### S-parameter Bisection

For example; given s-parameters for a transmission line of a 10" lengthcan the matrix be split into two 5" lengths. Assume that the passives-parameter obeys reciprocity. The reason I'm asking is that I have a test fixture on each end of mymeasurement that I'm trying to de-embed. The insertion loss can besubtracted very easily, but the return loss and other parameters have agreat deal of error dealing with de-embedding from one side of the DUTonly. I'm hoping to break the fixture into two equal parts withouthaving a direct point of measurement to do so otherwise. Merrick M. MoellerThe information contained in this electronic mail message is privileged and confidential information, may be subject to the attorney-client privilege and is intended solely for the use of the addressee. If you are not the intended recipient, any disclosure, copying, distribution, or the taking of any action in reliance on the contents of this message is strictly prohibited. If you have received this message in error, please notify me immediately.

mmoeller
10 years 5 months 23 days

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Answered bywolfgang.maichen
10 years 5 months 23 days

You'll need to convert the S-parameter matrix into an ABCD-Matrix first. Then you can split up the latter (take the "square root") and convert the result back into S-parameters. The reason is that S-parameters implicitly assume that all your ports are terminated to 50 Ohms (or whatever your reference impedance is), and that is not necessarily true for the center of your cable where you want to do the virtual split.Wolfgang"Moeller, Merrick"Sent by: si-list-bounce@xxxxxxxxxxxxx11/10/2009 10:04 AMTo ccSubject[SI-LIST] S-parameter BisectionIs it possible to split a passive S-parameter matrix into two equalsections? For example; given s-parameters for a transmission line of a 10" lengthcan the matrix be split into two 5" lengths. Assume that the passives-parameter obeys reciprocity. The reason I'm asking is that I have a test fixture on each end of mymeasurement that I'm trying to de-embed. The insertion loss can besubtracted very easily, but the return loss and other parameters have agreat deal of error dealing with de-embedding from one side of the DUTonly. I'm hoping to break the fixture into two equal parts withouthaving a direct point of measurement to do so otherwise. Merrick M. MoellerThe information contained in this electronic mail message is privileged and confidential information, may be subject to the attorney-client privilege and is intended solely for the use of the addressee. If you are not the intended recipient, any disclosure, copying, distribution, or the taking of any action in reliance on the contents of this message is strictly prohibited. If you have received this message in error, please notify me immediately.

Answered byweirsi
10 years 5 months 23 days

If you want to break the line down into smaller pieces I think you will need to convert to an equivalent circuit model, perform the splitting and scaling that you desire and then if you want to stay in S parameters, convert back. Scaling only makes physical sense if the transmission line is well behaved over the frequency range of interest. The return loss problem you describe implies one or more substantial discontinuities. You should try and determine if those exist within your fixture, your DUT, or at the interface. For ideas on how to do rigorous deembedding, you might want to look into the Physical Layer Reference Design that Teraspeed and Simberian developed. You can contact Al Neves in the Portland office.Steve.Moeller, Merrick wrote:> > Is it possible to split a passive S-parameter matrix into two equal> sections? >> >> For example; given s-parameters for a transmission line of a 10" length> can the matrix be split into two 5" lengths. Assume that the passive> s-parameter obeys reciprocity. >> >> The reason I'm asking is that I have a test fixture on each end of my> measurement that I'm trying to de-embed. The insertion loss can be> subtracted very easily, but the return loss and other parameters have a> great deal of error dealing with de-embedding from one side of the DUT> only. I'm hoping to break the fixture into two equal parts without> having a direct point of measurement to do so otherwise. >> >> >> Merrick M. Moeller>> >>>> The information contained in this electronic mail message is > privileged and confidential information, may be subject to the > attorney-client privilege and is intended solely for the use of > the addressee. If you are not the intended recipient, any > disclosure, copying, distribution, or the taking of any action > in reliance on the contents of this message is strictly > prohibited. If you have received this message in error, please > notify me immediately. >>

Answered bybrett.grossman
10 years 5 months 23 days

Merrick,I've run into this situation bunches of times, and I will say that your success may depend on how many assumptions you are able to make.Consider that if the data you have is a 2-port s-parameter matrix, you have essentially 4 knowns (S11, S12, S21, S22).If you wish to split it into two 2-port matrices (a & b), with no assumptions, this is 8 unknowns (S11a, S12a, ..., S11b, S12b,...).So with no assumptions, you can see the problem will be difficult to solve (8 unknowns vs. 4 knowns). However, it may not be unrealistic to say that the two s-parameter matrices are equivalent (i.e. you split your passive device in half and each half is the same). In which case one matrix becomes the transpose of the other, such that:S11a = S22bS12a = S21b...By using these assumptions and simplifying the problem in this way, it is possible you could arrive at a solution in theory. In practice I've found a few of the assumptions I'd need to make, I simply can't accept. Also keep in mind that strictly speaking you can't cascade s-parameters, and would need to convert them into t-parameters to solve the problem (and likely back to s-parameters for your application). In the case you are dealing with > 2-ports, the translation to t-parameters can be ambiguous. Check out the following:J. Frei, X.-D. Cai, and S. Muller, Multiport S-parameter and T-parameter Conversion with Symmetry Extension, IEEE Trans. On Microwave Theory and Tech., Nov. 2008, pp2493for a reference.There is also a reference (though I do not have a citation), which address this problem with a software tool that I believe you can purchase. You may look up a company called Ultimetrix or google the name Vahe Adamian for the approach they have developed for splitting a fixture into 2-halves.Best regards,-Brett-----

Answered byzabinski.patrick
10 years 5 months 23 days

> Is it possible to split a passive S-parameter matrix into two equalsections? Yes - but with several caveats.We tried several approaches over the years, and as Brett mentions, itcomes down to the assumptions you make. The square-root approach is reasonable under a very-limited set ofsituations where there are no launch effects and the structure isexactly symmetrical. If you inject a TDR and see any anomalies at thelaunch (i.e., connector, probe point, ...), then the square-root methodquickly falls apart. For the majority of board-level structures, theconnector launches are significant enough to warrant this approachuseless.Another approach is bi-section whereby you assume the line issymmetrical - but there can be some launch effects. There are moreunknowns than equations, so you need to make some assumptions thatinvite inaccuracies and/or completely wrong answers. We developed anapproach several years ago (**), and it has worked fairly well for us inmany situations. Unfortunately, when return loss is high (-15 dB), thenthe approach becomes a bit inaccurate. When insertion is excessive (-10dB), then the approach falls apart.(**) Daniel, E. S., N. E. Harff, V. Sokolov, S. M. Schreiber, and B. K.Gilbert: Network Analyzer Measurement De-embedding Utilizing aDistributed Transmission Matrix Bisection of a Single THRU Structure.Proceedings of the 63rd ARFTG Conference Digest, pp. 61-68, June 11,2004, Dallas, Texas. Another approach is to develop custom structures such that you can usethem for in-situ VNA calibration. SOLT, LRM, ... can all be implementedin structures, but that approach too has several challenges -particularly in areas of repeatability, calibration coefficients, etc.There does not appear to be a quick-n-easy approach - at least not thatwe've found.The most reliable - and often most time consuming - approach generallyfollows Steve's advice of creating a model to match your measurement,breaking the model into two, then using the sliced model to yourdeembedding parameters. It requires several steps, good SI analysistools/skills, and a bit of luck.If you find a quick-n-easy solution, let us all know.Good luck,Pat ZabinskiMayo Clinic

Answered byl.boglione
10 years 5 months 22 days

Hi,Just a few comments:- mathematically, any transmission type of matrix could do (ABCD ortransmission S par) as long as the single matrices MA and MB (MA precedingMB) can be cascaded into M = MA*MB- MA and MB may not represent the same physical object (e.g. given a TX lineL unit of lengths long, MA is L/3 and MB is 2*L/3), hence the majorindetermination in the phases of the 12 and 21 terms (what counts is theproduct 12*21)- if MA and MB correspond to the same physical object (e.g. each tx line isL/2), then the square root approach may make sense, assuming symmetricity ofthe physical object (e.g. if the M object is SMA connector+tx line L+ SMAconnector and it is to be split into MA=SMA+L/2 tx line and MB=L/2 txline+SMA connector, MA and MB are reciprocal but not symmetrical)- the best approach in my opinion would be to make a second tier TRLcalibration of your fixture if possible (I used this approach tocharacterize two Cascade GSG probes at Q band and worked very well);otherwise, the mathematical deembedding may be possible, but pay a greatdeal of attention to the physical implication of your calculations (and ofthe assumptions that may be made to get to the final result)- even if obvious, once MA and MB are determined, you must get M=MA*MB back:MA and MB may still be "wrong", but if M<>MA*MB then something is certainlywrong- Agilent ADS, AWR Microwave Office and most likely other programs have Sparameter blocks that provide the deembedding feature (based on cascadingblocks with matrix algebra) once MA and MB are knownLooking forward to any comments.Luciano-----

Answered byerdinih
10 years 5 months 22 days

Merrick,The solution is simple and available in any undergrad microwavetextbook. The S-parameters should be first converted into T-parametersand then cascaded to represent the original structure. However, theconversion involves matrix inversions and any noise in the originalparameters may be amplified and corrupt the converted parameters. Forsimulation results, this is seldom a problem but measurement resultsmay need to be post-processed before any conversion.I especially emphasized the transmission coefficients (T-parameters)instead of notorious ABCD parameters because T-parameters areexpressed in terms of reflected and transmitted power at the portsjust like s-parameters while the ABCD parameters are in terms ofvoltage and current.IhsanOn Tue, Nov 10, 2009 at 1:04 PM, Moeller, Merrickwrote:>> Is it possible to split a passive S-parameter matrix into two equal> sections?>>>> For example; given s-parameters for a transmission line of a 10" length> can the matrix be split into two 5" lengths. Assume that the passive> s-parameter obeys reciprocity.>>>> The reason I'm asking is that I have a test fixture on each end of my> measurement that I'm trying to de-embed. The insertion loss can be> subtracted very easily, but the return loss and other parameters have a> great deal of error dealing with de-embedding from one side of the DUT> only. I'm hoping to break the fixture into two equal parts without> having a direct point of measurement to do so otherwise.>>>>>> Merrick M. Moeller>>>>>> The information contained in this electronic mail message is> privileged and confidential information, may be subject to the> attorney-client privilege and is intended solely for the use of> the addressee. If you are not the intended recipient, any> disclosure, copying, distribution, or the taking of any action> in reliance on the contents of this message is strictly> prohibited. If you have received this message in error, please> notify me immediately.>>

Answered byal
10 years 5 months 22 days

Guys,I would first create a specification and requirement list detailing THRU(transmission sans DUT) accuracy, insertion and return loss numbers versusbandwidth, etc., your calibration has to be significantly better thanyour DUT, but not a LOT better to make most practical measurements. If asimple THRU on your test board has -15dB return loss (using simple SOLT cal)at 5GHz and your DUT has similar numbers your in trouble no matter what youdo, simply put your fixture may need a redesign. We have found poorfixture design, and inconsistency wreaks havoc on ALL the de-embedding andcalibration approaches (TRL/LRM, T-matrix, using TDNA measure-modelingmethods, etc.,). So as to not fall into a rat hole and succumb to matrix and calibrationmadness we typically specify our calibration objectives first, based on ouroverall measurement objectives (again, related to the DUT performance), thenselect test board materials (FR4 versus low loss dielectrics), calibrationapproach, calibration kit (for TRL), launch (simple SMA versus 2.92mm). This approach becomes much more important when there is a team of folksaddressing the problem. By establishing a specification and having theteam (and customer) first buy into it you make life easier for yourselfalso. Alfred P. Neves <*)))))><{ Hillsboro Office: 735 SE 16th Ave. Hillsboro, OR, 97123 (503) 718 7172 Business (503) 679 2429 Mobile Main Corporate office: Teraspeed Consulting Group LLC 121 North River Drive Narragansett, RI 02882 (401) 284-1827 Business (401) 284-1840 Fax http://www.teraspeed.com Teraspeed is the registered service mark of Teraspeed Consulting Group LLC -----

Answered byhassan
10 years 5 months 22 days

BODY { font-family:Arial, Helvetica, sans-serif;font-size:12px; }Merrick, I'm sure you've benefitted from lots of very good responses that havebeen provided on this question so far. I've personally learnt a lot. As you may already know, your problem is not unique - many of us havefaced same problem and there are no easy solutions. I like the idea of combining software and hardware tools to solve theproblem. These are the steps I'd recommend: 1. Measure s-parameters of at least 3 long thrus (SMA+line+SMA) ofdifferent lengths. The insertion loss of a long line is less affectedby the return loss contribution of the SMA launch (assuming good SMAlaunch to begin with). 2. Use software tools (e.g. Agilent ADS) to simultaneously fit allthe s-parameters measured in (1) to a transmission line model. Linelength should be one of the model parameters. 3. Measure s-parameters of a short thru of your interest. This willbe more affected by the return loss of the SMA. 4. Use software tools again to fit the s-parameters measured in (3)to the transmission line model created in (2) and an assumed SMA model(you can use a simple pi RLC model: two shunt capacitors + series Rand L). You can assume that the two SMA launches are identical (not sobad an assumption if the lauch in already known to be very good). 5. Tune the SMA and line models further so that they also closely fitthe s-parameters of all the thrus measured in (1). 6. Use software tools with the tuned SMA model and the tuned linemodel to create s-parameters of your half fixture. Good luck. Hassan. On Tue 11/10/09 12:04 PM , "Moeller, Merrick"mmoeller@xxxxxxxxxxxxxxx sent: Is it possible to split a passive S-parameter matrix into two equal sections? For example; given s-parameters for a transmission line of a 10"length can the matrix be split into two 5" lengths. Assume that the passive s-parameter obeys reciprocity. The reason I'm asking is that I have a test fixture on each end of my measurement that I'm trying to de-embed. The insertion loss can be subtracted very easily, but the return loss and other parameters havea great deal of error dealing with de-embedding from one side of theDUT only. I'm hoping to break the fixture into two equal parts without having a direct point of measurement to do so otherwise. Merrick M. Moeller The information contained in this electronic mail message is privileged and confidential information, may be subject to the attorney-client privilege and is intended solely for the use of the addressee. If you are not the intended recipient, any disclosure, copying, distribution, or the taking of any action in reliance on the contents of this message is strictly prohibited. If you have received this message in error, please notify me immediately.

Answered bysanjeev_gupta
10 years 5 months 22 days

Hello All,When it comes to splitting S-parameter into two equal half you can use ADS. It is a much simpler process.Please send me your personal email if you need an ADS example by tomorrow along with the methodology utilized.Thanks and regards,Sanjeev GuptaAgilent Technologies, EEsof Division-----

Answered bykgrhoads
10 years 5 months 21 days

>I especially emphasized the transmission coefficients (T-parameters)>instead of notorious ABCD parameters because T-parameters are>expressed in terms of reflected and transmitted power at the ports>just like s-parameters while the ABCD parameters are in terms of>voltage and current.I'm curious about this comment, could you amplify? Please.Are you recommending against ABCD matrices in the intermediate step because the final result will suffer or be less accurate? Obviously,if calculations could be done with infinite precision, it shouldn'tmatter -- so why does it matter here?SincerelyKevin

Answered byerdinih
10 years 5 months 22 days

In microwave applications, i.e. when dealing with waveguides, thevoltage and current will be path dependent (not unique) on thecross-section of the guide for high order modes. In this case the y(and abcd) parameters may not even be defined and one would have nooption but resorting to the t-parameters in order to cascade thestructures. However, for all SI applications that I know, thetransmission line theory (the lowest waveguide mode) must prevailwhere the lines are connected to driver and receiver circuitry. Inthis case the voltage and current at the line ends will be uniquelydefined and preferring abcd parameters over t-parameters or vice-versawill not really matter from a practical point of view.The truth is any circuit simulator based on modified nodal admittance(MNA) matrix will eventually convert the s-parameters intoy-parameters. However, if switching between the circuit parameters isrequired more than once before putting the whole structure into theMNA matrix the use of t-parameters still seems more advantageous sincethey are of the same genre as the s-parameters and one doesn't have toworry about the reference impedance in the conversion. It may be aminor point but worth consideration...Regards,IhsanOn Wed, Nov 11, 2009 at 3:39 PM, Kevin G. Rhoadswrote:>>I especially emphasized the transmission coefficients (T-parameters)>>instead of notorious ABCD parameters because T-parameters are>>expressed in terms of reflected and transmitted power at the ports>>just like s-parameters while the ABCD parameters are in terms of>>voltage and current.>> I'm curious about this comment, could you amplify? Please.>> Are you recommending against ABCD matrices in the intermediate step> because the final result will suffer or be less accurate? Obviously,> if calculations could be done with infinite precision, it shouldn't> matter -- so why does it matter here?>> Sincerely> Kevin>

Answered byshlepnev
10 years 5 months 21 days

Ihsan,I just wanted to clarify a few things on the descriptors and current andvoltage definitions. If conversion from S to Y for MNA is possible thenconversion from S to ABCD is also possible. The exceptions are someidealized cases like ideal short-circuit or open-circuit conditions forinstance. In fact, conversion from S to T may be also problematic if S[1,2]or S[2,1] are zeroes or close to zero for instance (despite on the samegenre as you put it). ABCD matrix as well as Y matrix will relate currentsand voltages that are always defined as long as the waves are defined (wavescan be defined through current and voltage or vice versa). Though, it maynot be the static definition through the surface and line integrals, but themicrowave definition through projections of the magnetic and electric fieldson the modes or eigen-waves of the wave-guiding structures. They aredifficult or impossible to measure, but are still defined. Waves are alsodefined through the same projections, but easier to measure. Note, thatTelegrapher's equations and transmission line theory work fine for thewave-guiding structures even for high-order and evanescent modes. The limitsare imposed by the definitions of the currents and voltages used in theequations and by how the impedance and admittance per unit length arecomputed. The static definition of the current and voltage and quasi-staticsolution for the p.u.l. parameters restrict the use of the equations to thefrequencies where the cross-section of a line is much smaller than thewavelength and only quasi-TEM modes are propagating. The projectiondefinition of the current and voltage and electromagnetic solution forp.u.l. parameters provides accurate description of the transmission lines orwave-guiding structures up to optical wave-length without any restriction onthe size of the cross-section or on the type of the wave propagating alongthe line. And the circuit theory can still be used for accurate analysis ofthe nets composed of the appropriately defined models of transmission linesand discontinuities. This is the basis of the fast de-compositionalelectromagnetic analysis of nets practically without frequency limits (ifall elements of a net are localized that does not always hold for PCBapplications).Best regards,Yuriy Shlepnevwww.simberian.com -----

Answered byshlepnev
10 years 5 months 21 days

Hassan,I just wanted to point out that the transmission line model used for such(or similar) model-based bi-section or de-embedding approach is the mostcritical element and defines the accuracy of everything that follows. The t-line model must be verified up to the maximal frequency and includeeffects of dielectric and conductor dispersion and high-frequency dispersionif the maximal frequency is above 3-5 GHz. Note that with a quasi-staticmodel such fitting may be possible even above those frequencies, but it maytranslate the t-line model deficiencies into the models of the transitionsand you may not achieve simultaneous match in magnitude, phase and groupdelay.The best way to verify the t-line model is to get rid of the reflections atall. It can be done by following the first step in the standard TRLcalibration procedure, by conversion T-matrices of two line segments intodiagonal T-matrix of the difference and then into the reflection-lessblock-diagonal S-parameters. Such S-parameters are normalized to thecharacteristic impedance of the modes propagating in the line and are calledgeneralized modal S-parameters. There is only one unique S-parameter tocompare with the model for a single-ended line (instead of two) and just twounique S-parameters for differential line (instead of six in case ofsymmetrical pair). It greatly simplifies the verification of the t-linemodels. It also makes it possible to extract dielectric or conductorproperties with high accuracy. In collaboration with Teraspeed we haveverified the method up to 40 GHz. The electromagnetic models for t-line isthe must if you what good accuracy over extremely wide frequency band above3-5 GHz.Best regards,Yuriy Shlepnevwww.simberian.com-----

Answered bycolin_warwick
10 years 5 months 21 days

Hi,We uploaded Sanjeev's method as a guest post on my blog:http://signal-integrity.tm.agilent.com/2009/s-parameter-bisection-using-optimization/hth-- Colin WarwickSignal Integrity Product Marketing Manager, Agilent EEsof EDA-----