This page is to get deeper into measurement of pickup resonance frequency and calculation of equivalent capacitance of a coil where it is impossible to use a capacitance meter because any measurement with LCR meter would be completely bogus.
Equipment needed:
- Pickup under test
- Variable frequency function generator
- Two channel oscilloscope
- 100 k resistor
Test Circuit
What is shown in Fig 1 is the circuit for measuring pickup resonance, there is a pickup (obviously) in series with a resistor, here 100 kΩ, V1 is the function generator, the voltage V1 is measured with one channel on the oscilloscope, the voltage across Rmeas is V2, measured by the other channel on the oscilloscope. R1 and L1 are known from measurement.
The voltages are referenced to the triangle in the bottom left corner, the Common.
The schematic for the pickup indicates a standard equivalent diagram for a single coil pickup, as frequency of source V1 is increased and we are closing in on the resonance frequency we notice that at lower frequencies of V2 is lagging V1 which means that the frequency we are running at is below resonance, the impedance of the pickup at that point is dominantly inductive. As we increase frequency, the waveform for V2 is beginning to line up with V1 (in phase). When they line up perfectly, in phase, which means we have resonance. Going beyond the resonance frequency, we see that V2 is now leading V1, this means that the pickup impedance is mainly capacitive. Bottom line, we have found out resonance frequency, in this case 10.7 kHz.
Resonance means that
XL = XC
XL = 2 ∙ π ∙ fo ∙ L1 = XC = 1/(2 ∙ π ∙ fo ∙ C1)
Combined we get the expression
4 ∙ π2 ∙ fo2 ∙ L1 ∙ C1 = 1
or solving for fo
fo = 1/( 2 ∙ π ∙ √(L1 ∙ C1) )
If we add some figures to illustrate this, in Fig 2 we have the case where the frequency is lower than the resonance frequency, the red curve representing V1 is ahead of the blue that is representing V2, the red curve is leading the blue curve.
If we increase the frequency, we get to a point where V2 is in phase with V1, indicated by the two curves crossing the 0 line going positive at the same time, Fig 3. This means we have resonance, and the frequency associated is the resonance frequency at which we can calculate the pickup capacitance.
Increasing the frequency further, we see that the blue curve, V2, is now leading the source voltage, V1, meaning that the capacitive impedance is lower than the inductive impedance and therefore the dominant one. Fig 4.
Another indicator that resonance is reached is shown in Fig 5, as we can see from the curves, the amplitude of V2 is at its lowest value, but determining the point where the amplitude is the lowest can be somewhat difficult and therefore not as accurate as the phase method.
The peak of the Z curve is indicating resonance, the flatness of the curve, however, makes it difficult to determine where maximum is. As shown earlier, it is much easier to determine this point by looking for the crossover of L and C impedances. Another way of describing this is to say that the phase shift is 0 at resonance, the impedance reacts as a resistance (without being one).
Just as a reminder, we are looking at a capacitive impedance and an inductive impedance in parallel, which means that the total impedance is mainly determined by the inductance at lower frequencies and by the capacitive impedance at higher frequency. The point where they cross, the resonance frequency, the total impedance is actually purely resistive. It should be mentioned that the coil resistance is included in the inductive impedance, if you look at the blue curve, it would be 5k at 0 Hz. This also indicates, as illustrated under Guitar Electronics, how little influence the coil resistance actually has on the performance of the pickup.
Finding Pickup Capacitance
The resonance frequency of the pickup itself is of great interest, but another benefit we get here is that the true capacitance or maybe better, the equivalent capacitance, can be calculated by using and rewriting an earlier equation, solving for C1 instead of fo:
C1 = 1/(4 ∙ π2 ∙ fo2 ∙ L1)
That completes the equivalent diagram for the pickup as we see in Fig 1, the value for the equivalent capacitance C1 has been calculated, which completes our mission and it shows how to find the capacitance of a pickup, first measure the resonance frequency and from there calculate the capacitance. Let me emphasize here: There is no way the capacitance can be measured with a meter, LCR or otherwise! If you think otherwise you are fooling yourself, if you repeat it to others you are spreading misinformation (I am too polite to say that you are lying)!