How to calculate S11 from time domain response (TDR)?

Hello!

There is an example of calculating the response in the time domain (TDR) for a given reflection coefficient (S11) - https://www.mathworks.com/help/rf/ug/modeling-a-high-speed-backplane-part-3-4-port-s-parameters-to-differential-tdr-and-tdt.html.

How to solve the inverse problem - to find the reflection coefficient (S11) from the time domain response (TDR)?

Answer 1

[Ayush Modi]

Hi Stepan,

You can calculate the S11 parameter from tdr data by performing Fourier Transform analysis. Here is an example to demonstrate how you can achieve this:

Step 1: Calculate Hann window using "hann" function.

windowed_tdr = tdr .* hann(length(tdr));

Step 2: Calculate fourier transform uisng "fft" function.

% Calculate fft
fft_result = fft(windowed_tdr);

% Process the FFT result
% Normalize the frequency axis
Fs = 1 / (t(2) - t(1)); % Sampling frequency, assuming uniform time step
n = length(fft_result); % Number of points in FFT
f = (0:n-1)*(Fs/n); % Frequency vector

% Scale the FFT result to account for the length of the signal and the window function
fft_scaled = fft_result / (sum(hann(length(tdr))) / length(tdr));

Step 3: Extract s11 parameters

% Extract S11
s11 = fft_scaled(1:n/2); % Take only the first half of the FFT result
s11_magnitude = abs(s11); % Magnitude of S11
s11_phase = angle(s11); % Phase of S11

Please refer to the following MathWorks documentation for more information on:

• hann - https://www.mathworks.com/help/signal/ref/hann.html
• ftt - https://www.mathworks.com/help/matlab/ref/fft.html

Hope this helps!