RC_integrator.m

clear; clc; close all;

% Parameters
wp = 1;   % rad/s

% Frequency axis
w = logspace(-2, 2, 1000);

s = 1j*w;

% Transfer functions
H1 = wp ./ s;          % lossless integrator
H2 = wp ./ (s + wp);   % lossy integrator

% Magnitude (dB)
mag1 = 20*log10(abs(H1));
mag2 = 20*log10(abs(H2));

% Phase (deg)
ph1 = angle(H1)*180/pi;
ph2 = angle(H2)*180/pi;

% Plot
figure;

% ---------------- Magnitude ----------------
subplot(2,1,1);

semilogx(w, mag1, 'LineWidth', 2); hold on;
semilogx(w, mag2, 'LineWidth', 2);

% Vertical line at wp
xline(wp, '--k', '\omega_p', ...
      'LineWidth', 1.5, ...
      'LabelVerticalAlignment', 'middle');

grid on;
xlabel('\omega (rad/s)');
ylabel('Magnitude (dB)');
title('Magnitude Response');

legend('\omega_p/s', '\omega_p/(s+\omega_p)', ...
       'Location', 'southwest');

% ---------------- Phase ----------------
subplot(2,1,2);

semilogx(w, ph1, 'LineWidth', 2); hold on;
semilogx(w, ph2, 'LineWidth', 2);

% Vertical line at wp
xline(wp, '--k', '\omega_p', ...
      'LineWidth', 1.5, ...
      'LabelVerticalAlignment', 'middle');

grid on;
xlabel('\omega (rad/s)');
ylabel('Phase (deg)');
title('Phase Response');

legend('\omega_p/s', '\omega_p/(s+\omega_p)', ...
       'Location', 'southwest');