# Help measuring inductance of custom-made coil

I am testing some coils that will be used in a resonant circuit as antennas for very low frequencies (<100 Hz). The coils work great, but the only way I have to tune is trial and error.

If I measure them with an RLC meter I get an impedance of about ~70 H using the 120 Hz settings and ~115 H using the 1 kHz option. I don't think that's correct, as the tuning capacitor for that value is not the best and I get a stronger signal using capacitors much smaller than that. The resistance of the coil is about 18 kΩ (DC) and has a core.

I tried measuring the inductance using several methods. The only one that seems to work is the phase shift method and that gives me a value of 15 H. Again, I don't think that's right and which is even more surprising is that the phase shift goes down when I increase the frequency to the kHz range (it should be increasing with the frequency).

Any advice of how to measure the inductance of large inductors (and with high impedance) precisely?

• What's the self resonant frequency (SRF) of the inductor? With many turns over a ferrite rod the interwinding capacitance of the inductor will be large.
– qrk
Commented Dec 16, 2023 at 20:51
• I think it is around 18KHz. Commented Dec 17, 2023 at 0:08

If you have a current probe and an oscilloscope, you can put it in series with a power FET, give a short, low duty cycle pulse to the FET gate, and measure how fast the current ramps up in that time. V=L*dI/dt, so if you divide your input voltage V by your current ramp rate dI/dt, you get your inductance.

This method captures both the linear range of the inductor and the saturation current, where your inductor stops behaving linearly.

Edit: if you don't have a current probe, you can use a small sense resistor in series and measure the current on a voltage probe. Just know that you now have an RL series circuit, and the current measurement is only valid while the voltage across the resistor is small compared to the total voltage.

• I prefer this method, because it gives the full L(I) curve incl. non-linearity irrespective of parasitics to a very large extent. Commented Dec 17, 2023 at 17:25
• @tobalt agreed; especially in power applications, finding the saturation current of inductors tells you a lot about how they behave and their useful regions of operation. Commented Dec 17, 2023 at 18:59

You are right. Measuring the phase is the "only" mean to determine L.
Note that the capacitive value should be "high" as "parasitic".

After "some" test, I simulated this circuit.
The phase curve shows the "best" ... the "deviation" of the value of the self.
Note that the phase goes "high" before going down while increasing frequency ...

Added the TRansient Analysis for that circuit.

Without a description of the component itself, it doesn't seem useful to suggest ways of testing, or frequency or impedance to do it at. So, I'll discuss impedance itself, and how and why we use inductance.

A lossy reactive element, has a capacitance or inductance that varies with frequency.

An "ideal", in a sense, lossy inductor, might be modeled by taking an element $$\|Z| \propto \omega^\alpha\$$ for 0 < α < 1 (or more generally, a reactance for -1 < α < 1, i.e. including the capacitance case). In which case, we have (roughly speaking[1]) $$\Q = \tan |\alpha|\$$, and thus the resistance and reactance are proportional as well, fixed to each other by this ratio.

Which means, in general, real inductors "aren't", but they're close enough: say, for a Q > 10, L is within 10% per decade of frequency. If that's close enough for what you're doing, heck yeah, call it a L µH inductor.

So, while I don't know what you have, it may simply be so lossy that an inductance isn't very meaningful, or, is only meaningful at the design frequency. You will need a meter to test at that frequency to know for sure.

It might also be nonlinear, particularly if the magnetic loop is a closed path of permeable material (ferrite, iron, etc.), in which case it depends on excitation level as well, and you'll need to verify operation either in intended use, or a test jig that roughly emulates it.

[1] I still haven't been able to find a working-out (or accomplish it myself) of the Kramers-Kronig relations, as applied to this function. (Or, much of any functions at all, as a matter of fact. But plenty of articles employing it on recorded data, or showing off endless proofs of the relations themselves...) I suspect partly because the bare function is non-causal, but, I don't see where a unit step solves it. Alternately, I'd gladly wire a resistor in series and parallel to make a finite-impulse-response composite network (i.e., it has the stated asymptotic slope over some given frequency range), but doing that exactly analytically seems beyond my knowledge at the moment. Anyway, considering the Fourier transform of this and similar functions, the above seems close enough.