# How do I find the return loss of a transformer from its 4-port S-parameter data?

I'm looking for information on the performance of Mini-Circuits T16-1-KK81+ transformer. The transformer is well-characterized, Mini-Circuits provided both insertion/return loss charts and raw S-parameter measurements for download.

I'm having difficulties on reproducing the official return loss chart using the raw S-parameters.

It's a 4-port VNA measurement with 16 S-parameters, the s4p file says,

!Model: T16-1
!Run/Lot/Date Code: MW42300//0640
!DATA FOR: UNIT#1
!Fixture/SN/Due: 90-2-20-233/72223/07-24-2009
!Connection: PORT-1 - pin<4>; PORT-2 - pin<6>; PORT-3- pin<3>; PORT-4 - pin<1>;
!PORT EXTENSION DONE ON TEST FIXTURE WITH LOSS ON AND MISMATCH ON


The primary dot is Pin 4, or port 1, so the return loss should be a plot of S11, but the plot looks like this,

In no way it resembles the official return loss curve,

I thought the script I used to plot the chart was broken, but I don't see obvious issues in my code. I suppose the difference is due to the termination. I guess the VNA measurements were done with four 50Ω ports, but the return loss chart in the datasheet assumes a matched 800Ω load, is it correct?

How should I proceed to reproduce the return loss chart?

• You could try doing a two port measurement on just pins 4 and 6 with an 800 Ohm resistor across pins 1 and 3. I am unable to look at the datasheets right now, but it seems odd to me that they use an 800 ohm load, is that common? – Ben Watson Oct 18 '19 at 6:02
• @BenWatson I don't have the actual device, and just trying to find a way to obtain information based on the public data. I'll try reading through their application notes to see how did they measure the S parameters. – 比尔盖子 Oct 18 '19 at 6:05
• @BenWatson The application note says, "Return loss, or VSWR, is measured at the primary winding, with the secondary terminated in its theoretical impedance". It's a 1:16 (impedance) transformer, so I think the figures in the datasheet is measured with a 800Ω matched load, and by doing some arithmetic, I think I should be able to transform the S-parameter as if it's terminated by 800Ω load and reproduce the datasheet chart. – 比尔盖子 Oct 18 '19 at 6:10
• Oh I see now. Yes the S11 ought to vary with a changing load. Is there any reason why you dont trust their official Return Loss chart? You can email them for clarification and they should get back to you within a week! – Ben Watson Oct 18 '19 at 6:17
• I suppose so, unfortunately it makes them less useful for cross checking if their other charts are under different load conditions. Sorry I couldn't be helpful! – Ben Watson Oct 18 '19 at 6:47

By reading some application notes, I discovered, indeed, that the 4-port S-parameters measurements file is meant for creating a model of the transformer, and it can be used with a simulator directly, such as Genesys or ADS. Those are expensive tools unavailable for hobbyists, but I also found the free and open source Qucs simulation supports n-port S-parameter file as well.

To use the s4p file for simulation...

1. Create two power sources and specify their input impedances, in this case, 50 Ω and 800 Ω, and ground them.

2. Create two equations for S11_dB and S21_dB, and create a "S-parameter simulation", set the simulation type to log, set the start to stop frequency, and set the number of points.

These steps are needed for all simulations. A quick way of setting the skeleton up is using the filter synthesis wizard to obtain a random filter, and delete all the R, L, C components.

1. Add a "n-port S-parameter file". edit the properties and change the number of port to "4", set the file location to s4p file provided by Mini-Circuit. Since port 1/2 are the primary side, port 3/4 are the secondary, we need to rotate the device by 90 degrees, a bit awkward but it does the job, finally ground the Ref port.

Run the simulation.

It works, we get identical results just like the datasheet (the only difference is the definition of positive/negative)! We can now even plot the results in different format, such as a Smith chart and a VSWR chart, hooray!

There is still ~4 dB of difference, probably due to measurements under different conditions, or due to artifacts of the simulator or its setup, that worth further investigation.

Update: Agilent ADS produces the same simulation result. Thus it's probably related to measurement conditions.