# s21(transform freq vs phase to time vs log magnitude)

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#### aboosama

##### Newbie level 2
any body can help to transform from freq vs phase to time vs log magnitude for s21 by using matlab or mathcad.

Heya aboosama - I'm not sure what you're asking for is valid. S-parameters are defined as steady-state wave scattering parameters, and are assumed to be time-independent.

A possible exception (interpretation) of time-dependence is in performing TDR (time domain reflectometry) with network-analyser measured S parameters. This involves constructing a time domain solution by applying the inverse FFT of the frequency-domain S-parameters. A *brilliant* set of MATLAB scripts for this (and other tasks) is located on the Mathworks file exchange: https://www.mathworks.com.au/matlabcentral/fileexchange/22996-rf-utilities-v1-2

If you're just interested in the log magnitude value of the complex s21 quantity, then you can plot this with plot(20*log10(abs(s21)));

thank you mr thylacine1975 for your fast response ,Im using VNA as gpr (ground proping radar) i tried to determine the locations of targets under ground from the transmission coffetionet S21 between two antennas from the phase vs freq graph of s21.

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so i have data (freq 3.6Ghz-7.6Ghz with step 40Mhz) 105 point and each freq has its corrspponding phase,i want to plot log magnitude vs time to get the refflections time to determine the distance of the target.

Ah! The TDR tools I mentioned will probably get you a good way there... perhaps something along the lines of this after you install the RFutils:

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path(path, 'C:\Program Files\MATLAB\R2010a\toolbox\RFutils');
path(path, 'C:\Program Files\MATLAB\R2010a\toolbox\RFutils_M');
path(path, 'C:\Program Files\MATLAB\R2010a\toolbox\RFutils_S');

Er = 2.7;  % Effective permittivity of propagation path
Zo = 50;   % Ohms (VNA reference impedance)

Zin  = Zo*(1+S11)./(1-S11);
[distance, Reff] = tdr(Zin, Zo, Er, freq);  % Units: dist = mm, R = ohms

Where S11 is the (complex mag/phase) one port reflection coefficient VNA measured data (at frequencies 'freq'). I know your application involves the measurement of S21, but I expect you'll see 'features' (variations in the output Reff) at the correct places (i.e. distance) with the S21 data set. Happy experimenting!

P.S. This might be of interest too: http://www.glcharvat.com/Dr._Gregory_L._Charvat_Projects/Cantenna_Radar.html

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