determination characteristic impedance

How would you obtain the characteristic impedance (Zo or Zc) of a microstrip (or any 2-port network for that matter) from its scattering parameter 2x2 matrix ( [s11 s12 ; s21 s22] ) alone ?

Thanx in advance............

From the magnitude of S11 or S22, you can determine ZC. Unfortunately, there are two equally valid solutions, one >50 ohms, and one <50 ohms, so you have to determine which solution is correct.

Can you elucidate on the method using magnitudes please?

I have a simulation software to cross check with - so no probs there :)

Plot your measurement in the smith chart. It circles around Z0. But that is only in case your reference impedance is well defined as in SOLT calibration. For TRL calibration your reference impedance is the characteristic impedance of your calibration lines.

I more specifically want a hand-calculation method to get Zc from S parameter data at a given frequency . i.e from just one given 2x2 s-parameter matrix

If you have a transmission line and either measure its S11 on a 2 port network analyzer, or measure its reflection coefficient when a 50 ohm load is attached to the far end of the line, you will measure a reflection coefficient:

Γ = (Zl-Zc) / (Zl + Zc) = (50-Zc) / (50 + Zc).

Make the measurement, perform the above complex math, and you can deduce your characteristic impedance Zc.

Thanks a lot for the method ..........

But if i'm not wrong there is a method of converting s-parameters to ABCD matrix partially and obtain Zc by comparing elements to the transmission line form of ABCD matrix? I tried but i'm only getting Beta (or complex gamma) from it by comparing A and D - B & C still depend on Zc - and i'm not able to proceed to obtain Zc.