How to get the transmission line parameter from S parameter

s parameters transmission line

Hi, everyone. I have a question about getting transmission line parameter such as wavelength, charateristic impedance, damping factor etc. from the S parameter measurement.

BTW: Is it any restricts for measured TLN dimension such as required the TLN length less than half wavelength? Thanks..

transmission line s-parameters

Convert your 2-port s-parameters to ABCD matrix. You can write down the ABCD of a seciton of TLN, Then, you can compare them to get the complex gamma and Zc. Regards.

abcd parameters transmission line

Hi, Jian. Thanks for your reply. Is the method you mentioned used in IE3D "finding the Transmission Line Parameter"?

I saw the help document said that the length of the transmission line should be shorter than half-wavelength, in fact, I got a weird solution for a longer one. But if the microstrip line interacted with other structure, such as EBG around, I think the shorter transmission model can not includes all the mutual coupling effect, how can I solve it? Thanks in advance

scattering parameters of transmission line

Hi, Winglj:

If you are using EM solvers to get the S-parameters, the solver should be able to calculate most of the transmission line parameters for you like Z0,γ, time delay, effective ε , L/C per length etc. From those parameters, you can calculate some other parameters you needed. eg. wavelenth λ=v/f=c/(sqrt(εeff)*f), where c is the speed of light in vacuum(roughtly 3e8m/s).
I don't think there is a restriction to the TL length that you can measure or model. The problem is: the longer the TL length under test/simulation becomes, the lower the frequency would be, start from which, the S-parameters you obtained becomes not nicely behaved due to resonance.
However, depends on what kind of models you want to extract from the results, there is restrictions to the TL under modeling(not measurement or simulation).
For example, if you want to model the TL using lumped element circuits such as L, C, LC or RLC sections, usually the length of the TL cannot exceed quater-wave since the bandwidth of those lumped element equivalent circuits can not go to that high(again, it depends on the topologies and the number of sections you used to model the TL).
An ideal TL model with only Z0 and time delay(TD) can model the S-parameters quite well up to the first resonant frequency(roughtly quarter-wavelength). If the TL length is long, I would suggest you model it using an lossy TL model with Z0, TD and loss tangent (LT). This kind of model usually has a very large BW that can mimic the behavior of your TL under test to a very high frequency range(several wavelength).

Hope above comments can give you some idea.

Regards,

transmission line s parameters

U can calculate physical parameter from S parameter (if use program, such @ds or etc, u can Optimize your W an L of line to reach exact S parameter) and then calculate other param of line from formuls or use a calculator to calc them.
For many kind of transmission lines we have calculators which have very good results to ~10 GHz, such as TXLine(microwave Office) or Lincalc(@ds).

s parameters of a transmission line

Hi Winglj -- The ABCD approach described by Jian is correct. You can find more detail in:

Unification of double-delay and SOC electromagnetic deembedding
Rautio, J.C.; Okhmatovski, V.I.;
Microwave Theory and Techniques, IEEE Transactions on
Volume 53, Issue 9, Sept. 2005 Page(s):2892 - 2898

I think I might have been the first to describe the ABCD matrix way of getting Zo and Eeff in:

J. C. Rautio, "A De-Embedding Algorithm for Electromagnetics," International Journal of Microwave & Millimeter-Wave Computer-Aided Engineering, Vol.1, No. 3, July 1991, pp. 282-287.

and

J. C. Rautio, "A New Definition of Characteristic Impedance," MTT International Symposium Digest, Boston June 1991, pp. 761-764.

If anyone knows earlier references to this approach, please post them.

As for R, L, C, and G, just get S-parameters for an extremely short piece of line. Do this by having a length of line that is at least two substrate thicknesses long and de-embed to as short of a length of line as possible (very high accuracy is needed, so you should use a shielded analysis for this approach). Then load the S-parameters into the data viewer in SonnetLite and go to the output menu and select RLCG parameters. This works for coupled lines too (RLCG become matrices.) The RLCG can be used in various versions of SPICE. See the SonnetLite manuals for details.

I am puzzled by the comments on length of line limitations. The limits I know of are that the ABCD approach needs more than zero length. I find that at least 1 degree or so is usually plenty. The length can not be within 1 degree or so of a multiple of a half wavelength (such a line looks electrically like a zero length line, see Fig. 6 of my Sep 2005 paper above, note the difference between shielded and unshielded results), and the S21 of the line can not be really really close to zero mag (like -100 dB).

If you actually use an L and a C (and R and G) to model a transmission line, it will look like a low pass filter. The model loses validity above the cut-off frequency. So then, you split the L and C in two and make two sections, same total L and C. Now, the low pass cutoff is higher and the model works higher. Continue the process until you have an infinite number of L and C and you have waveguide theory. For lossless homogenous lines (same dielectric everywhere) this has no upper limit on line length, provided you get accurate values of LC. For lossy homogenous and for all inhomogeous lines, like microstrip, problems kick in with dispersion. RLCG change as a function of frequency. But if you get RLCG as a function of frequency, there is still no upper limit on line length.

s parameter transmission line

because of your interesting to ABCD param:

s-parameters transmission line

Hi, Winji:

The reason for the L of the TLN must be shorter than lambda/2 (half wavelength) is due to the following fact. If your TLN has little loss, you will get the 50-ohm normalized S11 = 0 or S21 = 1 at those frequency points where the L is exactly integrals of lambda/2 and it really does not matter what Zc it is. Basically, it is not a 1-to-1 mapping at the integrals of lambda/2. You can not find the Zc from the 50-ohm (or any Zc) normalized s-parameters. In fact, it is not only exactly at the frequency points where L is exactly integrals of lambda/2. The accuracy of the adjacent frequency points is also affected. That is why we suggest people to use the L less than Lambda/2. In some sense, you can use some length over lambda/2. However, you just need to skip those points close to integrals of lambda/2. You can plot a curve vs. frequency and plot the average line for it.

Regards.

Added after 2 minutes:

Hi, Winji: I forgot to answer your question about EBG. (1) EBG is no longer precisely a traditional TLN structure. (2) In case you want to find its corresponding TLN parameters by fitting it, you just use a long line and avoid the points close to integrals of lambda/2. Regards.

s parameter viewer

Hi, thanks for everyone replys. After reading some comments, I thinks I have some idea about extracting the transmission line parameter from S-parameter. But I still have some question about the techniques...

The ideal lossless TL model is characterized by characteristic impedance Z0 and Time Delay TD, and I think the propagation constant should be β=2*pi*f*TD/L, and accounting into lossy, complex Z0 and γ will be needed. The ABCD matrix for TL also depends on these two key parameters. So by comparing the converted ABCD matrix from S Matrix and the ideal TL ABCD matrix, we can get the corresponding Z0 and γ.

However, the ABCD matrix for TL length=lamda/2 is constants for all Z0, that is why we cannot use that length to extract TL parameters.

But I am thinking about if we get the time delay from measurement, supposed in inhomogenous environment such as microstrip line, the time delay TD depends on frequency since dispersion, can we calculate the wavelength lamda and propagation constant beta from the equation: w*TD=beta*L?

which w is the angular frequency, TD is time delay, beta is propagation constant and L is the tested transmission line length.

Thanks.

transmission line s-parameter

Hi, Wingji:

I think your formula w*TD = Beta*L is correct. If you use time domain measurement, you do need to find the Beta from it. I think you can get the Beta from the s-parameters and you may not need to solve it from TD. After you fit the s-parameters (frequency domain data) into ABCD, you should be able to find Zc and beta anyway. I think you get the point where we should make sure the L should be smaller than lambda/2. Certainly, it is ok if you use L larger than Lambda/2 while L is far from integrals of Lambda/2. However, you will see many up and down in the exacted zc and Beta can be significantly off the average value when the L is getting close to the integrals of lambda/2. This is especially true for measured s-parameters. Happy Thanksgiving Day.

Best regards.