Charles Eric LaForest, PhD., GateForge Consulting, Ltd.
A method for directly measuring a magnetic guitar pickup's (or any large inductor's) resistance, inductance, self-resonant frequency, and then calculating its parasitic capacitance and series Q factor, without using an LCR meter.
Measuring high-frequency (RF) inductors is easily done using an LCR meter, but these are expensive and don't always work well for large inductors used in the audio frequency range (DC to 100 kHz), such as magnetic guitar pickups, because if the LCR meter uses too high a test frequency, the substantial parasitic capacitance of a large inductor will distort the measurement.
Instead, we can gradually build up a set of simple measurements using a basic first-order LR low-pass filter circuit, which avoid parasitic distortions and requires only one resistor and some low-end test equipment:
Alternately, any test equipment with a Bode Plot function, such as the Red Pitaya, can automate a lot of this process.
A Bourns
RLB0913-104K
100mH inductor (L) is specified as having a 210Ω
nominal coil resistance and a self-resonant frequency (F) of 100kHz.
Thus, given C = ((1/(2*pi*F))^2)*(1/L), it should have a parasitic capacitance of
25.33pF, and given Qs = (1/R)*sqrt((L/C)), a series Q factor of
299.20 at self-resonance.
To measure the inductance, we can use a simple first-order LR low-pass filter
composed of a series inductor with a resistive shunt (R) to ground at the
output, which has a resonant frequency of F = R/(2*pi*L). At the resonant
frequency, the current through the resistor (and thus the voltage across it)
drops by -3dB (0.707) of the maximum value at DC. Given that measured
frequency, and an exactly known resistance, we can use L = R/(2*pi*F) to
calculate the inductance.
To avoid any measurement error created by the reactance of the parasitic capacitance of the inductor, we must measure at a low enough frequency. We can make an estimate based on the specs and some measurements.
Ideally, if we make an LR low-pass filter using a 100Ω resistor and add to that the 210Ω coil resistance which is in series, we should see the -3dB point at 493.38Hz. At that frequency, the reactance of the calculated specified parasitic capacitance, 25.33pF, will be 12.73MΩ, which is in parallel with the coil resistance and thus has no significant effect. The scope probe resistance and capacitance, being around 1MΩ to 10MΩ and a few single-digit pF, have no significant effect.
In practice, we measure the resistance of the coil at 206Ω and of the resistor at 98Ω, for a total of 304Ω. This gives a calculated -3dB frequency of 483.83Hz. We first send a small DC voltage (1V), which won't create an excessive current (3.29mA), through the filter to get our baseline voltage (322.37mV) across the resistor (since it forms a voltage divider with the coil resistance). We then increase the voltage frequency (sine wave), maintaining 1Vrms (1.41Vp) at the input, until the output voltage drops to 227.91mVrms (322.37mVp, same as the DC value).
We have to ensure the current through the inductor is not excessive to avoid magnetic saturation, which would distort our reading by artificially lowering the inductance. Check your spec sheet.
We measured this point at 461Hz, which gives us a measured inductance of 104.95mH.
Now that we have a known inductance, if we can measure the self-resonant frequency of the inductor, we can calculate the actual parasitic capacitance, as we did above when considering the inductor specifications. The parasitic capacitance is in parallel with the inductance, and so both together will present maximum impedance to the flow of current at self-resonance.
We can use our existing first-order LR low-pass filter and drive it with an increasing input frequency until we find a minimum voltage across the resistor. The actual voltage does not matter at this point, only that it is a minimum. Although the spec tells us the self-resonant frequency is 100kHz, we should sweep through frequencies one decade above and below this estimate to make sure we find the minimum.
We found the minimum at 200kHz, which for a measured inductance of 104.95mH, gives us a calculated parasitic capacitance of 6.03pF and a series Q factor of 640.23.