Q-factor calculation

How to calculate the Q factor of a microwave resonator using matlab? From a S12 plot

Answer 1

[Xianglin]

There are several ways:

1, Use the 3dB bandwidth to calculate the Q.

2, Fit the lorranze function

Answer 2

[the cyclist]

Here is what ChatGPT suggested:

% Load S12 data (replace 'your_data.csv' with your actual file)
data = csvread('your_data.csv');

% Extract frequency and S12 data
freq = data(:, 1);
S12 = data(:, 2);

% Identify resonance frequency
[min_S12, min_index] = min(S12);
resonance_freq = freq(min_index);

% Calculate bandwidth at -3 dB points
dB_3 = min_S12 - 3;
[~, lower_index] = min(abs(S12(1:min_index) - dB_3));
[~, upper_index] = min(abs(S12(min_index:end) - dB_3));
bandwidth = freq(upper_index + min_index - 1) - freq(lower_index);

% Calculate Q factor
Q_factor = resonance_freq / bandwidth;

disp(['Resonance Frequency: ' num2str(resonance_freq) ' Hz']);
disp(['Bandwidth: ' num2str(bandwidth) ' Hz']);
disp(['Q Factor: ' num2str(Q_factor)]);

Answer 3

[the cyclist]

Here is what the MathWorks AI Chat Playground suggested:

% Step 1: Load S12 data
S12_data = [freq, S12]; % Replace freq and S12 with your actual data

% Step 2: Fit a curve to the S12 data
fit_result = fit(freq, S12, 'gauss1'); % Replace 'gauss1' with the appropriate curve fitting function

% Step 3: Extract resonant frequency and bandwidth
resonant_freq = fit_result.b1; % Replace b1 with the appropriate parameter name from the fit result
bandwidth = 2 * sqrt(log(2)) * fit_result.c1; % Replace c1 with the appropriate parameter name from the fit result

% Step 4: Calculate Q factor
Q_factor = resonant_freq / bandwidth;

% Display the Q factor
disp(['Q factor: ', num2str(Q_factor)]);