Measure inductance with nanoVNA and coax

[kronos]

I need to measure some inductances, and I like using the nanoVNA (I do not own an LCR meter). One obvious way to measure an inductance with the nanoVNA is to connect it to Port 1, and see, at each frequency, the series R and series L as measured in the Smith Chart. However, I have found that these measurements are sometimes not very exact or reliable, I have found that the phase measurement is far more reliable and exact. So I have come up with a way to measure an inductance using the phase measurement in Port 1, and would like to share it, for anyone that finds it useful.

You connect a known coax cable to Port 1 (known Zo, velocity factor, and length). I use a small coax which came with the nanoVNA, with Zo=50 ohm, vf=0.66, l=0.215 m, and connect the inductance at its end. The nanoVNA is previoulsy calibrated in an adequate frequency range.

When the impedance as seen by the nanoVNA becomes infinite, the phase of \$\Gamma\$ is zero (and the Smith Chart crosses the x axis on the right of the chart). We can measure the frequency where this happens. The phase plot is like this:


At this frequency, all parameters are related in this equation: \$Z_o=wL\cdot tan\frac{w\cdot l}{v_p}\$, where you can calculate the inductance L. \$v_p\$ is the phase velocity, \$v_p={vf}\cdot c\$,and c is the speed of light in vacuum.

I have produced a list with various zero-phase frequencies and their corresponding inductances.
 calcL.pdf (411.57 kB - downloaded 181 times.)

For example, I connect an inductance to my coax, and I measure with the nanoVNA a zero-phase frequency of 11 MHz. The inductance is then 9.6 uH.

You can change the frequency range and the coax length to measure different inductance ranges. This method allows the measurement of very small inductances: if you measure a zero-phase frequency of 175 MHz, the inductance is 18 nH. It provides good resolution at these small inductance values. I hope this is useful to somebody, at least it is to me.

[G0HZU]

I have one of the early (small and cheap) nanovnas here and across HF and into VHF I find it is almost as good as a lab VNA when measuring inductance.
See below for a basic s11 measurement of a small 33nH SMD inductor. One set of traces is for the nanovna and the other is for a lab VNA. I used basic settings on the lab VNA so the traces are still a bit noisy.

You can see the agreement is very good. This is using a basic cal kit for the nanovna and I used a different (better) cal kit with the lab VNA. As you can see there is not much difference in the results? 

[kronos]

You can see the agreement is very good. This is using a basic cal kit for the nanovna and I used a different (better) cal kit with the lab VNA. As you can see there is not much difference in the results?

And that is taken directly from the Smith Chart? In my case, with a nanoVNA V2, I find that the measured inductances in the Smith Chart show a big variation. In general, values at the outer circle (\$\lvert\Gamma\rvert=1\$) show more problems than in inner circles. I will check again.

[G0HZU]

Hi, I'm just post processing the raw s11 data dumped from the nanovna.

Here's a better comparison below. I think I used the same cal kit for both measurements of a 240nH SMD inductor. Note that I'm using an early version of firmware and one of the early Hugen 2.8" nanovnas with the blue PCB.  At the time this was the one to buy.

I also use my own software to calibrate the nanovna and to dump data from the nanovna. I also found that later versions of the firmware aren't as good (as in accurate) despite all the added features. I've been using network analysers all my career up to many GHz so I do try to explore and get the best from any instrument that I own. I'm pleased with what this nanovna can deliver up to about 50MHz. Above this it starts to lose performance rapidly compared to a lab VNA.

I think the agreement below is very impressive!

[radiolistener]

However, I have found that these measurements are sometimes not very exact or reliable

When you connect inductor or capacitor to VNA through coax cable, you will measure inductance or capacitance of both coax cable + inductor/capacitor. Reactance of coax cable depends on it's length and frequency. This is why you see not reliable result.

In order to eliminate coax cable effect from measurement you're needs to calibrate your VNA through coax cable which will be used to measure inductor/capacitor. Another way is to setup electric delay of the coax cable in VNA settings. You can measure it in TDR mode for coax cable with open end.

Also note that any wires, include legs of inductor/capacitor also have it's own reactance and also will affect your measurement. So, you're needs to use as short wire/legs as possible in order to reduce measurement error.

[kronos]

I think the agreement below is very impressive!

Yes it is! I use the own display of the nanoVNA. I did a couple of tests, and yes, it gets in the ballpark at some frequencies, and far off at others, specially for bigger inductances (still below SRF). If the inductance is really unknown, how do I know the correct value? I am probably doing something wrong. This is why I did a couple of equations and tried only using the phase information, taking advantage of the transmission line effects of the coax.

[kronos]

When you connect inductor or capacitor to VNA through coax cable, you will measure inductance or capacitance of both coax cable + inductor/capacitor. Reactance of coax cable depends on it's length and frequency. This is why you see not reliable result.

I was referring to the measurement directly in Port 1 when I talked about unreliable. This is why I tried connecting a coax and taking advantage of the transmission line effects, in order to only look at the phase of s11. The reactance of the coax (better, the transmission line effects) is taken into account, as I calculate the input impedance as seen by the nanoVNA and determine when the s11 phase is zero.

I do not know, at least it seems to deliver plausible and correct results, possibly I am overcomplicating it. But it was fun!