how to calculate s parameters

EM solvers like HFSS, CST MWS, IE3D, ADS Momentum etc can easily calculate multi-port S-parameters over a large frequency range. Does anyone implemented or knows the detailed similar algorithms to extract the S-parameter using some numerical methods like RWG based triangle-discritized patch using MOM?

There are a lot of detailed publications talking about the calculation of the far-field from the obtained current density coefficients in the scattering/radiation area, but little was found to get the S-parameters for the simple RF/microwave circuits such as microstrip filters, baluns, couplers etc.

Thank you in advance for your reply and sharing of the experience, if any!

Hi, Smithchart:

There are many ways. I documented a few ways in my Ph.D. thesis (Jian-Xiong Zheng, Dept. of ECE, Univ of Coloardo at Boulder, 1990). Some of them are from other users and some of them came up to me. One simple way I came up was the 3-point method:

You solve the current at 3 uniformly spaced points Ja, Jb, Jc. The current should be free of higher order modes.

J = a * exp ( - gamma * z ) - b * exp( gamma * z )

If you calculate (Ja+Jc) / Jb, you will be able to find gamma. From gamma, you can find a, and b.

This will allow you to find the relative incident and reflected wave on one port at an excitation state. Using some linear algebra, you will be able to find the s-parameters of a general N-port structure. The detail is in my thesis. Interestingly, I even do not keep a copy of it.

Best regards,

Dear Jian:

Thanks a lot for your information. Is your thesis named as "Electromagnetic Modeling of Microstrip Circuit Discontinuities and Antennas of Arbitrary Shape" ?

Really unfortunate that I googled for it in vain for quite a long time.

Again. Thank you just the same for your reply and the "hints".

Best regards.

Hi, Smithchart:

I think it is close. Thanks!

Best regards,