R,L,C and G calculation from S-parameters

I am trying to calculate Zo, R, L, C and G as a function of frequency of a transmision line from measured s-parameters.

I am using the following formulas,

, (1+S11)^2+S21^2
Zo^2 =Zr^2 ---------------------
′ ′(1+S11)^2-S21^2

′ ′ 1-S11^2+S21^2
gamma*length =-log( --------------------- ± K)
, 2*S21

, (S11^2-S21^2+1)^2-(2*S11)^2
where K = (---------------------------------------)^1/2
, (2*S21)^2


R + jwL = gamma*Zo
G + jwc = gamma/Zo

The problem is at some points in the frequency plot the R,L,G and C values jump from one value to the other. Sometimes I get negative values.

Has anyone used these formulas before? if so any suggestions or if there are other formulas.

Thanks

Don't have time to check your equations for correctness. However, you can get Zo and gamma*L from my paper:

J. C. Rautio, "A New Definition of Characteristic Impedance," MTT International Symposium Digest, Boston June 1991, pp. 761-764.

Basically, convert to ABCD parameters and then the Zo and sin(gamma*L) are very easy to get. If you get non-physical vaules from your measurement data, that means that measurement data is bad, or how you did your code is bad. You can check your code by taking S-parameters from any of the circuit theory tools, like AWR or Agilent/Eagleware.

If you can not get a copy of the paper, give me your email address and I will send you a pdf.

Thanks Rautio,

I got your paper. I will try as you said.

Are AWR and Agilent/Eagelware free software tools. Where can I get them?

I think AWR at least has a free download demo, but not sure. You can download the free Sonnet Lite and use the EM analysis for S-parameters, or you can use the nice little netlist analysis tool that is part of Sonnet.