Faking SPDT three-port S-parameters

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New for August 2016! 

If you have ever designed and then built and tested switch matrices, switched filter banks, time delay units or anything where switch isolation plays a key role, you will know that three-port data is absolutely required to have confidence in the design.  Yet many switch suppliers provide only two-port S-parameter data, typically only the on and off state with (if they are not stupid) the third port terminated.

Note: if the switch supplier took three sets of S-parameters of a symmetric switch with one pole selected (port 1 to port 2, port 1 to port 3 and port 2 to port 3) you would have everything you need to complete the three-port matrix.

We will divide this page into two sections: first, the theory of how to do this, then an actual implementation (which we don't have yet).

Theory

A while ago we requested that someone show us a technique for building a 3-port 3x3 S-parameter matrix (S3P file) of a SPDT switch from two, two-port measurements (S2P files). One measurement is from the common port (port 1) to the port that is selected (call it port 2) and one measurement is from the common port to the port that is selected as off (port 3).  Some further assumptions: the switch must be symmetric, i.e. the two paths are physically close to identical (we will forgive an occasional air bridge to pass control signals); and the third port is terminated in each measurement, otherwise the data you are looking at is pretty much garbage. Unless you like to do linear interpolation, the two S2P files should contain the same frequencies.

Below, "The Professor" schools us on how to do convert to an S3P file, resulting in a slightly imperfect result which is probably good enough for most designs.

1) Because the two-port measurements for both the ON and the OFF case (or common-to-selected and common-to-unselected cases) would have been made with the unmeasured port terminated, then S11, S12, S21, and S22 for the 3x3 matrix would be the same as those of the ON, or common-to-selected case, assuming that port 1 is the common terminal, port 2 is the selected terminal, and port 3 is unselected.  Since the unmeasured port was still terminated, S11 for the ON case should actually be the same as for the OFF case (assuming the switch is symmetrical), since in either case both the selected and unselected output ports are terminated.

2) S13 and S31 (again assuming port 3 is the unselected terminal) should be equal to S12 and S21 (respectively, but they're equal anyway) in the OFF state (or common-to-unselected) measurement.  Again, this is because in that measurement port 2 of the switch was terminated.  It wouldn't matter whether port 2 was terminated with a network analyzer port or a dummy load, as long as the load was of high quality (high return loss).

3) S33 for the switch (port 3 unselected) should be the same as S22 for the OFF state measurement, for the same reasons as (2).

4) S23 and S32, the isolation between the selected port and the unselected port, are the only ones that require any calculation.  First, assume that the switch is constructed with a common input branching to two output paths, with either series or shunt (or both) switching devices in the two output paths.  This would be the case for any electronic SPDT RF switch, but not for a mechanical transfer switch.  There is a certain amount of loss associated with the switching device in the ON path (small series resistance or shunt conductance) that's measured in the S21 and S12 measurements of the switch in the ON state.  There is also some phase shift (delay) that shows up in these measurements.  Then, there's a finite amount of isolation associated with the switch in the OFF path (small shunt resistance or series conductance) and phase length that shows up in the S12 and S21 measurements of the switch in the OFF state.  Since a signal going from port 2 to port 3 (or in the opposite direction) has to go through both the ON path and the OFF path, S23 (and S32) of the three-port matrix should be approximately equal to the product of S21 in the ON measurement and S21 in the OFF measurement.  The reason this result is approximate is that there's a small path length from port 1 (the common port) of the switch to the switch's internal branch point, and the delay from this length will be embedded into both the ON and the OFF state S21 measurements,   But a signal going from port 2 to port 3 of the switch doesn't propagate down that path, so S21(ON) times S21(OFF) will include slightly more delay and phase shift than the switch will actually have in an S23 (or S32) measurement.  As far as I can see, this uncertainty in the delay or phase shift in S23 and S32 can't be resolved without making an actual S23 or S32 measurement of the switch.  It's probably never a problem, because most designers wouldn't be concerned with phase shift to an isolated port, only the magnitude should matter.

Below is the S-matrix created from two port data to fill in three ports

Note that because the circuit is reciprocal, you can substitute S21 for S12 in any of the fields. But don't mix up S11 and S22!  Using this simplification and preferring S21 over S12, the matrix becomes:

 As you can see, only two vectors in the matrix must be calculated, and they are identical.

This technique was checked out using a name-brand RF simulator tool, building a switch model, doing the math and comparing results.  "Accurate enough" results were obtained.  The phase of S23 and S32 were off, by twice the electrical length of the transmission line from the common port of the switch to the branch point.

Implementation

Here is the problem... now we know what is needed, but how to do it conveniently and generate a "Touchstone" compatible S-parameter file?

At this point you want to note that You should note that if you have S-parameters in decibels, the calculation of S23dB is the simple addition of S21dB(on) + S21dB(off), and angleS23 is the addition of   angleS21(on) + angleS21(off).

We thought about creating an Excel file to do the math, but it would be awkward reading and then outputting in S-parameter text. Can someone help us out with an executable file, or Java script that we could post as a on-line calculator?

More to come....