Inductance and Frequency Meter

In principle, it's easy to measure the inductance of a coil. Use it, along with a capacitor of known value, to determine the resonant frequency of an oscillator circuit; then feed the oscillations to a frequency counter. Knowing the frequency and the capacitance, you can calculate the inductance using the formula from Physics 101:
where f is in Hertz, C is in Farads and L is in Henries.

The bad news is, your capacitance is never really known; component tolerances and stray capacitance from nearby wires muddy the picture. The good news is, you don't always need high accuracy; fair-to-good will often suffice. The other good news is that a low-cost microcontroller, such as the Arduino Uno, can measure frequencies via its built-in counters and timers. You can use software to compensate for systemic errors and to format the results in pleasing ways.

Best of all, there's no need to invent this wheel; it's all published on the Net. I stole the oscillator circuit from Lukas Fässler's inductance meter. I downloaded Martin Nawrath's frequency-counter library for the Arduino chip. Sparkfun's Arduino Pro Mini has the important Arduino features and costs less than $10. Starting with these, I tinkered until I was satisfied.

Here's the circuit I ended up with. This was my first experience with the Eagle layout program, hence some of the clunky line crossings. The connectors on the right edge go to the little Arduino chip. The Arduino pin assignments are described in the LFmeter program, called a "sketch" in the Arduino world.

Some things that may not be obvious in this circuit:

• It's helpful to zero the meter now and then. To do this, short-circuit the test probes — there's a fixed 10µH coil in series with the probes, so the oscillator will still run at some high frequency — and press the pushbutton. The pushbutton, conditioned by the debouncer, is fed to an input pin on the Arduino. Software does the rest.
• The sine wave from the oscillator is squared up by one gate of the 4093, a quad NAND gate with Schmitt-trigger inputs.
• As a handy side effect of measuring inductance, we can also measure the frequency of an external signal. The signal is cleaned up by another gate on the 4093.
• Two outputs on the Arduino (I picked pins 7 and 8) are used to enable either the internal oscillator or the external frequency source. The chosen signal is fed to pin 5 on the Arduino. This pin supports high-frequency interrupts. Some writers have claimed that it can handle pulses up to 4 MHz, but that seems dubious given that the Arduino's clock is only 16 MHz. To be safe, the circuit is limited to less than 1 MHz.
• I powered everything from a 9-volt battery, but the chips all require 5 volts.The Arduino has a built-in voltage regulator, but I wasn't sure it could handle the current — it just looks so tiny. So I put a full-size regulator in one corner of my circuit board. This is surely overkill, but that's OK.

I packaged everything up in a tin gift box that I found on sale for $6 at Staples. I'd have preferred to spend less, but the tin contained a half pound of tasty mint-flavored fudge, which offset some of the pain. The artwork on the box was tasteless, but spray paint fixed that.

Click an image to view its enlargement

The Arduino microcontroller is the little blue thing in the top-right corner. Despite it's small size, it has more computing power than my first store-boughten computer, a TRS-80.

Initial trials

To see how accurate the meter was, I measured a bunch of store-bought coils. For the small coils, under 500 µH, the meter more-or-less agreed with the labeled inductances. The discrepancy was roughly 10%, more than the 5% tolerance of the inductor but still in the ball park. But the descrepancy grew greater as the inductors got larger. At 5 mH, it was off by 40%. The bigger coils were even worse. But why?

Some hypotheses came to mind:

1. Inaccurate frequency measurement: The Arduino's clock might not be exactly 16.00 MHz. Or the pulse-counting routine might be stopping too soon or too late.
2. Might the ohmic resistance of the coil affect oscillator frequency? Tiny inductors are wound with very thin wire, so resistance is not negligible.
3. Or, might the capacitors be far off their labeled value?
4. Gremlins and evil spirits. Or if you prefer, the unknown unknowns. A competent engineer might have better insight. But in my experience, "demons" is always a plausible explanation.

To test hypothesis #1, I lashed together a crystal oscillator, using some precision radio-frequency crystals left over from my ham-radio days. (Those days were in 1968. I never threw out the crystals, because they were sure to come in handy some day. And lo! That day arrived.) Turns out that the frequency counter was spot-on: less than a tenth of a percent error.

I decided not to try to untangle the other possible causes. Instead, the Arduino would just apply a correction formula in software. After all, computing is what computers are good for. I fed all the measured values into a spreadsheet, turned them into graphs and used the spreadsheet's curve-fitting tool to find a suitable formula.

Dividing the data into three regions, each with its own formula, proved to be the best compromise between simplicity and a close fit.

Adding these fudge factors to the code, I got decent agreement between my meter readings and the store-boughten coils. This meets my standard for "fair to good accuracy," which is all I need for the upcoming projects I have in mind.

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