Signal Integrity

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.

• Download the S-parameter bisection PDF
• Download the ADS S-parameter bisection project .zap file
• Agilent EEsof EDA Evaluation License Request Form
• Quick Start for Signal Integrity Design Using Agilent ADS evaluation guide (PDF)

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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