To compare the gain of the filter at two frequencies with the theoretical gain where the theoretical Bode plot and actual gain plotted on semilogarithmic scale using “semilogx”.
You may refer to this link for more information on this function.
Matlab code and output is given below.
% Define the parameters
R = 1e3; % Resistance in ohms
C = 1e-6; % Capacitance in farads
F1 =100; % Frequency 1 in Hz
F2 = 4e3; % Frequency 2 in Hz
% Define the transfer function H
H = tf([R*C, 0], [R*C, 1]);
% Calculate the Bode plot for H
[mag, ~, wout] = bode(H);
% Convert magnitude to linear scale
mag = squeeze(mag);
% Interpolate the theoretical response at specific frequencies F1 and F2
theory_resp_F1 = interp1(wout, mag, 2*pi*F1, 'linear', 'extrap');
theory_resp_F2 = interp1(wout, mag, 2*pi*F2, 'linear', 'extrap');
% Plot the theoretical Bode magnitude plot
figure;
semilogx(wout/(2*pi), 20*log10(mag), 'g'); % Convert to Hz and dB
hold on;
% Plot the actual gain at frequencies F1 and F2
actual_gains = [theory_resp_F1, theory_resp_F2];
actual_freqs = [F1, F2];
semilogx(actual_freqs, 20*log10(actual_gains), 'ro');
% Set plot properties
xlabel('Frequency (Hz)');
ylabel('Gain (dB)');
title('Response of RC circuit');
legend('Theoretical Gain', 'Measured response');
grid on;
% Release the plot hold
hold off;
