 3/3 % P16_4_1bv.m

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Unformatted text preview: clear all close all % define system b = [1,8]; a = conv([1,2.4,4],[1,0.5]); h = tf(b,a); w = logspace(-2,2,300); % frequency vector [mag,phs] = bode(h,w); % calculate bode plots mag = squeeze(mag); phs = squeeze(phs); magdb = 20*log10(mag); % calculate magnitude in dB subplot(2,1,1) semilogx(w,magdb,'k','linewidth',2); grid xlabel('frequency, rad/sec') ylabel('dB') title('Magnitude Plot for Problem 2') subplot(2,1,2) semilogx(w,phs,'k','linewidth',2); grid xlabel('frequency, rad/sec') ylabel('deg') title('Phase Plot for Problem 2') 20log(0.1) = − 20 dB s 10 s + 10 1 10 100 0 -20 90 0 dB Deg -90 s 10 s + 10-20 10 20-30-40 0.1 1 10 100-50 20log(4) = 12 0.5 s + 0.5 4 s 2 + 2( .6)(2) s + 2 2 dB ω-180-135-90-45 45 90 0.01 0.1 1 10 100 deg ω 0.5 s + 0.5 4 s 2 + 2(.6)(2) s + 2 2...
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