Dear Microwaves Colleagues,

An issue with complex characteristic impedances as recently been reported with the RF Python package scikit-rf, which has led to many discussions. Maybe people here would have interesting advices or comments about that problem, which is the following.

Most EDA softwares, such like ADS or ANSYS Circuit implement power-wave formulation of the scattering parameters, and not the pseudo-wave formulation. The differences between these two formulations have been discussed since long in the literature (see [1]-[2] for instance for pro-pseudo waves, [3]-[4] for pro power-waves), each having advantages and inconveniences. However, when characteristic impedance are real valued, there is no difference between these two formulations.

However, when the characteristic impedances are complex valued, differences should appear. In particular, from ref [1] it is said that when using pseudo-waves with complex-valued reference impedances, the electromagnetic reciprocity condition does not necessarily mean that the scattering matrix is symmetric. But, even complex-valued reference impedances, EDA software like ADS and ANSYS always give symmetric S matrices...

So, my question is, are you aware of EDA softwares implementing pseudo-wave formulation?


[1] R. B. Marks et D. F. Williams, « A general waveguide circuit theory », J. RES. NATL. INST. STAN., vol. 97, nᵒ 5, p. 533, sept. 1992, doi: 10/gf3wcs.
[2] D. Williams, « Traveling Waves and Power Waves: Building a Solid Foundation for Microwave Circuit Theory », IEEE Microwave Magazine, vol. 14, nᵒ 7, p. 38‑45, nov. 2013, doi: 10/ggc2zn.
[3] J. Rahola, « Power Waves and Conjugate Matching », IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 55, nᵒ 1, p. 92‑96, janv. 2008, doi: 10/fgnf7j.
[4] S. Llorente-Romano, A. Garca-Lampérez, S. H. Yeung, T. K. Sarkar, M. Salazar-Palma, et S. W. Ting, « Characterization of Microwave Circuits: S-Parameters », in Wiley Encyclopedia of Electrical and Electronics Engineering, Hoboken, NJ, USA: John Wiley & Sons, Inc., 2015, p. 1‑18.