Calculate Zo from S parameters

It seems like the Zo of a cable should be embedded in the 4 S parameters from a 2 port measurement. Does anyone know these formulas?

If the line is not exactly 50 ohms then it will act as a quarter wave transformer, thus S11 is a circle on the Smith chart. Read off the input impedance at -90 degrees phase of S11(Zin will be real), then Z_line=sqrt(Z_meas*50).

S11 is the input Z and S22 is the output Z, and if it's a cable S21=S12 the
loss of the cable and S11=S22.

Plot S11 & S22 on a Smith Chart and read the impeadance.
Assuming you know the Zo of you S-Par file, or assume it's 50 Ohms.

Cheers

Hi
This ADS design is for such calculation
i think this help

Hi.

You can calculate Z0 and electrical length by open/short method which is described in microwave text.

Here get two input impedances,
(1) Zshort ; Port 2 is shortened
(2) Zopen ; Port 2 is opened

Then these impedances are expressed like following.

Zshort=Z0*tanh(theta)
Zopen=Z0*coth(theta)
theta=gamma*Length

Z0=sqrt(Zshort*Zopen)
theta=arctanh(Zshort/Zopen)

It is possible to make fomulus for Z0 using Sij, but using simulator is more easy.

Note : In actual measurement, Open conditions are realized by Lamda/4 length short extension attached to port 2.