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Should I now expand the Thévenin expression, first it's likely that I make mistakes while expanding the equations but, second, I will need more time to format the expression in a nice low-entropy format.%% Circuit constants R = 10000 C = 22e-9 %% Set up transfer function % Create "s" as a transfer function for use later s = tf ( 's' ) % Use s to generate transfer function for circuit H = ( s * R * C ) / ( s * R * C + 1 ) % Generate list of frequencies must use angular frequencies in bode command F = logspace ( 1, 5, 1000 ) Omega = 2 * pi * F % Use bode command to analyze transfer function = bode ( H, Omega ) HMag = squeeze ( HMag ) HPhase = squeeze ( HPhase ) %% Make plot figure ( 1 ) clf % Magnitude plot on top subplot ( 2, 1, 1 ) semilogx ( HOmega, 20 * log10 ( HMag ), 'k-' ) xlabel ( '\omega, rad/s' ) ylabel ( '|H|, dB' ) % Phase plot on bottom subplot ( 2, 1, 2 ) semilogx ( HOmega, HPhase, 'k-' ) xlabel ( '\omega, rad/s' ) ylabel ( '\angle H, rad' ) Estimates from Time Series Data

If I count the time needed to determine the expression using FACTs, it does not exceed a few minutes. As shown in the below plots, all three expressions deliver the exact same response: As I said, should you spot a small deviation, then review the individual sketches and fix the guilty one without restarting from scratch as any other analysis would require:īecause the roots are real in this circuit (the quality factor is low), you can try to model the transfer function with two cascaded poles and a zero. I usually build a high-entropy expression obtained with Thévenin in this case and make sure both answers are rigorously similar in magnitude and phase. This is it, we have everything to be happy and a Mathcad sheet can check these results. The methods relies on determining the time constants when the stimulus - \$V_\$. However, and it could be the issue for an exam, I am not sure if the person who reviews your contribution will recognize it as a valid method as he/she perhaps expects the classical KVL/KCL approach.

If you want to be fast and be efficient to determine transfer functions, there is no other way than resorting to the fast analytical circuits techniques or FACTs that I describe in my book on the subject.