[SOLVED] Scattering matrix cascading : simple case with Ansoft Designer & HFSS

[Hash]

Hello everyone,


I'm trying to understand how Ansoft Designer makes the link with HFSS when one uses the "push excitation" command.

My final goal is to plot with HFSS the electric field into an antenna which is loaded by a complex admittance (actually, a plasma). HFSS can't calculate this particular admittance (the medium in front of the antenna is a complex full tensor permittivity...), but I have a code which do it very well : this code gives me the scattering matrix of this load. Ansoft designer seems adapted to my problem, since I can easily import a scattering matrix and connect it to the ports of my antenna. Using the "push excitation" option in Designer, I should obtain the correct loading into HFSS, then the correct Efield.



Anyway, before going into complex things, I'd tried to model a simple case : a rectangular waveguide connected to a complex load. This problem can be solved by hand (see also attached for a presentation of the test case)

Let \[ \left[ S^{WG} \right] \] the scattering matrix of a regular section of a rectangular waveguide. I've modelled a simple rectangular waveguide in HFSS and solve for a frequency : as expected, the scattering matrix is close from the ideal case which is \[S^{WG}_{11}=S^{WG}_{22}=0\] and \[S_{12}^{WG}=S^{WG}_{21}=1\]

Let \[ S^{L} \] the scattering parameter of a complex load. For example, I took \[S_L=0.5+0.3i \].

Using the network theory, one founds that the reflected power \[a^{WG}_2\]wave from the load into the waveguide is :
\[a_{2}^{WG} = b^L = S^L a^L = S^L b_2^{WG}=S^L (S_{21}^{WG} a_1^{WG} + S_{22}^{WG} a_2^{WG}) \approx S^L a_1^{WG}\]
(see the attached .ppt for a sketch)
Thus, using the scattering parameters of the waveguide calculated by HFSS, I find :
\[a_2^{WG} \approx ~ (0.5+0.3i)*(0.9678-0.25103i) = 0.5593 + 0.1649i = (0.583, 16.42°) \]

According to the HFSS documentation, the "scaling factor" should be :\[SF=1/2 \left|a_2^{WG}\right|^2\]
which should give :

1/2*abs((0.5+0.3i)*(0.9678-0.25103i))^2=0.1699

However, using Designer and pushing excitation in HFSS, I find a scaling factor of SF=0.2596 ! (And a non-zero phase, which I do know how Designer/HFSS calculate it...)

Is someone here know what's wrong with this simple test case ?

I've attached the Designer and HFSS file in case.

Many thanks in advance,

Best regards

 

[Hash]

Hello,


Anyone who master scattering parameters definition in HFSS & Designer ? Even the HFSS support don't want to help me !


Best regards,

 

[ksugahar]

The definition of the scattering parameters in HFSS and Designer is common, not so special.

 

[Hash]

Hello,

The definition of the scattering parameters in HFSS and Designer is common, not so special.

What do you mean ?

I agree with you on the fact that the HFSS (& Designer) definition of the S parameters is common. However, the link between S-parameters and 'Scaling Factor' is not clear (to me for sure). Using basic S-matrix algebra, I can't find the same results with a simple model.

 

[drops]

For 1W input power, a1 = sqrt(2) + 0*j (and not 1)
This is because:
P_incident = |V+|² / (2*Zo) (V is peak value)
and
an = Vn+ / sqrt(Zo)

This still does not give the same values as HFSS.
Are all of your ports (in HFSS and designer) normalized to the same impedance (e.g. 50 Ohm)?

Best regards

 

[Hash]

Hello, and thank you for your answer,

For 1W input power, a1 = sqrt(2) + 0*j (and not 1)
This is because:
P_incident = |V+|² / (2*Zo) (V is peak value)
and
an = Vn+ / sqrt(Zo)

Did you took these definitions in Designer or HFSS's help ?

HFSS's support gives me the following explanation, which should come from the help (but I didn't managed to find it!)

In the simple one-port case, S11 relates an incident mode to a reflected mode in the manner

b = S11 a

where "a" and "b" are complex numbers representing the inward and outward travelling modal fields.

The total voltage V at the port plane is related to a and b using the port impedance Zo:

V = sqrt(Zo) (a + b)

Combing the above two equations gives the expression for V in terms of a:

V = sqrt(Zo) (1 + S11) a

When Designer pushes V, the quantity a is computed by solving this expression for a in terms of V, Zo, and S11. The displayed Edit-Sources scaling factor is then

Scaling_Factor = 0.5 * |a|^2

The 0.5 factor is applied since the incoming voltage V is a peak-phasor quantity and HFSS operates using RMS phasors. The physical interpretation of the Scaling_Factor here is the incident modal power due to the source in Designer.

Are all of your ports (in HFSS and designer) normalized to the same impedance (e.g. 50 Ohm)?

In Designer, in the "port definition", I've checked the "one port data" option of the HFSS model, i.e. Designer should use the characteristic impedance of the HFSS model. So, if I'm right, the characteristic impedances should be the same.

 

[drops]

Both formulas are from this lecture note:
**broken link removed**

 

[Hash]

Both formulas are from this lecture note:
**broken link removed**

OK.

Because the definition of general scattering parameters may vary from a software to an other.

In HFSS's help, S parameters are defined in a modal way :

At each port, the modal representations of the electric and magnetic fields assuming K modes are:

\[E = \sum_{m=1} (a_m+b_m) e_m\]
\[H = \sum_{m=1} (a_m-b_m) h_m\]

where am and bm are unitless complex amplitudes of the incident and reflected modal fields, respectively. Given a particular electromagnetic structure, it can be categorized in terms of the incident and reflected/transmitted modal amplitudes using the NxN generalized S-matrix, S:
\[b=Sa \]
where a and b are unitless complex modal coefficient vectors. The size of these vectors, N, is the total number of modes obtained by adding up the number of the modes on all ports.

Digging in the help, I can only find that concerning the scaling factor in the Edit Source menu:

• The excitation’s magnitude specifies time-averaged incident power in watts.
[...]
• Generally, use the default value of 1. This specifies that the solution’s E- and H-fields be scaled such that the excitation wave delivers 1 watt of power. To view the solution at some other power, enter a positive value.

what is really unclear to me, is relationship between the unitless complex amplitudes of the incident (and reflected) modal fields am (and bm) and the scaling factor. And finally, how the scalling factor are calculated from Designer ?

 

[drops]

I have found a way to calculate ScaleFactor / OffsetPhase, using Qucs:
Qucs project: Quite Universal Circuit Simulator
It works for my project.

 

[Hash]

Thank's a lot for digging this problem. Actually, I've drop this problem but I didn't found the solution. I'll recontact the HFSS support.

I didn't know this software. I'll look at it, thank you !

 

[Hash]

I have found a way to calculate ScaleFactor / OffsetPhase, using Qucs:
Qucs project: Quite Universal Circuit Simulator
It works for my project.

Looking at your results, I've a few comments/questions :
- The frequency used in my test case is 3.7 GHz (in your file, the power source was @1GHz, but the results is the same : what mean this parameter ?)
- The offset phase sign in HFSS is defined by the sign of the port field line. So a +/- 180° difference is understable.

Thus, I've also found a scaling factor of 0.34, exactly half of the scaling factor defined in the HFSS doc... That would means that there is something wrong the HFSS doc. Anyway, this is not the result that Designer find... So I still do not understand...

Some extra comment:
- In fact, the port impedance may also be defined as the characteritic impedance of a rectangular waveguide ? (for the fundamental mode here). This characteristic impedance is Zc=455.7152 Ohm. (in your file, this was 50Ohm, the same in the S-parameters description files). The final result (traveling waves or scaling factor) is the same, since it only a matter of normalization.

 

[Hash]

OK, I've found in the Qucs documentation that the quantities are defined in RMS, not peak. This explain the factor 2 of the scaling factor.

But this still do not explain the Designer result.

PS : I've made the simulation directly with a rectangular waveguide instead of the 2port Smatrix : results are the same.

 

[drops]

- The frequency used in my test case is 3.7 GHz (in your file, the power source was @1GHz, but the results is the same : what mean this parameter ?)
- The offset phase sign in HFSS is defined by the sign of the port field line. So a +/- 180° difference is understable.

The frequency property of the power source can be ignored. It is overridden by the ac simulation block
If you define emf in the other direction, than the 180° offset disappears.

 

[drops]

OK, I've found in the Qucs documentation that the quantities are defined in RMS, not peak. This explain the factor 2 of the scaling factor.

Do you mean the paragraph
"Sometimes waves are defined with peak voltages and peak currents. The only difference that appears then
is the relation to power "
in the "technical papers? (link: **broken link removed** )
This does not refer to the measured U and I quantities as I understand.

The qucs "Workbook" (link: **broken link removed** )
says:
"Please note that all voltages and currents are peak values and all noise voltages are RMS values at 1Hz bandwidth."

 

[Hash]

Do you mean the paragraph
"Sometimes waves are defined with peak voltages and peak currents. The only difference that appears then
is the relation to power "
in the "technical papers? (link: **broken link removed** )

Yes, this is what I understood from this doc. Am I wrong ?


I've now understood how HFSS's scaling factor are calculated from Designer. The scaling factor in HFSS are:
\[SF=\frac{1}{2} \left\vert{} a \right\vert{} ^2 \]
where a is the power wave associated to a port, defined by the usual formula:
\[a=\frac{v+i Z_0}{2\sqrt{Z_0}} \]

Taking voltage and current from probes in Designer and taking Z0 as the characteristic impedance of the waveguide (265.49Ohm in my case) leads to the SF=0.26 as calculated in HFSS. OK.

But now, I'm not able to find the same result in Qucs... There is somewhere some impedance renormalization (I guess) which I do not understand...

---------- Post added at 09:11 ---------- Previous post was at 08:57 ----------

The qucs "Workbook" (link: **broken link removed** )
says:
"Please note that all voltages and currents are peak values and all noise voltages are RMS values at 1Hz bandwidth."

Well, if I apply the power wave formula of the previous post, I obtain a scaling factor of 1 as expected. If the voltages and current were peak values, then I should divide these quantities by sqrt(2), and thus I will obtain a scaling factor of 0.5.

 

[Hash]

OK, so finally I managed to find how to achieve the same results in Qucs than in Designer/HFSS.

Attached, there is 3 similar Qucs simulation file and the associated S-matrices of the waveguide and the load.

If I well understood, in order to get the same results than in HFSS/Designer, I have to:

1. The Scattering matrix of waveguide, which is a touchstone the 2-port file, must be renormalized to the characteristic impedance of the waveguide (ie adding R 265.49 in the file). Otherwise, I get SF=0.34 instead of SF=0.26.
2. The scattering matrix of the load, which is a 1-port touchstone file, must be normalized to 50 Ohm

If I'm right, based on the second item, it would means that a S-parameter device in Designer is always normalized to 50 ohm.


Moreover, this imply for Qucs that:

• In Qucs, the waveguide element is the same than the 2port file renormalized to 265.49 Ohm reference impedance (the reference impedance is the characteristic impedance of the waveguide, which is quite logical)
• In Qucs, a equation-based component defined by its S parameters assumes a 50 Ohm reference impedance (and it can't be changed to another value).

 

[Hash]

Hi,

I've finally understood the problem: in Designer, when creating a N-port bloc-device (my load in my example), Designer assumes that the S-parameters of this N-port device are normalized to 50 Ohm. It seems that it cannot be changed.

A workaround solution is to create a touchstone file with the correct characteristic impedance of the N-port defined inside, and import it into Designer. Then Designer will normalize the S-parameters of the device with the correct characteristic impedance.


Best regards,