Hi everyone.

I've been using a nanoVNA to measure complex impedance of some components (by series, shunt and shunt-through methods).
At 100 MHz, a simple 350 nH handmade air core inductor (0.04 ohm DCR) shows quite high resistive component, about 30~60 ohm.
The reactive component does seem about right (inductance falls just a little bit, to about 320 nH).

My problem is understanding where the high resistive loss come from.
There're no losses due to hyteresys or eddy currents, and the skin effect is not enough to be the root cause (at 100 MHz, DCR should raise by a factor of 40, but still should be on the order of 1 ohm).

The inductor is a simple 7 turn rectangular section using pvc insulated 0.5 mm/AWG24 diameter wire.
At 10 MHz, I get about 0.5~1.5 ohm.

Thanks in advance for any clue or help.

 

At high frequencies, the current flows in a wire only very near the surface. This effect is called skin depth. So the cross sectional area of your wire is far less than you think it is, hence the high resistance. Lots wire is often used for high frequencies. It consists if many very fine wires, so the skin depth effect is minimized.

 

A complex impedance can be represented in several different ways. As you go up in frequency, deviations from ideality cause things to appear counter intuitive. You need to look at the evolution of the impedance as a function of frequency to understand what is happening. I'm not there and I cannot look over your shoulder to see what might be happening.

 

This effect is called skin depth.

I considered that. As I said, "the skin effect is not enough to be the root cause (at 100 MHz, DCR should raise by a factor of 40, but still should be on the order of 1 ohm)".

 

It does appear that there is a problem with the resistance measuring accuracy of the network analyzer at that frequency.
How is the coil connected to the analyzer and how long are the wires from the analyzer to the coil?

 

How is the coil connected to the analyzer and how long are the wires from the analyzer to the coil?

Here, the coil is placed in series with the analyzer ports, to measure S21. The analyzer is fully calibrated with the test fixture in place, for the frequencies of interest. The 50 ohm coaxes are short (about 10 cm/4"), but included in the calibration too. At 100 MHz I would expect some innacuracies (particularly with S11 delay/phase or the reactive component of impedances), but not so much on the resistive component. Is it a reallistic expectation?

As a side note, a 50 ohm resistor measures close to 50 ohm at 100 MHz, just shows some inductance (as expected, due to the component leads).

 

My FM transmitter uses thick enameled wire with 8 small tight round turns. It is about 100nH and tunes to 100MHz with a 5-35pF trimmer capacitor.

Your coil is way too large and its turns are very far apart.

 

Your coil is way too large and its turns are very far apart.

Definitely, yes. But I'm not trying to build a good inductor right now. The question is why the measured resistance (losses) could be abnormaly high when measured with a VNA. The inductor in the picture is just a quick test. I've repeated the same measurements with other air core inductors, better wound on thick enamel wire, and the resistive component is high for all of them (although the thicker the wire, the lower the resistance, as expected).

 

Definitely, yes. But I'm not trying to build a good inductor right now. The question is why the measured resistance (losses) could be abnormaly high when measured with a VNA. The inductor in the picture is just a quick test. I've repeated the same measurements with other air core inductors, better wound on thick enamel wire, and the resistive component is high for all of them (although the thicker the wire, the lower the resistance, as expected).

Plain and simple. We are not there, and we cannot see what you are seeing. What you think are resistive losses may be the result of a vector sum of reactances, both primary and parasitic as a function of frequency, that look like resistive losses. What does the VNA output look like?

The following article may provide some insight:
https://owenduffy.net/blog/?p=17298

 

What you think are resistive losses may be the result of a vector sum of reactances, both primary and parasitic as a function of frequency, that look like resistive losses.

Thank you. That makes sense. I've done some more experiments adding compensation for the electrical length, and I do get differences in the "losses".

The following article may provide some insight:
https://owenduffy.net/blog/?p=17298

Thanks again, I'll read it thoroughly.

 

Radiation resistance? Or perhaps it's resonating (with 7pF at 100MHz) and the circulating currents are much higher than the input currents leading to higher losses?

 

If you sweep a real inductor over a considerable frequency range, the Smith chart will look like orbits around the origin, starting at a point slightly to the right of the +jω-axis. At certain places along the first orbit, as you approach the positive real axis, the impedance will "appear" to be almost purely resistive with a cartesian value that looks like:

\( Z\;=\;R + jX\;=\;100 -j3 \)

which I will admit "looks" mostly resistive despite not having much in the way of actual resistance at lower frequencies.

 

Magnetic losses into air core is pure nonsense. Instead You have a large losses into Focault effect in wire skin. Solutions: silvercoating; litcendrating; take simple thicker wire; clean off oxides and spray good lack. Silvercoating MUST be hammered otherhow no effect or negative effect. Litcendrating have very sharp positive effect. Last two methods helps only slghtly.