# Measuring small inductances

I'm working on a small hobby project - a small (230V wall plugged) coreless induction furnace. I generally know what I'm doing, chosen a topology, calculated inverter and coil parameters, desired resonance frequency etc. Now my problem is - how do you, in reality, measure the very small inductance that the coil would have, on the order of 1-5 microhenrys? Is banging the coil with a voltage step and measuring the time it takes to reach certain current a good idea, and if not - how?

Or am I trying to reinvent the wheel and should I just shop for a LCR meter? I've seen some very reasonably priced models (for examplpe Voltcraft products, ~100 EUR) that are advertised as capable of measuring from 0.1 uH. Are they any good?

Arguably, the easiest way is to just measure it:

      +--------+
|        |
|      [50R]
|        |
|       [C]
[GEN]      |
|        +------+
|        |      |
|       [L]  [SCOPE]
|        |      |
+--------+------+


With $C$ known, adjust the generator's output frequency for a peak across the scope, then determine the reactance of the capacitor with:

$$X_c=\frac1{2\pi fC}$$

Next, since the reactance of the capacitor and the inductor will be equal at resonance, (the frequency at the maximum amplitude of the peak on the scope) solve for the inductance with:

$$L=\frac{X_c}{2\pi f}$$

Both equations can be combined:

$$L=\frac{1}{(2\pi f)² C}$$

You may need to adjust the value of the $R$ in order to get a nice peak.

• Are you familiar with Mathjax? It is integrated into the site. Your formulas could be a lot more readable by using it. – JYelton May 29 '14 at 15:49
• OK, thanks. I've only been here about a week and I'm still working out the kinks. – EM Fields May 29 '14 at 16:31
• No worries, that's what the comments are for: to help inform. Also don't forget the schematic editor (via CircuitLab). – JYelton May 29 '14 at 16:45
• I dig the ASCII art, though. So 90s! :) – rsz May 30 '14 at 7:41

Regarding "

Is banging the coil with a voltage step and measuring the time it takes to reach certain current a good idea

"Banging" the coil is an adequate method, but no need to measure current.

Simple definition of "banging a coil" : Placing a capacitor in parallel with an inductor. Connect oscilloscope across the resonant LC circuit. Then using 9 volt battery, connect negative lead to circuit. Quickly tap and remove the positive lead to the other side of the resonant circuit. Observe the decay ringing frequency. Calculate inductance L using frequency and known capacitor value.

You will be resonating the coil so I would use capacitors you are happy with i.e. C0G/NP0 that have a reasonable tolerance (maybe 5%) and use the circuit resonant frequency to tell you the inductance by using a re-arrangement of the standard formula: -

$f_0 = \dfrac{1}{2\pi\sqrt{LC}}$

I'm presuming you have a frequency counter to measure the resonant frequency. Even a scope will do to give half-decent indications of frequency.

• Allright, I just realized in my case this actually boils down to "don't measure it, just tune for the resonance". What I fear is that the coil I'll wring from some copper pipe will be far from the inductance I shoot at - that's why I asked about measuring it. – rsz May 29 '14 at 12:50
• @rsz - you don't have to power it up as an induction oven - use an oscillator and tune it to peak with some known capacitance. Whatever the peak is you can still re-arrange the formula in my answer to calculate inductance. I make coils that have to transmit power over a couple of inches (maybe 1 watt) and I use a signal generator, some arbitrary capacitance and an o-scope for setting it up and calculating inductance - it makes no difference what power level you use or how you generate the signal. – Andy aka May 29 '14 at 13:27

Measure its "resistance" (actually, impedance X) when a high frequency signal is fed into it (in the MHz).

X = 2*pi*F*L where X in Ohms, f = Hz and L = Henries

• Allright, but how do I, using the cheapo hardware at hand, measure impedance while feeding a high freq signal? Does it actually mean to feed the coil from a signal generator with stabilized voltage, and measure average current? That seems easily doable, but would a low-end multimeter plugged in series measure the high freq AC current correctly? Moreover, how would I separate the measured impedance into the real and imaginary part? – rsz May 29 '14 at 12:42
• @rsz, the reason one uses a high frequency is so that the reactive part of the impedance is much larger than the resistive part: $Z = R + j\omega L \approx j \omega L$ for $\omega L >> R$. – Alfred Centauri May 29 '14 at 12:50
• You really need a scope. You feed a sinewave signal into the coil which is in series with a resistor (say, 100R) and measure the voltage dropped across the coil. That will give its "resistance" which is generally equal to X. – user32885 May 29 '14 at 12:56

Observing the slope of the current ramp for a known applied voltage works quite well.

Place a small resistor in series with coil, one end to ground.
Apply a square wave (voltage step via a suitably high current driver.
Turn off drive after a =suitable period - inductor will "ring - arrange to dissipate the energy in some manner (Resistor + diode across coil / diode to supply / diode only across coil / zener / whatever.)
Repeat with square wave drive of whatever duty cycle suits.
Observe voltage across series resistor on scope.
You should get quite a reasonable triangular current waveform when V is applied.
I ~~= V x t /L (assuming R small wrt Xl)
For say 12V square wave and 5 uH you should get 12V / 5uH = 2.4A per uS ramp.
With Rseries = 1Ohm you get 1V/A and are liable to interfere with Xl.
0.1 Ohm = 100 mV/A which is probably low enough.
R really should [tm] be relatively non inductive.
A short length of Nichrome or Constantan works well.
(These or similar zero temperature coefficient of resistance materials are about essential for the current reference resistor. Nichrome is reasonably available but toaster or heater elements are a source of such. Soldering requires an act of parliament (troublesome to obtain in the US) or a special flux or lots of scratching and scrubbing at soldering temperature plus some luck.
Clamping works.

You can calibrate Rseries by establishing a known fixed current through it from a psu and measuring voltage drop across the resistor. .

You MIGHT expect that OTS 0.1Ohm resistors were 0.1R at the body connections but I have seen ons where they must have assumed a certain amount of lead length in the resistance so they were < 0.1 R. So, trust them not - measure.

• Thanks for your comments. FWIW, I am pretty sure soldering kanthal works good after a copper strike is plated on it (it has to be cleaned and etched in alkali before plating, though). Never tried nichrome, but I would assume the same. Also, nichrome is far from zero temperature coefficient of resistance. Of course it's much simpler to just clamp it :) – rsz May 29 '14 at 14:34
• @rsz - NiCr is close enough to zero tempco for practical purposes in this application. Change in resistance is 0.00004 per degree C. Shunt does not want to be designed to glow in the dark :-). At 25C rise the change is +1%. Keep rise to a degree or few and you can get around +0.1% . Other variables will swamp this handsomely in all systems that people have suggested here. – Russell McMahon May 30 '14 at 23:29

Although I spent years using some of the methods stated here, I find that a \$20 LCR meter from china through ebay saves me lots of time when I deal with inductors a lot. In a pinch, the mathematical methods work fine, but if you find yourself continually needing to measure coils at any point, you'll enjoy a cheapo LCR meter greatly. From my experience the cheap ones show a reading within 1% of what the manufacturer rated the coils at.