# [SI-LIST] Re: S-parameter Bisection

• From: "Grossman, Brett" <brett.grossman@xxxxxxxxx>
• To: "Moeller, Merrick" <mmoeller@xxxxxxxxxxxxxxx>, "si-list@xxxxxxxxxxxxx" <si-list@xxxxxxxxxxxxx>
• Date: Tue, 10 Nov 2009 15:07:32 -0800

```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 = S22b
S12a = 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, pp2493

for 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

-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On
Behalf Of Moeller, Merrick
Sent: Tuesday, November 10, 2009 10:04 AM
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] S-parameter Bisection

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

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