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complex characteristic impedance

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elektr0

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complex reference impedance

Hallo,

embedded transmission lines (microstrip and coplanar waveguides)
in general have complex characteristic impedances Z, due to losses.

Is there any need to express the scattering matrix of such "complex lines"
with complex reference impedances, or can we still use the Touchstone
export file for real reference impedance.

Thanks for any reply.

Added after 50 minutes:

Or to mention another aspect.
In general voltage sources have complex output impedances. What to do, if we want to connecting it to a device, described by its s-matrix.
Is it possible to normalize each s-matrix in a cascade to an arbitrary real reference impedance without loosing information, even if we have to do with complex in and output impedances.
 

Hi Elektr0 -- For microwave work, you should always use S-parameters exactly normalized to 50 Ohms, with a couple rare exceptions for expert users. The problem with most EM analysis data is that a line integral of E-field (or some other equivalent calculation) results in only an approximate value for Zo. (If you don't like the value of Zo you get, just change the line integral until you are happy.) If you have an error of, say, 10% in Zo of the line (including the imaginary part), then there will be 10% error in the resulting S-parameters that have been normalized to 50 Ohms.

If you talk to EM theory guys, they frequently use S-parameters normalized to whatever Zo the line happens to be, even if they don't know what the Zo is (which is the usual case). This can result in big problems if used by a microwave designer who incorrectly thinks the data is correctly normalized to 50 Ohms. I recommend never using such data in microwave design.

I have also encountered EM theory guys who say that there is no correct definition for Zo when there is loss or when there is more than one dielectric. This is incorrect, and those who say this are simply not fully informed. Then there are others who say that all definitions are correct and any value for Zo is fine. I call these people the "equal opportunity" guys. They are also wrong. (Sorry for the blunt language, but I think it is needed.)

So, always use 50 Ohm normalized S-parameters for microwave work.

I am now in Tokyo waiting for a delayed flight to Seattle, so I might not be able to post responses for a day or two, big weather problems in Seattle, power out, tel. lines down, etc.
 

s-parameter current voltage power wave

elektr0 said:
embedded transmission lines (microstrip and coplanar waveguides)
in general have complex characteristic impedances Z, due to losses.
Is there any need to express the scattering matrix of such "complex lines"
with complex reference impedances, or can we still use the Touchstone
export file for real reference impedance.
The answer depends on the definition of S-matrix. In transmision lines theory usually it is assumed that we operate with single-mode S-matrix which is loaded with transmision lines (50 Ohms) at the ends.
In that case you must always normalize you s-matrix with proper impendance.
In EM theory S-matrix is multimoded and the reference impedance of each mode is complex and depends on freq. Such S-matrix is named Generalized, and you don't need to do any normalization at all
BUT you always have keep in your mind that output and input impedances (for each pairs of modes) of two multiplicated S-matrixes should be the same (!)
I know only one program which support generalized s-matrix, it's CST Design Studio. Surprisingly but Ansoft Designer has not such feature even HFSS is a best tool for generalized s-matrix calculation :)


Is it possible to normalize each s-matrix in a cascade to an arbitrary real reference impedance without loosing information, even if we have to do with complex in and output impedances.
No. It means that you will include between your lossy transmision lines additional one without losses. That is not corect and will cause non-existent reflections.
You have to cascade s-matrixes in generalized form (without normalization !) and then calculate complementary s-matrix which describes the transition from connecting lines (50 Ohm ?) to your actual lossy structure.
Finally you will get one s-matrix with 50 Ohms input(output) .


rautio said:
The problem with most EM analysis data is that a line integral of E-field (or some other equivalent calculation) results in only an approximate value for Zo. (If you don't like the value of Zo you get, just change the line integral until you are happy.)
The remedy is to use "power" definition of Z = P/(I^2) where
P = Int (ExH)ds - over the port surface and
I = Int (H)dl - over a path around the port
 

power waves and the scattering matrix

@navuho

Thanks.
What do you think about Power-Wave-S-Matrix and Pseudo-Wave-S-Matrix, which are valid for complex reference impedances.

See **broken link removed**

Added after 25 minutes:

@navuho

I agree with you, and would say cascading the generalized s matrices of several high frequency structures, which are all simulated in the same line environment is ok.


Nevertheless, if we simulate for a RF-device or discontinuity and apply line deembedding. The result is a scattering matrix only for the DUT. Without the lines, but characterized in this specific line environment.
Lets say, we characterized a discontinuity in a microstrip line with strip width 50 microns. After deembedding and renormalizing to a different impedance, we hope to get the characteristic of the same discontinuity but embededded in microstrips with another strip width x=?. RIGHT or NONSENSE ?


Thanks for your help. Greets elektr0.
 

coaxial impedance step discontinuity calculation

elektr0,

You've found the best paper on the subject. Dylan and Marks explain why I dislike the power based definitions: power waves are not waves. Power waves do not satisfy the 1D Helmholtz equation, and this means you give up certain very nice features of the S matrix.

1.) Deembedding. Since power waves do not satisfy the wave equation, deembedding is not the simple pre- and post- multiply by the phase change.

2.) Smith Chart. The Smith chart is based on the fact that the relation between Z (or Y) and S is a bilinear transformation. This is no longer true for power waves.

3.) Extension to higher order modes. Waveguide modes in cutoff do no transmit power; hence, power based S parameters for these modes do not exist.

The psuedo-wave definition of Dylan and Marks, is good, but I don't think many people use it. The simple voltage definition given in most microwave texts (e.g. Pozar) is also good, although I prefer to normalize the incident and reflected voltage wave by the sqrt(Zo). All definitions should give the same result when all ports are normalized to the same real value (like 50 ohms).

As to your second question, yep, you're right. The normalization impedance represents the impendance of the line that the incoming and outgoing waves are on. It is completely independent of the structure itself.

-Wiley
 

cascaded blocks s parameters

@ Wiley

Why are scattering parameters, referenced to complexe impedance necessary in your opinion ?


I think you didnt get my last question.
I am not sure if RENORMALIZATION is applicable to nonTEM guided wave applications. If we simulate the same discontinuity in two different complex line environments. For example a PCB-Via with strip width 50 um and strip width 150 um. If we RENORM the results from calculation 1. Is it possible to get the results from calculation 2 ???
 

equivalent voltage and current of non-tem lines

elektr0 said:
Lets say, we characterized a discontinuity in a microstrip line with strip width 50 microns. After deembedding and renormalizing to a different impedance, we hope to get the characteristic of the same discontinuity but embededded in microstrips with another strip width x=?. RIGHT or NONSENSE ?
Thanks for the article. Ok, I'm EM-guy, that means I always try to think in terms of EM-fields component. So, attempt to describe the discontinuity in nonphysical, imho.
Because it corresponds to s-matrix with infinity number of modes you need to take into account. Instead, I prefer to add lines to the discontinuity and calculate
"true" s-matrix with limited (!) number of modes. You will never fail or get unpredictible mistake with this method while the analitical solution is always a trade within using approximations.

Wiley said:
Since power waves do not satisfy the wave equation, deembedding is not the simple pre- and post- multiply by the phase change
What do you mean under "power waves" ? Waves (or modes) are defined only by port boundary conditions and it doesn't matter what kind of Z definition you use.
Morevover, deembeding is not applicable at all in a case of lossy media.

Wiley said:
Waveguide modes in cutoff do no transmit power; hence, power based S parameters for these modes do not exist
Again generalized s-matrix doesn't depend on any impedance def because it is simply unnormalized (!)
It just reflects the fact of signal (amplitude) trasmission between ports and modes. Waveguide below cutoff is an ideal attenuator in that case.

Added after 18 minutes:

elektr0 said:
If we simulate the same discontinuity in two different complex line environments.

What is "the same" discontinuity ? If you mean equal relation between input and output impedances then it will not be the same in the case of complex (lossy ?)
lines because losses depend on actual line crossection. But if losses is small you may neglect it and describe both obstacles as the same one.
 

real complex characteristic impedance

Nice discussion above. I am very tired right now, one flight left on my return from Japan. I hope this post makes sense, I will try my best.

I think nearly all the points made above are correct, but I think a couple need a little work.

First, for certain applications, it does not matter what Zo, complex or otherwise, you use to normalize your S-parameters. In fact, as pointed out above, you do not even need to know what the Zo is as long as you always make connections between ports that are normalized to exactly the same Zo. But one more thing is needed to get correct results...the program/equations you use to connect S-parameter blocks must agree with you as to what normalizing Zo is used.

The problem I had before I got into EM, when I was doing GaAs MMIC design, was some step discontinuity models from the EM guys. The step discontinuity looked really big, i.e., just like a transformer from the input Zo to the output Zo. This was generalized S-parameters. But the EM guys did not tell me that. I used them in a program that assumed 50 Ohm S-parameters. I got really crazy results. So, just watch out for this problem. This is why I always advise microwave designers (with a couple exceptions for very advanced users) to always use 50 Ohm S-parameters everywhere. EM theory guys can do many different things, but when they hand data to a microwave designer, they should be very clear about what they are giving to him.

There are cases where you must know the normalizing Zo, there is no other alternative. For example, if you need to know the actual current on a transmission line, you need to know what Zo the S-parameters are normalized to. It does not matter what the Zo is, but you need to know it. This is important for things like non-linear harmonic balance, or SPICE analysis. If you get the wrong current, you get the wrong answer. You also need to know the Zo if you want to extract a lumped model. Any error in Zo causes error in the lumped model.

Second, it is possible to de-embed through lossy and non-TEM lines, and it can be done exactly (to within numerical precision). Most recent details are in my paper last year on Unification of SOC and Double Delay in MTT Trans. You can get it from IEEE Xplore or email me and I will reply with a copy. Use my last name"at"ieee.org. In Sonnet, we have been de-embedding through lossy (sometimes extremely lossy) lines and doing it exactly since 1991.
 
scattering matrix complex normalization

elektr0 said:
@ Wiley

Why are scattering parameters, referenced to complexe impedance necessary in your opinion ?

From the designer's prespective, I don't think S parameters with complex Zo's are at all necessary. As I mentioned all definitions (should) reduce to same thing if all ports are renormalized to 50 ohms. If you are using complex Zo's then when incoporating your EM solution into a larger circuit, you have to be careful what definition the EM simulator is using and what definition the circuit simulator is using. But if your EM solution is normalized to 50 ohms, as Jim says, there's nothing to worry about.

However, if you're developing the models for the designer, it becomes important to understand S parameters with complex Zo's. If you want to know how the TRL measurement came up with Zo of the reference line, you need to have a basic understanding of S parameters and cascade matrices with complex Zo's. (Particularly for high loss lines.) The same is true for EM simulations. Although all measurement and simulation software that I know of will renormalize everything to 50 ohms upon request, so even when developing models, it is not essential knowledge.

elektr0 said:
I think you didnt get my last question.
I am not sure if RENORMALIZATION is applicable to nonTEM guided wave applications. If we simulate the same discontinuity in two different complex line environments. For example a PCB-Via with strip width 50 um and strip width 150 um. If we RENORM the results from calculation 1. Is it possible to get the results from calculation 2 ???

If we continue with your example: At a discontinuity higher order modes are excited, so let's add 300 um deembedding lines and place the ports at the end of these lines to make sure these modes have decayed fully. After we obtain the S parameters for the via and deembedding lines, we deembed the S parameters inward 300 um. The deembeding accounts for the phase change and loss introduced by the TEM mode of the deembedding lines. What is left is the via discontinuity and the higher order modes excited by the via coupling to the 50 um line. If you renormalize these S parameters to a 150 um line, the coupling is still to a 50 um. Does this make sense?

Added after 44 minutes:

navuho said:
Wiley said:
Since power waves do not satisfy the wave equation, deembedding is not the simple pre- and post- multiply by the phase change
What do you mean under "power waves" ? Waves (or modes) are defined only by port boundary conditions and it doesn't matter what kind of Z definition you use.
Morevover, deembeding is not applicable at all in a case of lossy media.

Wiley said:
Waveguide modes in cutoff do no transmit power; hence, power based S parameters for these modes do not exist
Again generalized s-matrix doesn't depend on any impedance def because it is simply unnormalized (!)
It just reflects the fact of signal (amplitude) trasmission between ports and modes. Waveguide below cutoff is an ideal attenuator in that case.

The term "power wave" comes from Kurokawa's original article "Power waves and the scattering matrix", MTT March 1965. He defines the S parameters based on incident and reflected power, which do not travel like waves. And it is simple to show that this definition is invalid for waves in cutoff. This is the definition that most people in the circuit community use, and the point of my previous post is that this definition is not desirable in the Microwave and EM communities.

One other thing (which may be a semantic difference): deembedding is applicable to lossy media. Probably the most common case is removing the extra loss caused by "deembedding arms".
 

pcb via equivalent circuit

I would say that the "re-normalization" of s-parameters contributes a lot to the mis-understanding between "EM theory guy" and designer.

"re-normalization" creates a false sense of "security". It might not be appropriate to cascade a series of s-parameter matrices even though all of them were "normalized" to the same 50 ohm. For example, you could have two 50ohm coaxial lines with different dimensions. Although they both have 50 ohm characteristic impedance, simply cascade the two s-paramters matrices would throw out the effect of a "step" discontinuity. This might be the reason they put so much emphasis on the connectors/adapters used in VNA measurement.

"re-normalization" does not correspond to a realistic physical process. Even if all s-parameters computed by all EM solvers are normalized to the same 50ohm, designers should still take care to use them.
 

numerical calculation of characteristic impedance

Many good points above. Loucy's point on cascading is esp. well taken. In this case, proper design when cascading S-parameter blocks that are both normalized to 50 Ohms but have different physical port dimensions is to include the S-parameters of the resulting step discontinuity betwen the two S-parameter blocks.
 

cascading impedance matrices

Hallo,

of course a transition betwwen different line geometries has to be considered.

Wiley wrote

If we continue with your example: At a discontinuity higher order modes are excited, so let's add 300 um deembedding lines and place the ports at the end of these lines to make sure these modes have decayed fully. After we obtain the S parameters for the via and deembedding lines, we deembed the S parameters inward 300 um. The deembeding accounts for the phase change and loss introduced by the TEM mode of the deembedding lines. What is left is the via discontinuity and the higher order modes excited by the via coupling to the 50 um line. If you renormalize these S parameters to a 150 um line, the coupling is still to a 50 um. Does this make sense?

Let us discuss this subject. EM field solution results can be expressed through scattering parameters, which are in this case nothing more than the power conditions at each port (maxwell conformed).

Deembedding is more advanced for lossy structures but possible.

Renormalization algorithms, implemented in CAE tools make extensive use of the equivalent voltage and current. If we dismiss equivalent voltage and current, we cannot use RENORM. Anyway, Collin, MontgomeryDicke, DyllanMarks, Brews have shown the existence of equivalent voltage and current for arbitrary guided wave situation. These u,i are no longer potential differences or simple conductor current, but special field averages, related to the complete field (Etang, Elong, Htang, Hlong). p=0.5 u i* is valid.
Lets say we are able to determine these equivalent u,i at each port, then an equivalent Z-Matrix exists, and the formal assumption for RENORM is fulfilled.
What is it good for.
1)
If we want to compare the results with measured ones. We need a model for the transition of the DUT lines to the VNA-lines, and then Renorm to a frequency constant 50 ohm reference impedance might be senseful, because the VNA uses fairly TEM transmission lines (Coax).
2)
May be we can express the equivalent Z matrix of the pcb via in terms of a
normal spice RLC equivalent circuit . Of course it is valid for the situation we simulated. It expresses the reaction for the defined incident field mode patterns.
Changing the strip width of the embedded transmission lines, will not change the field patterns dramatically. As Wiley wrote the coupling of the higher order modes is included only for the orignal strip width, but it might be an engineering approach to apply RENORM here, without simulating for each strip width.
3)
Due to the fact, that all presented RENORM algos can be reversed, for comparison purposes we can RENORM to 50 ohm. But comparison is bit less, when accurate modelling is the aim.


Comments please. Any further applications for RENORM ???
 

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