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S-Parameter Bisection Using Optimization Techniques

Posted November 12th, 2009 · 11 Comments · Application Note

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This guest post from my colleague Sanjeev Gupta is a response to a question posted by Merrick M. Moeller on the si-list.

In de-embedding a device-under-test (DUT) from its test fixture, it is often desirable to bisect S-parameters into two equal halves. As described in literature, this can be achieved by first converting the S-parameters into a T-matrix and then using a simple mathematical operation. However, this method can only be applied to 2 port S-parameters and even then certain restrictions apply. There is no closed form methodology available today which allows the splitting of an arbitrary set of S-parameters into two equal halves.

This paper presents an optimization-based methodology to split an arbitrary set of S-parameters into two equal halves using Agilent’s Advanced Design System (ADS). The method here can be applied up to six ports. The technique could be extended to a higher number of ports but will require additional efforts. It is assumed that the S-parameters are generated using symmetrical structures which are cascaded back-to-back with arbitrary termination.

Rather than relying on an exhaustive set of test fixtures, calibrations and measurements, the technique presented in this post relies on the computing power of today’s desktop computers. The methodology does not make any assumptions regarding fixture models and topology. The extraction mechanism is purely mathematical and does not rely on the physical constraints and topology of the structure. Thus, unphysical behaviors are avoided.

Post script: Things to experiment with to gain further speed improvement

  • Formulate the goals as a weighted distance in the complex plane
    mag(S(1,1)-S(3,3))/mag(S(3,3))< delta
    mag(S(2,1)-S(4,3))/mag(S(4,3))< delta
    mag(S(2,2)-S(4,4))/mag(S(4,4))< delta
  • Pick start values closer to expected answer, e.g. sqrt(2) scaling and phase of half section being half of total phase

(Thanks to Herman Westra for these suggestions)

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11 Comments so far ↓

  • Sven Erik Elfgren

    I think there are more than one solution to the
    split s-parameterboxes. (more than one possible minima in the optimization) which means that if you use this to try to find out what source imedance your device “sees” you may get the wrong answere. (Assuming you put a device between the two symetrical boxes after the
    opt procedure.)

    • Colin Warwick

      Thanks for the observations, Sven.
      We’ll give it some thought and get back to you and post an update here. Stay tuned!
      — Colin

      • Arthur Bradley

        To show that there is no unique solution try adding a transformer to your test circuit. If you change the ratio T and adjust the impedances between the transformers as T^2 the combined circuit S parameters are unchanged but each half will have a different response. Each half circuit is a valid solution.

  • rfcooltools

    Basically to split a two port s2p into either two symmetric circuits or a cascade of two you can solve (abcd)*(abcd’)=ABCD for a,b,c,d for each frequency. In doing this there will be four solutions for each of the a,b,c,d of which one will be correct. You can use the software at http://www.rfcooltools.com where this is implemented for you.

    • Madhu Rengarajan

      Hello rfcooltools, Can you provide some step-by-step instructions on how to bisect an .s2p file using the tool?

      • rfcooltools

        Hello Madhu,

        I will make a video shortly, but in the mean time.
        step1 : select s2p series component from the series component panel and choose the file you want to bisect. This will make the component appear in the schematic window. (if it does not show up then the parsing of the s-parameter failed, if so please send me the file at provide_feedback@rfcooltools.com and I will incorporate this file format into the parser).
        step2 :grab the s2p component in the schematic window and insert it into the schematic.(wire will turn green where the insertion will occur).
        step3: depending on whether your file is approximately symmetric (two identical circuits back to back) or asymmetric (one circuit to split into two cascaded circuits) choose the icon in the s-parameter bisection panel. Complete the dialog and save the file.
        Finally: the file containing the bisected s2p is ready to be used.

        Please email any questions or comments or suggestions to provide_feedback@rfcooltools.com
        Thanks
        Jeremy

  • Mats Fredriksson

    This optimization method works sometimes, but fails miserably in many cases. I’ve tried to come up with better goals / methodology but I haven’t been able to find something that is robust and works in all cases.

  • Esa Tiiliharju

    thank you for an interesting approach.
    to complement this, could you please give an example of a good cook-book style reference on the mathematical techniques on splitting the T-matrix ?

    > As described in literature, this can be achieved >by first converting the S-parameters into a >T-matrix and then using a simple mathematical >operation. However, this method can only be >applied to 2 port S-parameters and even then >certain restrictions apply.

  • How to split S-parameters into two symmetric halves? For de-embedding.

    […] form, that is not always guaranteed. If you are an Agilent ADS user, there is an example at: S-Parameter Bisection Using Optimization Techniques I hope it can help. Mazz Reply With Quote + Post New Thread […]

  • Andrei

    Hello Colin,

    Thank you for detailing this approach. I’ve tried it as well but I can’t manage to save the 2 halves as s2p touchstone files. Is there a way? I need them for deembedding.
    Also I’m curious if the impedance response matches.

    Thank you!

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