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When it comes to measurements with VNA, my experience tells me that whenever there is a "dip" in the S11 parameter, your takeaway should be that there is a resonance there (this is how the bandpass of a filter or an antenna is most commonly calculated).

However, for circuits with very high Z, basically everything is reflected, so you cannot really use S11 to measure them. In fact different sources in literature indicate the "series/transmission" as the correct setup to measure a high-impedance DUTs, whose Z is then calculated through S21.

How can I identify the resonances in this case? In the following example I measured a big coil and saw both how its S-Parameters as well as the impedance calculated from them looks like. I do not believe there is a resonance by marker 1, but I might be wrong.

S-Parameters and impedance magnitude

S-Parameters and impedance phase

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3 Answers 3

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The sudden sign change at S21 indicates a resonance.

This document can help you with the calculations:

http://www.karinya.net/g3txq/chokes/s21.pdf

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  • \$\begingroup\$ Wouldn't this work for "VNA"s that do not measure wave quantities? As far as I can see online, the formula is much more complicated than that. Moreover, how can you proof that there is no resonance where the reflection method is used? \$\endgroup\$ May 21, 2021 at 11:22
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S parameters are not the best representation to find resonant frequency. Depending on which VNA you have, most have a Z mode that allows to plot impedance instead of S parameters. Z parameters are the best one to see resonant frequency. You will see the impedance go toward infinity at resonance.

You can find it either by plotting over frequency the magnitude of the impedance or by displaying the real and complex part.

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Personally, I find it much better to use the smith chart display. Where the trace crosses from the bottom half to the top half the impedance is totally real (no imaginary part) which is the definition of resonance. Observing dips in the magnitude response is all well and good, but you are not really using the vector network analyser to its full potential if you are only looking at magnitudes.

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    \$\begingroup\$ The bottom two plots from the question are phase so the OP isnt looking only at magnitude. The difficulty in the smith chart display is that it obscures frequency. If you want to compare multiple measurements vs freq a smith chart doesnt help much. \$\endgroup\$
    – Matt
    May 20, 2021 at 23:54
  • \$\begingroup\$ Unfortunately the Smith Chart too seems like to be unable to help in S21 case ( electronics.stackexchange.com/questions/452701/… ) and the S11 is so noisy that I fear it wouldn't make sense anyway. \$\endgroup\$ May 21, 2021 at 11:14
  • \$\begingroup\$ Also in the diagrams, there are both magnitude and phase of both S-Parameters and impedance \$\endgroup\$ May 21, 2021 at 11:40
  • \$\begingroup\$ How would you see a resonant frequency on a smith chart? You define it as the place were the signal pass closest to the end of your plot? If so, it is a pretty hard way to measure it! \$\endgroup\$
    – Julien
    Jul 26, 2023 at 18:15

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