How can I make a DIY inductance measurement?

[stratotarts]

I've been thinking about pickup inductance measurements. Is there a simple, inexpensive way to obtain a very accurate inductance measurement that would match the readings of a standard meter like the Extech? At the moment, my system only yields an estimate because it just applies a parallel capacitance and calculates the inductance from the resulting resonant frequency. There are two problems with that, the inherent one is that each unit is tested at a different frequency. In order to test every unit at the standard 100Hz, something like a capacitor substitution box would be necessary since a variable capacitor of sufficient value is not practical. Secondly, more of an implementation problem though, the Rightmark audio software balks at the pilot tone levels when the frequency is set so low. It might work with the software oscilliscope but that doesn't solve the whole problem. The current method yields results measured at about 800Hz-1500Hz depending on the inductance. I can imagine a system (like the Extech) where a fixed 100Hz signal is applied and the phase/amplitude is measured and converted to an inductance value. A main focus of my efforts since day one has been to make everything as cheap as possible to encourage more casual experimentation, to include people like kids and students, and to provide options for people who live in countries with exhorbitant import tariffs or shipping restrictions. Does anyone have any ideas?

[aquin43]

The problem is that you don't have access directly to the inductance only to the series combination with the pickup resistance which is a fair bit larger than the reactance of the inductance at 100 Hz so that the overall phase angle is only about 16 to 20 degrees.

A method that suggests itself, if you have access to an oscilloscope that can do X-Y plots is something like the following.

Assuming that you can measure frequency and resistance accurately and can somehow get hold of one accurately known capacitor, you can compare the phase of the current through the pickup with the phase of a low pass RC filter. The advantage of this method is that it is a null method where you tune to make the Lissajous curve collapse into a line. There is no need for simultaneous level matching just keep the levels on screen more or less the same. Once you have the phase null, you can measure the potentiometer as set and calculate the phase of the capacitor voltage. This will give you the phase angle of the pickup impedance and, since you know its resistance (plus 1k0) that will give you the reactance of the inductance. That and the frequency will give the value.

I haven't worked out the formula yet, but it will be pretty simple.

Edit: The frequency doesn't appear in the formula, which is another advantage.
The formula is L = Rpot * (Rl + Rt) * C

Where Rpot is the pot plus its series resistor
Rl is the pickup resistance
Rt is the resistance in series with the pickup
C is the capacitor

Edit:

Where one side of the coil is connected to the frame of the pickup, it would probably be best to drive the frame from the oscillator which will be the lowest impedance point and measure the current coming out of the  live terminal.

Arthur

[stratotarts]

Brilliant! I get it. Thanks, I will try it out.

[aquin43]

Sorry, I made an elementary mistake.

The correct formula is   L = Rpot * (Rl + Rt) * C  (corrected in edit above)

The two time constants are C * Rpot and L/(Rl+Rt) and they must be equal, hence the formula.

Arthur