Frequency Response Analysis in MATLAB

Frequency Response Plots in MATLAB

Frequency response analysis shows how a system (LTI system, filter, amplifier, etc.) responds to different input frequencies. Key plots: Bode plot (magnitude & phase vs. frequency), Nyquist plot (complex plane), Nichols plot.

Key Functions

• bode(): Bode plot (mag/phase in dB/degrees vs. log frequency).
• nyquist(): Polar plot of G(jω) in complex plane.
• nichols(): Nichols chart (mag in dB vs. phase).
• freqz(): For digital filters (discrete-time).
• margin(): Stability margins (gain/phase margins).

Basic Steps

1. Define System: Transfer function sys = tf([1 2], [1 3 2]) or state-space.
2. Plot: bode(sys); grid on;.
3. Customize: Set frequency range, labels, limits.
4. Analyze: Read bandwidth, resonance peaks, phase margins.

Example Code

% Define a second-order system (low-pass filter)  num = [1];
den = [1 2 50];
% ω_n = 7.07 rad/s, ζ = 0.141  sys = tf(num, den);
% Bode plot  
figure;
bode(sys);
grid on;
title('Frequency Response: Bode Plot');
xlabel('Frequency (rad/s)');
% Or manual control  [mag, phase, w] = bode(sys);
figure;
sub
plot(2,1,1);
semilogx(w, 20*log10(squeeze(mag)));
grid on;
ylabel('Magnitude (dB)');
title('Bode Plot');
sub
plot(2,1,2);
semilogx(w, squeeze(phase));
grid on;
ylabel('Phase (deg)');
xlabel('Frequency (rad/s)');

For Digital Filters

% FIR/IIR filter  b = fir1(30, 0.3);
a = 1;
% 30-tap FIR low-pass  [h, f] = freqz(b, a, 512, 1000);
% fs = 1kHz  
figure;
plot(f, 20*log10(abs(h)));
grid on;
title('Digital Filter Frequency Response');
xlabel('Frequency (Hz)');
ylabel('Magnitude (dB)');

Applications

• Control systems: Stability, bandwidth analysis.
• Filters: Cutoff frequency, roll-off verification.
• Amplifiers: Gain flatness, phase shift.
• Power electronics: Converter transfer functions.

Pro Tips: Use bodemag(), bodephase() for separate plots. Add rlocus() for root locus comparison. Always check units (rad/s vs Hz).