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.
For those who may be interested, we have finally decided to stick with power waves definition.
Despite being not correct in some case with complex characteristics impedance, it is the most common implementation and such the most expected results by users.
First of all, quantify your approximation : how much non-real is your caracteristic impedance ? If, for instance, my characteristic impedance is 50 + 0.1j Ohm, I would simply drop the imag part.
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