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ps3_soln

# ps3_soln - num_H =[1(L*Cp 0 den_H =[1(1/Ro/Cp R/L(1/L/Cp(1...

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EE 497E Problem Set 3 Solutions -7- Problem 1:

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EE 497E Problem Set 3 Solutions -8- Problem 1: % EE 497E Spring 2008 % Problem Set 3 Solutions % Characterstic impedenace of interconnect cables Ro = 50; % Probe Coil L = 8e-6; R = 5; % Operating frequency fo = 5e6; wo = 2*pi*fo; % Find Cp and Cs Cp = 1 /( wo*Ro*sqrt(R / (Ro - R) ) ); Cs = 1/(wo^2*L - wo*sqrt(R*(Ro-R))); % Zin(s) num_Zin = [L*Cs, R*Cs, 1]; den_Zin = [L*Cp*Cs, R*Cp*Cs, Cp+Cs, 0]; % find Zins(s) over a 500 kHz region centered at fo span = 500e3; Npts = 10000; f = fo + linspace(-span/2,span/2,Npts)'; w = 2*pi*f; s = 0 + j*w; Zin = polyval(num_Zin,s) ./ polyval(den_Zin,s); % plot real and imag parts of Zin figure(1) plot(f/1e6, real(Zin), f/1e6, imag(Zin)) ylim([-59,59]); grid ylabel( 'Ohms' ); xlabel( 'Freq [MHz]' ) legend( 'Real part Zin' , 'Imaginary part Zin'

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Unformatted text preview: num_H = [1/(L*Cp), 0]; den_H = [1, (1/Ro/Cp + R/L), (1/L/Cp)*(1+R/Ro) + 1/L/Cs, 1/(L*Cs*Ro*Cp)]; % Find the magnitude and phase [mag_H, phase_H] = bode(num_H, den_H, w); % Find the Q-factor max_H = max(mag_H); index_fo = find( mag_H == max_H ); calc_fo = f(index_fo) index_3dB_BW = find( mag_H >= max_H/sqrt(2) ); calc_3dB_BW = f(max(index_3dB_BW)) - f(min(index_3dB_BW)) Q = calc_fo/calc_3dB_BW % plot the Bode plot figure(2) subplot(211) plot(f/1e6, 20*log10(mag_H), ... f(index_3dB_BW)/1e6, 20*log10(max_H/sqrt(2))*ones(size(index_fo)), 'r' ) title( 'Bode Plot of Vi/Vnr' ) legend( 'magnitude response' , ... [ '3 dB Bw is ' , num2str(calc_3dB_BW/1e3, '%0.5g' ), 'kHz' ]) ylabel( 'Mag [dB]' ) subplot(212) plot(f/1e6, phase_H) ylabel( 'Phase [deg]' ) xlabel( 'Freq [MHz]' )...
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