Amplitude-dependent phase

[naegele97]

Hi everyone,
I am using the LibreVNA for characterizing copper coils that have resonance frequencies around 25MHz.
I've noticed a slight but very reproduceable amplitude dependency of the phase as depicted in the attached picture.
Is there a specific reason for that?

In order to get this plot I performed 50 sweeps at each amplitude between -40dB and 0dB, while keeping the RBW and
span constant at 10Hz and 100kHz respectively. I then extract the phase at a given (and always the same) frequency i.e. sweep data index.
Since I compared the data from LibreVNA with other commercially available VNAs that didn't exhibit this behavior
I was wondering if there is a known answer for this amplitude dependency of the LibreVNA.

[jankae]

I don't have a good answer explaining this behavior yet (and have not seen but also not looked for it before). But I do have a couple of questions to better understand it:

• Which S parameter is used to plot the amplitude? And what does the S parameter measurement look like? (please share a Touchstone file if you have it)
• Which phase value is the correct one? What does another commercial VNA report as the phase for that frequency?
• Did you calibrate for each amplitude level or did you use the same calibration?
• If you used the same calibration, at what amplitude was it done?

[naegele97]

I am sorry for not providing enough information.

Below is a comparison plot with a Rhode&Schwarz ZNLE (https://www.rohde-schwarz.com/de/produkte/messtechnik/vektornetzwerkanalysatoren/rs-znle-vektornetzwerkanalysatoren_63493-447936.html)
and a Rigol DSA 815 Spectrum Analyzer (which is not capable of measuring phases: https://www.rigolna.com/products/spectrum-analyzers/dsa800/dsa815/bundle/).

The upper plot depicts the resonance frequency of a S21 (transmission) measurement. The devices from Rigol and Rhode&Schwarz go with their factory calibration and I calibrated the LibreVNA with a SOLT calibration at 0dB assuming ideal short, load, open, and through standards (I did not use the LibreVNA calibration kid but the standards that where in the LibreVNA package). With the exception of a slight offset (could be attributed to a different error model in the calibration or different calibration standards?) the behavior of the LibreVNA and the premium vector network analyzer from Rhode&Schwarz are similar. The phase behavior, however differs. Please note that compared to my
plot I shared first the phase data of Libre VNA is intentionally shifted by 180° for comparing it to the Rhode&Schwarz. Please also note that for S11 the phase behavior of LibreVNA is similar.

The data for the plot was acquired as follows (I sadly don't have a touchstone file for that):
50 S21 frequency sweeps with 601 data points were performed between 25.475 to 25.575MHz at an IF BW of 100 with 0 dwell time, and no averages. 1 sweep took 12.5 seconds. All sweeps were then averaged by hand for the amplitude (dB) and phase.
A parabola was fitted to the averaged amplitude data in close proximity (+-5KHz fitrange) to the resonance in order to acquire the fit extremum data. The phase on the other hand was always acquired at a fixed frequency.
The procedure was repeated for amplitudes between -40dB and 0dB in steps of 2dB.

The LibreVNA was operated for 30minutes before the start of the calibration and the measurement in order to properly heat it up beforehand. A heat sink was additionally used to prevent overheating.

[jankae]

Thank you very much for the details. I just checked on one of my units and can see a similar behavior (about 3-4° of phase drift in S21 when changing the power from -40 dBm to 0 dBm). For this measurement I connected a short SMA cable directly between the ports:

I think this is due to different components in the LibreVNA (e.g. mixers and amplifiers) getting closer to their saturation point. In details like this it just can not keep up with professional VNAs from R&S. You should be able to improve the situation by repeating the calibration process for different amplitudes but of course that is also much more work.

[naegele97]

I actually went through with it and repeated the test with each amplitude having its own calibration curve between -40 to 0dB in steps of 2 (but at a IFBW of 1kHz for a faster measurement. The issues is IFBW independent anyway). The slope looks only a little bit different as displayed below:

I marked your response as answer since that "problem" cannot be solved easily without extensive debugging.

For future reference I would like to remark that this behavior is independent of:
-Sweep range
-IFBW
-Averaging
-Calibration with the provided calibration standards assumed to be ideal.

[jankae]

Thank you so much for checking whether individual calibrations help. I am a bit surprised that they seem to make almost no difference.

How large is your S21 at the frequency of interest? If it is close to 0 dB, I would expect the calibration to correct for most of the amplitude-dependent phase error. If it is much smaller, the amplitude on the port 2 receiver will be very different between the calibration and the DUT measurement and this could explain the result you are seeing.

If that is the case, it might help to use a through standard during the calibration that has a similar S21 as your DUT (e.g. an attenuator). But this could create its own problem, especially for S11/S22 calibration coefficients and requires careful configuration of the calkit definition. Probably diminishing returns at this point and we most likely will have to accept phase error as a limitation of the LibreVNA.

[naegele97]

Thank you for your suggestion, my |S21| is indeed much lower with approx. -20dB. Is it possible that the calibration standards limit the calibration quality? There must be a reason why manufactures like Rhode&Schwarz offer calibration kits costing more than the LibreVNA itself besides the profit margin.

[naegele97]

I repeated the measurement with the suggestion you've made and indeed, the phase behavior of S21 is gone:

It is, however, still present in a S11 measurement.

[jankae]

Is it possible that the calibration standards limit the calibration quality?

That is possible but it would not show up like this. A bad calibration due to low quality calibration standards usually does not show up at all (unless you know how to check). A cheap calibration standard may deviate from its coefficients (if coefficients are supplied at all) or maybe its behavior drifts with temperature. Both would limit the accuracy of your calibration but you would not notice at first glance. All your measurements would just be slightly off. Unless you know the DUT behavior very well or have another VNA (and calkit) to double-check, such small errors are usually not obvious (and would be constant with different amplitudes).

Better quality calibration standards are manufactured to tighter tolerances and sometimes individually measured.