Making 2-port measurements without S-Params

[Andrew_K]

Andrew_K, what's happening?  Are you getting any good results?

in one of your posts you show how you have hooked and measured a couple of two-ports labeled "DUT1" and "DUT2".  Does one of those include that high resistance cable you described early on?  If so, does that mean that the other DUT only contains passive components capacitors, inductors and resistors connected in a network?  Can you post a schematic of what's in that particular DUT?

Sorry, it's been a while. Took a much needed vacation.


I do get reasonable results using the first set of equations you provided. The results agree with my own at lower frequencies. At higher frequencies, my method seems to be more inaccurate when Zopen approaches Zshort. Which makes sense. I think this will always be a limitation with this method of measurement.

Once I have measurements that I (mostly) agree with, I convert to H parameters, then attempt to estimate the transfer functions to import into QUCS for "Function Defined" network blocks.
H parameters give the best results for fitting. If I were to fit Zshort/Zopen directly, or fit to Z parameters, the estimated fits might not agree where Zshort approaches Zopen. The estimated functions may cause one parameter to shoot past the other, when really they approach asymptotically. It's more robust to fit to H parameters.

Approaching F->0 or F->∞, I can remedy measurement noise by chopping my measurements to the region where they make sense. Then fill in data using assumptions. For example, the voltage gain -> 1 at DC, voltage gain -> 0 at HF. I can use the measured results to get the shape in the area where measurements seem valid.

I am getting fairly good results with this method. Importing into QUCS, I can calculate the AC response with the rest of the circuit. Then, I can use the AC response to calculate the step or impulse response. This seems to agree fairly well with the real-world measurements.


This may not be important anymore, since I am getting results that work for what I am trying to do... But I am struggling to find how my version of derivations has equivalence to your derivations algebraically. Numerically they agree. I might have to play around some more with the algebra to really understand the differences there.


To answer your other question, the DUTs I am measuring are all passive devices (cables).

[The Electrician]

This may not be important anymore, since I am getting results that work for what I am trying to do... But I am struggling to find how my version of derivations has equivalence to your derivations algebraically. Numerically they agree. I might have to play around some more with the algebra to really understand the differences there.

I start with this:

zis=1/y11, zos=1/y22, zio=z11, zoo=z22

Keeping in mind that your two-ports are reciprocal.

Using the conversion from Z to Y parameters, we can get:

Y11 = Z22/(Z11 Z22 - Z12 Z21)

Y22 = Z11/(Z11 Z22 - Z12 Z21)

Using this, we get Y11/Y22 = Z22/Z11

and then (Z11 Y11)/Y22 = Z22

Using the equivalences from the beginning, this becomes:

(Zio Zos)/Zis = Zoo

Now starting with your formula Z12 = Z21 = Sqrt(Z11*Z22 - Z22/Y11)

Leaving the Sqrt off until the end, we can convert Z11*Z22 - Z22/Y11 to Zio*Zoo - Zis*Zoo
and then Zio*Zoo - Zis*Zoo to Zoo(Zio-Zis)
Now using (Zio Zos)/Zis = Zoo, we replace Zoo in Zoo(Zio-Zis) to finally get Z12 = Z21 = Sqrt((Zio Zos*(Zio-Zis))/Zis)

And since the C element of the ABCD parameters is 1/Z21, the just above expression for Z21 can be reciprocated to give:

C = 1/Z21 = 1/Sqrt((Zio Zos*(Zio-Zis))/Zis) which is the formula for C in these formulas:



Those are the second set of formulas I posted in reply #48