NanoVNA-H4 – inductor challenge – part 2

Recall the fixture from NanoVNA-H4 – inductor challenge – part 1:

NanoVNA-H4 – inductor challenge – part 1 stated:

In fact, we have the underlying inductor connected by 35mm of 570Ω two wire transmission line, so there is a small amount of impedance transformation (which could be approximately corrected in this case by setting port extension to 20ps… but that is not done for this article).

Let’s explore that using Simsmith.

Firstly, the one way propagation time of a 35mm length of line with VF close to 1 is 116.7ps, two way (edelay) is 233.4ps.

We can undo the transformation by the transmission line by inserting a section with equivalent negative length.

Above shows the measured Z in magenta, and the adjusted Z in green representing the actual Z of the inductor at the coil ends.

So, above we have the true Z of the inductor at the ends of the coil.

If we can undo the transmission line in Simsmith, can we do something similar in NanoVNA?

Some NanoVNA firmware and some PC client programs have a port extension facility.

The port extension facility allows adjustment of the phase of s11 (wrt 50+j0Ω) to (partially) undo a physical port extension. But our port extension is 35mm of 570Ω, so we need to adjust it to the equivalent length of 50Ω port extension, \(edelay=233.4 \frac{50}{570}=20.5 \text{ ps}\).

Above is the measurement in NanoVNA-App with 20.5ps of port extension. Note that the self resonant frequency (SRF) reconciles with the adjusted Simsmith model.

Having calibrated the connecting transmission line out using port extension, we can now look at the impedance plot at the coil ends.

So, having largely removed the fixture effects, it is a little different… but it is nothing like zero resistance and reactance proportional to frequency.

Beware of convenient displayed values.

If we use NanoVNA with the out of the box default format for hammy Sammy, we might see the following display with marker near 20MHz.

So, looking at the Smith marker value, it informs that at the ~20MHz marker, the inductance is around 35µH… this is not a 35µH inductor. Is it a “35µH inductor” at any frequency? No, not really.

Above is the display formatted to show the Smith chart marker value as impedance (impedance is a complex quantity, R+jX).

This R+jX value is correct, but it is wrong to simply imply an underlying inductance without further information.

So, having undone the fixture effects to obtain a more accurate measurement of the coil itself, back to the original question, our understanding of an inductor remains questionable. What is going on here?

Continued at NanoVNA-H4 – inductor challenge – part 3.

Footnote: the screen captures from the NanoVNA-H4 are post processed to double their size and invert the colours so you can print this page without lots of toner or ink consumed.