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S parameters at very low frequencies

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Nov 8, 2022
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I use the Cadence PowerSI Model Extraction tool to get the S-parameters of a small and simple PCB.
this PCB is roughly a simple wire connecting 1 input connector to 1 output connector for 6 channels (then 12 connectors in total).
this PCB is about 15cm x 10cm large.

I'm surprised that the Model Extraction tool gives me different S-parameter phases (between -180° and + 180° depending on simulation options) for very low frequencies, let's say below 1Hz.
for me, at very low frequencies, the insulation is almost a leakage (big) resistor and the conductors are not inductive anymore, and then they are (small) resistors too.
in addition, the delay due to the size of the board is at the nanosecond scale and should not bring any phase difference for 1Hz waves.

then, all the S-parameters in transmission should have a phase equal to zero at low frequencies.

do you think this conclusion is correct?
do you have any idea why this kind of software, dedicated to S-parameter extraction, can make such an error and how to correct it?

thanks for your thoughts and help
best regards

I'm surprised that the Model Extraction tool gives me different S-parameter phases (between -180° and + 180° depending on simulation options) for very low frequencies, let's say below 1Hz.
For which parameter is that? S11,S22 or S21,S12?

Can you shown an example for such S matrix data?

Hello Volker,
thank you for your interest.
maybe I'm wrong but I would say that all Sij parameters should have a quasi-DC phase at 0.

here is a schematic of the board with its 12 ports,
the Sii parameters with a phase at 0 in DC,
and the Sij (with i different than j) parameters which have a phase at 0 or 180° in DC
(the Cadence tool provides several different phases between 0 and 180° if one selects different options).


  • Board schematic.png
    Board schematic.png
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    Sii phase.png
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    Sij phase.png
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maybe I'm wrong but I would say that all Sij parameters should have a quasi-DC phase at 0.

don't forget that reflection values at DC are close to perfect match for lossless lines, and you start to see very minor numerical precision errors. Let's call that numerical noise. Simulation results will never give you an exact zero reflection, and that very-close-to-zero result will have some very very small real and imaginary part (numerical noise). Essentially for such a location exactly at the centre of Smith Chart you would see the "phase of numerical noise" in reflection, i.e. phase random values.

For lossy lines, input impedance into the lines at DC is port impedance plus ohmic resistance of the line, so we have some small, well defined reflection coefficient in the right part of Smith chart and reflection phase would be 0 then.

For coupling between lines, I would expect similar numerical issues like reflection in lossless lines: you are down in numerical noise and thus calculated phase is random.

I agree that the tool could try to detect the special case (DC) and enforce zero phase, or enforce continuous phase extrapolation when going down in frequency. Some EM tools do that, but obviously yours gives you the plain numerical results with no such cosmetic correction. The question is if that gives any trouble further down the design flow?

Hello Volker,

thank you for your answer.
your explanation makes sense.

as I would like to extract an electronic model to import into some spice simulator, I would prefer to have a correct DC model if I want to do some time simulations.

I will try to load the raw S parameters and "correct" them to have a proper DC phase before converting them into an electronic model.
I hope it is doable :)

thanks again
best regards

Hello again,

you also might want to look at Broadband SPICE by a company Sigrity (acquired by Cadence).

I looked at that tool long ago for the same task: get meaningful circuit models from S-parameters that are not perfect. My EM tool supplier (Sonnet) later developed their own SPICE extraction, so I haven't used the Sigrity tool since then, but it might be a solution for your case.

Good luck!

Unfortunately, I already use Sigrity as the PowerSI tool is integrated into it... but I'm not an expert of it.
I tried to change several options and there is even a DC fitter that I use to calculate a DC response for the PCB and to change the S parameters simulation according to its results. thanks to this DC fitter, the DC phase of the PCB is not random anymore but is 0 or 180° :-(

I have some Matlab toolboxes to import/export Touchstone files used by Sigrity and the tool which converts S parameters into an electronic model, so I think I can do the correction "manually" by myself.

thanks for your help

I wonder if the phase of Sij for effectively uncoupled ports (|Sij| = 0) is of any practical relevance? I guess not.

It makes more sense to look at complex S values. For |S| < numerical resolution, phase of S has no information.

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