Question about calculating HFSS Z parameter

Hallo,

with the following equation

Znorm = (identity + S) (identity - S)^-1

it is possible to calculate the normalized z matrix from a given
scattering matrix.

To get the unnormalized Z matrix, we need to left- and right-multiply
with the diagonal matrices sqrt(Z1) and sqrt(Z2).

Does HFSS use the calculated Zpi as Z1 and Z2 or ...?


Thanks

Short answer: Yes.

Not quite as short answer: the normalized Z equals (Zo)^(-1/2) * Z * (Zo)^(-1/2). You can choose between Zpi, Zpv, and Zvi definitions for Zo, but I believe Zpi is the default.

@ Wiley.

There is no problem to get the normalized impedance matrix Znorm from a calculated scattering matrix S.


Znorm = (identity + S) (identity - S)^-1


To get the unnormalized impedance matrix, we need to use the characterisitic impedance Zc

Zunnorm = Z = Zc^{1/2} Znorm Zc^{1/2}

Because Znorm = Zc^{-1/2} Z Zc^{-1/2}.
There is a discrepancy to your equation. Could you please check it again.

---


However, I extract inductance (nH) values and quality factors of
embedded inductors. I get the inductor S matrix from TRL calibration. Therefore the reference impedance equals the native impedance, which is nearly 50 ohm in my case. 52.25 Ohm for f > 2 GHz and rises up to 60 ohm for 0 <= f < 2 GHz.

The extracted quality factors differ, if I treat the s matrix from TRL as being a
50 ohm s matrix to the quality factors from HFSS, which uses the native characteristic impedances.
I try to use the Zc from HFSS in my S to Z calculation.
I think HFSS uses a bit different S to Z algorithm, which also includes the phase of Zc (< 1 degree). May be a power wave formulation.


Does anybody have information on this topic.

HI
Zpi can be looked as characteristic impedance of port, for driven modal, the structure of waveport must be alike to the actual one to make sure that the characteristic impedance of port is right. so in some band, the impedance is not 50ohm.

Regards!
Edmund

@EdmundZheng

Well, that is right, but not an answer to my question.


I have implemented S to Z parameter conversion in MATLAB and I
get different results from that calculated in HFSS.
So, I think HFSS uses an algorithm, different to the above stated one.

Thanks for any information on this topic.

greets elektr0

@ Wiley.

There is no problem to get the normalized impedance matrix Znorm from a calculated scattering matrix S.


Znorm = (identity + S) (identity - S)^-1


To get the unnormalized impedance matrix, we need to use the characterisitic impedance Zc

Zunnorm = Z = Zc^{1/2} Znorm Zc^{1/2}

Because Znorm = Zc^{-1/2} Z Zc^{-1/2}.
There is a discrepancy to your equation. Could you please check it again.

---


However, I extract inductance (nH) values and quality factors of
embedded inductors. I get the inductor S matrix from TRL calibration. Therefore the reference impedance equals the native impedance, which is nearly 50 ohm in my case. 52.25 Ohm for f > 2 GHz and rises up to 60 ohm for 0 <= f < 2 GHz.

The extracted quality factors differ, if I treat the s matrix from TRL as being a
50 ohm s matrix to the quality factors from HFSS, which uses the native characteristic impedances.
I try to use the Zc from HFSS in my S to Z calculation.
I think HFSS uses a bit different S to Z algorithm, which also includes the phase of Zc (< 1 degree). May be a power wave formulation.


Does anybody have information on this topic.

Hi
Look at online help of HFSS, you will find they implement the same algorithm, like you said above,
"Zunnorm = Z = Zc^{1/2} Znorm Zc^{1/2}
Because Znorm = Zc^{-1/2} Z Zc^{-1/2}.
"
And in HFSS, the characteristic impedance of waveport is denoted as Zpi, Zpv,Zvi.

Regards!

Edmund

electr0,

I don't see a discrepancy in the equation I wrote. It's the same as what's Edmund has written, which is the same as what's in the HFSS help.

I am not sure I follow exactly what you are asking, so let me paraphrase: You have measured S matrix of an embedded inductor, which you used a TRL calibration to removed the effect of the probes. You also have the simulated (HFSS) S matrix of the same inductor. The Q from the measured data and the simulated data do not match. Is this correct?

I doubt HFSS is converting from S to Z incorrectly.

-Wiley

@Wiley,

I think the minus in your equations is false.

(Zo)^(-1/2) * Znorm * (Zo)^(-1/2) = false
(Zo)^(1/2) * Znorm * (Zo)^(1/2) = right

It is all about how to convert S to Z parameter if the characteristic impedance
is complex. In my case it is only slightly complex, but may be enough.

ADS for example uses the power wave formalism from KUROKAWA.
Which does not provide accurate results.

I think the above equations, which are well known for years and valid for TEM waves with real impedances, are used in HFSS for real impedances.
But if you have complex ones, HFSS uses power waves.
I am not sure yet, but I will find it out.


elektr0

electr0,

Hmm, I missed your reply last time I checked the board.

1.) I wrote the equation to normalize Z, not to unnormalized Z, so the negative signs are correct.

2.) If the Zo has a very small imaginary part, there is very little difference between the S parameters from the normalized Z and Kurokawa's power wave S parameters. If you plot the two S parameters, most likely the two curves will be right on top of each other.

3.) HFSS absolutely does not use Kurokawa's definition since waveguides in cut-off have a pure imaginary Zo. In Kurokawa's definition, the S parameters do not exist. Yet my rectangular waveguide in cut-off still produces correct results.

-Wiley