# Complex characteristic impedance and scattering matrix formulation

1. ## Complex characteristic impedance and scattering matrix formulation

Dear Microwaves Colleagues,

An issue with complex characteristic impedances has 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.

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2. ## Re: Complex characteristic impedance and scattering matrix formulation

Nobody ? ;(

Finally, we have chosen to stick with Power Waves definition, since most users are waiting for such results...

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4. ## Re: Complex characteristic impedance and scattering matrix formulation

Originally Posted by pancho_hideboo
Thanks, I'm aware of this thread, which I saw before posting this one.

But that does not answer my main question: are you aware of EDA softwares implementing pseudo-wave formulation?

Both ADS and ANSYS Circuit uses Power-Waves definitions. In order to compare Pseudo-Wave implementation in scikit-rf package, I need to compare with results obtained with such a definition.

5. ## Re: Complex characteristic impedance and scattering matrix formulation

Originally Posted by Hash
But that does not answer my main question:
are you aware of EDA softwares implementing pseudo-wave formulation?

Keysight ADSsim and Momentum : Power-Wave Formulation
Keysight EMPro : Pseudo-Wave Formulation

6. ## Re: Complex characteristic impedance and scattering matrix formulation

Originally Posted by pancho_hideboo
Keysight EMPro : Pseudo-Wave Formulation
Thanks. Do you, or someone here, have this software?

I would be interested in the following test : let's assume a 2 port network of S-parameters (defined for 50 ohm reference impedance) at 75.8 GHz

Code:
```[[-0.194 - 0.228j, -0.721 + 0.160j],
[-0.721 + 0.160j, +0.071 - 0.204j]]```
what would be the renormalized scattering matrix under a reference impedance of

Code:
`z_ref = 100 + 10j`
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7. ## Re: Complex characteristic impedance and scattering matrix formulation

There is no practical value to study S-Parameters for complex reference impedance.

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8. ## Re: Complex characteristic impedance and scattering matrix formulation

Originally Posted by pancho_hideboo

There is no practical value to study S-Parameters for complex reference impedance.
Well, thanks for the opinion, but anyway it can still be usefull.

For example I'm dealing with plasma, with cases of complex reference impedances. Also one can model matching circuits using complex reference impedances.

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