# Measuring small capacitor parallel to big inductance (Network Analyser)

So what I have at hand is a cheap network analyser that can present the measured impedance in form of the values of different equivalent circuit topologies, e.g. R-L series or RL parallel.

What I want to do is measure the electrical parameters of a simple PCB antenna structure, which is typically modeled as as capacitor (mainly inter-winding capacitance) parallel to ( R + L).

So I did the "SOL" calibration and measured S11. Concerning R and L, I chose the available Network Analyser Representation of the equivalent circuit called "RL" (I have no C//(R+L) representation available) This measurement shows the values for both, R-L series and R-L parallel equivalent circuits and I get reasonable values so no problem here.

But how can I determine the value of the capacitor? Is it possible at all? I thought of writing down the formula for the real and imaginary parts of the impedance of the topology I want to model (i.e. C//(R+L)) and solve it using the measured values of S11. Besides of being inconvenient I think I would get a wrong result since any physically capacitance present in the structure is already indirectly included in the values i get for R-L (by having a slightly smaller L than without cap), right?

(Of course the inclusion of the capacitor in the presented R-L values is possible only for a specific range of frequencies because above some frequency the capacitor will dominate and "get visible" in the measurements, but that does not help either...)

• What kind of network analyzer do you have? Any Link? How did you attach the analyzer, what kind of fixture did you use? – Ale..chenski Oct 17 '16 at 19:58
• The device is a DG8SAQ found here: sdr-kits.net and I simply connected the TX output of the device directly to the antenna (as I wrote above, before I did the open-short-load calibration). So no special fixture, just TX output of VNA per SMA cable to antenna feed point. – Junius Oct 17 '16 at 20:03

Set up your network analyzer to plot the response as magnitude of impedance ($\left|Z_L\right|$), with log scale on the y axis.

Assuming 1. your network analyzer can reach a high enough frequency, and 2. the connection from the reference plane to the termination you're trying to measure is short, you should see $|Z_L|$ increasing from low frequencies up to some peak and then decreasing after the peak.

The equation for the part of the curve where it's increasing is approximately $Z_L(f)=j2\pi{}fL$. The equation for the part of the curve where it's decreasing is approximately $Z_L(f)=\frac{1}{j2\pi{}fC}$. By picking out a couple of points on the appropriate parts of the curve, you should easily be able to estimate both $L$ and $C$.

If you already know $L$ you can get $C$ really easily knowing the resonance frequency (the frequency where the graph reaches its peak) is $f_R=\frac{1}{2\pi\sqrt{LC}}$.

• I am aware of how inductors and capacitors behave over frequency, but I think just "estimating" is a bit of a problem because I assume the capacitance is in the range of 10-15pF. Thanks anyhow, I will have a look at the "plain" abs(Z) data and see If i get the expected graph. – Junius Oct 18 '16 at 17:36
• If you don't get the expected graph, then your model (L and C in parallel) is not a good match for your actual load, and you need to find a better model. – The Photon Oct 18 '16 at 17:40
• Also, estimating is all you can do because no measurement is perfect. – The Photon Oct 18 '16 at 17:41
• Well, the application notes I found all use this model for that kind of simple PCB antenna so I guess it´s quite realistic ;-) Btw: Any hints on my question on whether the calculation I suggested, is a valid approach or Is there some mistake in it? EDIT: I mean the calculation of C out of the S11 data of the R-L equivalent circuit. – Junius Oct 18 '16 at 17:44
• Sorry, what you said about "Network Analyzer Representation" doesn't make any sense to me. That's a feature specific to the particular VNA you are using, so you'd need to talk to someone who also uses the same model VNA to get any more information about it. – The Photon Oct 18 '16 at 17:46