Measuring pickups Capacitance?

[Helmholtz]

This PDF is a prominent search result when searching for information on how to measure the response of guitar pickups. Any critique you have would be valuable to anyone who finds both that PDF and this thread.

I edited my first post and changed it completely as I noticed, that it was not the author's intend to plot the PU's impedance accurately. For the Lissajous method a series resistor of 56k seems fine.

Here are my comments on this http://www.syscompdesign.com/assets/...ar-pickups.pdf paper.

First of all I acknowledge that it gives some useful information regarding measurement methods of PUs' parameters. The description of a magnetic PU as a Variable Reluctance Sensor is perfect. But:

Measuring PU inductance via Lissajous figure
This is an excellent and accurate method to determine the inductance of a parallel resonant circuit like a PU. But it requires the capacitance to be known exactly.

There are two problems associated with measuring the inductance with an LCR meter at a fixed frequency:

1) The meter can only measure apparent inductance. The apparent L of a PU (parallel resonant circuit) increases steadily with increasing frequency below and up to resonance, caused by the effect of capacitance. Apparent L has no practical meaning for PUs and is only a theoretical way to descibe the systematic measuring error of LCR meters. As this error increases with frequency, the value at the lowest measuring frequency is the most meaningful.

2) Eddy current effects in conductive parts (especially in ferromagnetic cores ->magnetic skin effect) reduce the effective L with increasing frequency. Inductors with conductive, ferromagnetic cores do not have a single true inductance. Instead L is a function of frequency. This means that the L value at 100Hz is not per se better or truer than the value at a higher frequency.

What we actually want to know is the (effective) L at or close to the resonant frequency in real life operation. This is where the Lissajous method comes in. Done carefully, it can deliver the correct effective L at the chosen resonant frequency of interest.

As mentioned before, for accurate results the total capacitance Ctot= Cpu+Cadd needs be known exactly. If Ctot is too low by 10%, your calculated L will be too large by 10%.
Cadd can be easily measured with an LCR but also Cpu should be determined beforehand at least approximately.
The method indicated in the article, namely "overpowering" an unknown Cpu by a huge Cadd of several nFs, will give the effective L at a much too low frequency. The result will only be useful for PUs where L does not depend on frequency. But in these cases you may as well use your LCR meter at 100Hz.


And here is the more important part of my comments, dealing with measuring the PU's transfer response:

Measuring PU transfer response requires access to an input port. Inserting a signal voltage source in series with the inductor part as typically done in simulations is not possible in real life. Instead, the well accepted method is to use the PU coil as secondary in a current transformer arrangement. The idea is to inject a current into the PU coil (inductance) via a coupled external coil driven by constant current and measure the resulting voltage across the PU terminals. Mind that driving the external coil directly by a (low impedance) voltage source would load down the PU and change its frequency response.
The induced constant current in the PU coil produces a voltage across its inductance, rising proportionally with frequency and consequently the PU shows a typical bandpass behaviour.
The main requirement for the external primary circuit is that the drive current must stay constant for all frequencies to be measured. This means that not only the self-resonance of the field coil has to lie far above the highest frequency of interest but also that the impedance of the field coil stays negligible compared to the total series resistance (279 Ohms in the example). With the values given in the article the corner frequency for this requirement is around 1.2kHz. Above this frequency the drive current drops with 6dB/octave and distorts the measured frequency response as can be seen in the PU responses of figure 5. The cure is to increase the L/R ratio by a factor of 20 or more.

[Antigua]

1) The meter can only measure apparent inductance. The apparent L of a PU (parallel resonant circuit) increases steadily with increasing frequency below and up to resonance, caused by the effect of capacitance. Apparent L has no practical meaning for PUs and is only a theoretical way to descibe the systematic measuring error of LCR meters. As this error increases with frequency, the value at the lowest measuring frequency is the most meaningful.

2) Eddy current effects in conductive parts (especially in ferromagnetic cores ->magnetic skin effect) reduce the effective L with increasing frequency. Inductors with conductive, ferromagnetic cores do not have a single true inductance. Instead L is a function of frequency. This means that the L value at 100Hz is not per se better or truer than the value at a higher frequency.

What we actually want to know is the (effective) L at or close to the resonant frequency in real life operation. This is where the Lissajous method comes in. Done carefully, it can deliver the correct effective L at the chosen resonant frequency of interest.

As mentioned before, for accurate results the total capacitance Ctot= Cpu+Cadd needs be known exactly. If Ctot is too low by 10%, your calculated L will be too large by 10%.
Cadd can be easily measured with an LCR but also Cpu should be determined beforehand at least approximately.
The method indicated in the article, namely "overpowering" an unknown Cpu by a huge Cadd of several nFs, will give the effective L at a much too low frequency. The result will only be useful for PUs where L does not depend on frequency. But in these cases you may as well use your LCR meter at 100Hz.

Thanks for the write up. For some reason this forum truncates this URL http://www.syscompdesign.com/assets/...ar-pickups.pdf on your posts.

As for inductance varying with frequency, I've noticed that Fender pickups, with AlNiCo pole pieces and little to no other metal parts, show about the same inductance at 1kHz test freq as they do at 100 or 120 Hz. It's only pickups with steel cores that show incorrect readings. One reason I prefer taking down the loaded and unloaded resonant peaks of pickups is because 1) it's a value that relates more closely to audible performance, and 2) it overcomes errors that might arise from trying to solve for peak freq. from incorrect values for L and C.

Measuring PU transfer response requires access to an input port. Inserting a signal voltage source in series with the inductor part as typically done in simulations is not possible in real life. Instead, the well accepted method is to use the PU coil as secondary in a current transformer arrangement. The idea is to inject a current into the PU coil (inductance) via a coupled external coil driven by constant current and measure the resulting voltage across the PU terminals. Mind that driving the external coil directly by a (low impedance) voltage source would load down the PU and change its frequency response.

Can the field coil still load down the pickup even if the coupling factor is very small compared to a traditional transfomer?

The induced constant current in the PU coil produces a voltage across its inductance, rising proportionally with frequency and consequently the PU shows a typical bandpass behaviour.
The main requirement for the external primary circuit is that the drive current must stay constant for all frequencies to be measured. This means that not only the self-resonance of the field coil has to lie far above the highest frequency of interest but also that the impedance of the field coil stays negligible compared to the total series resistance (279 Ohms in the example). With the values given in the article the corner frequency for this requirement is around 1.2kHz. Above this frequency the drive current drops with 6dB/octave and distorts the measured frequency response as can be seen in the PU responses of figure 5. The cure is to increase the L/R ratio by a factor of 20 or more.

The PCSU200 shows "output impedance: 50ohm" https://www.velleman.eu/products/view/?id=407512 , so the field coil's impedance would need to be well below 50 ohms, otherwise series resistance must be added?

[Antigua]

Also a question, does anyone know these plots typically show a slope that is much lower than 6dB/oct below 200Hz?

[Mike Sulzer]

Also a question, does anyone know these plots typically show a slope that is much lower than 6dB/oct below 200Hz?

[ATTACH=CONFIG]48632[/ATTACH]

Without checking all the details of what you are doing, I would guess that it is the effect of the coil resistance.

[Antigua]

Without checking all the details of what you are doing, I would guess that it is the effect of the coil resistance.

This plot is with a 1meg resistor in series with the pickup, then comparing the voltage across the resistor and the pickup, but the same thing happens when using an external inducer coil in a transformer configuration.

[Mike Sulzer]

And here is the more important part of my comments, dealing with measuring the PU's transfer response:

Measuring PU transfer response requires access to an input port. Inserting a signal voltage source in series with the inductor part as typically done in simulations is not possible in real life. Instead, the well accepted method is to use the PU coil as secondary in a current transformer arrangement. The idea is to inject a current into the PU coil (inductance) via a coupled external coil driven by constant current and measure the resulting voltage across the PU terminals. Mind that driving the external coil directly by a (low impedance) voltage source would load down the PU and change its frequency response.
The induced constant current in the PU coil produces a voltage across its inductance, rising proportionally with frequency and consequently the PU shows a typical bandpass behaviour.
The main requirement for the external primary circuit is that the drive current must stay constant for all frequencies to be measured. This means that not only the self-resonance of the field coil has to lie far above the highest frequency of interest but also that the impedance of the field coil stays negligible compared to the total series resistance (279 Ohms in the example). With the values given in the article the corner frequency for this requirement is around 1.2kHz. Above this frequency the drive current drops with 6dB/octave and distorts the measured frequency response as can be seen in the PU responses of figure 5. The cure is to increase the L/R ratio by a factor of 20 or more.

I use coils with diameter equal to or smaller than a pole piece radius with 3 to 6 turns, driven from an audio amp through an 8 ohm resistor, with a current of about 1 amp. Coupling is very small. Driving a pickup with a pickup size coil, as some otherwise clever people do, seems like asking for trouble.

You can make a response model from the parameters derived from an impedance measurement that works well. I think the only reason for using a driving coil is to include the eddy current loss encountered in passing through an extra thick cover.

[Mike Sulzer]

This plot is with a 1meg resistor in series with the pickup, then comparing the voltage across the resistor and the pickup, but the same thing happens when using an external inducer coil in a transformer configuration.

In either case, the coil resistance places a lower limit on the magnitude of the coil impedance.

[Helmholtz]

Can the field coil still load down the pickup even if the coupling factor is very small compared to a traditional transfomer?

I have no values for the coupling factor. Generally a coupling factor below 100% introduces additional series inductance in the equivalent circuit. But why don't you just measure and compare? Call it loading down or not, in result the (high) frequency response will change.

The PCSU200 shows "output impedance: 50ohm" https://www.velleman.eu/products/view/?id=407512 , so the field coil's impedance would need to be well below 50 ohms, otherwise series resistance must be added?

You have to add the field coil's resistance to the series resistance for total circuit resistance Rtot. What matters is the Rtot/L ratio. It should be well above 150kOhm/H. In other words the corner frequency should lie well above the frequency range analysed and is given by f=Rtot/(2pi*L). This can be achieved by increasing series and/or coil resistance as well as by decreasing field coil inductance.

Also a question, does anyone know these plots typically show a slope that is much lower than 6dB/oct below 200Hz?

v2adfer.png

My impedance plots of PUs without anomalies show almost perfect -6dB/octave (i.e. capacitive) behaviour above ca. 100kHz. To stay ahead of noise floor I recommend max. generator voltage and automatic voltage scale.
Anomalies indicate that the PU's behaviour is not purely capactive (but disturbed by the interaction with a smaller separated part of the inductance) in the corresponding frequency range, thus no clear -6dB/octave slope.

[Helmholtz]

In either case, the coil resistance places a lower limit on the magnitude of the coil impedance.

But only below resonance. As the whole thing is shunted by the distributed capacitance, impedance tends to 0 for very high frequencies.

[Mike Sulzer]

But only below resonance. As the whole thing is shunted by the distributed capacitance, impedance tends to 0 for very high frequencies.

I believe Antigua's question was for below 200 Hz where the pickup coil resistance sets a lower limit on the magnitude of the pickup coil impedance.

[Helmholtz]

You are right, I am sorry. Did not read carefully. Impedance always starts horizontally with DCR from 0 Hz. But the bandpass transfer response is different and must have 0 signal at 0 Hz.

[Mike Sulzer]

And here is the more important part of my comments, dealing with measuring the PU's transfer response:

Measuring PU transfer response requires access to an input port. Inserting a signal voltage source in series with the inductor part as typically done in simulations is not possible in real life. Instead, the well accepted method is to use the PU coil as secondary in a current transformer arrangement. The idea is to inject a current into the PU coil (inductance) via a coupled external coil driven by constant current and measure the resulting voltage across the PU terminals. Mind that driving the external coil directly by a (low impedance) voltage source would load down the PU and change its frequency response.
The induced constant current in the PU coil produces a voltage across its inductance, rising proportionally with frequency and consequently the PU shows a typical bandpass behaviour.
The main requirement for the external primary circuit is that the drive current must stay constant for all frequencies to be measured. This means that not only the self-resonance of the field coil has to lie far above the highest frequency of interest but also that the impedance of the field coil stays negligible compared to the total series resistance (279 Ohms in the example). With the values given in the article the corner frequency for this requirement is around 1.2kHz. Above this frequency the drive current drops with 6dB/octave and distorts the measured frequency response as can be seen in the PU responses of figure 5. The cure is to increase the L/R ratio by a factor of 20 or more.

The current in the field or exciter coil creates an ac magnetic field that induces a voltage, not a current, in series with the pickup coil. This follows from Maxwell's equation or the law of magnetic induction. Current flows if there is a load on the coil, such as the coil capacitance or the loading caused by eddy currents in the cores, etc. (A so called current transformer is a tightly coupled transformer driven from a high impedance so that the current in the secondary is related to that in the primary by the turns ratio. The very loosely coupled situation here does not behave that way.)

You describe one way to make the current through the field coil independent of frequency: make the inductive reactance low compared to the dc resistance of the coil across the whole useful frequency range. A better way is to drive the coil with a current source, that is, a circuit with an output impedance much higher than the impedance of the coil at any useful frequency.

[Antigua]

The current in the field or exciter coil creates an ac magnetic field that induces a voltage, not a current, in series with the pickup coil. This follows from Maxwell's equation or the law of magnetic induction. Current flows if there is a load on the coil, such as the coil capacitance or the loading caused by eddy currents in the cores, etc. (A so called current transformer is a tightly coupled transformer driven from a high impedance so that the current in the secondary is related to that in the primary by the turns ratio. The very loosely coupled situation here does not behave that way.)

You describe one way to make the current through the field coil independent of frequency: make the inductive reactance low compared to the dc resistance of the coil across the whole useful frequency range. A better way is to drive the coil with a current source, that is, a circuit with an output impedance much higher than the impedance of the coil at any useful frequency.

Thanks for your last few posts, you cleared up several things that were not clicking for me before, especially about there being a voltage, but not necessarily a current unless a load exists on the pickup. I know that's a basic idea, but I was slow to connect the dots.

And the other point, about the resistance preceding the reactance at low frequencies, I modeled this with LTSpice. The different plot lines indicate three steps of resistance, 10k, 20k and 30k ohms, with the flat, low frequency portion extending further for each increase in step (as well as lowering the Q factor).



Something I'm confused about though, are the circumstances under which +6dB...-6dB/oct slopes emerge, as seen in "raw" bode plots, and the above LTSpice model, but only when the AC voltage source has been placed outside of the pickup.

When a pickup is modeled as with the AC source inside the pickup, as shown below, there is a 0dB/oct line, then the resonant peak, and then a -12dB/oct slope:



In practical testing, both the exciter / field coil method, as well we putting the pickup in series with the function generator, both yield +dB...-6dB/oct slopes, as seen in the first simulation. Driving the pickup with a series voltage obviously puts the voltage source outside of the pickup, but shouldn't the exciter coil method place the voltage inside of the pickup? Why does this testing method not result in a 0dB/oct..-12dB/oct plot, as is seen in the second screen shot?

Another issue with the model which has the voltage source inside the pickup, is as seen in the second screen shot, that increasing the series resistance from 10k to 20k to 30k has no apparent impact on the 0dB/oct slope, as it does with the-6dB slope in the first screen shot.

[Antigua]

I have no values for the coupling factor. Generally a coupling factor below 100% introduces additional series inductance in the equivalent circuit. But why don't you just measure and compare? Call it loading down or not, in result the (high) frequency response will change.

You have to add the field coil's resistance to the series resistance for total circuit resistance Rtot. What matters is the Rtot/L ratio. It should be well above 150kOhm/H. In other words the corner frequency should lie well above the frequency range analysed and is given by f=Rtot/(2pi*L). This can be achieved by increasing series and/or coil resistance as well as by decreasing field coil inductance.

In that past, I had measured a pickup using an exciter, both with and without a resistor in series with the exciter. It made no difference in the plot lines, but the added resistance made the exciter coil weaker, reducing the S/N ratio. So if the coupling is lower, the series inductance is higher, but apparently not high enough to interfere with measurements.

[Helmholtz]

In that past, I had measured a pickup using an exciter, both with and without a resistor in series with the exciter. It made no difference in the plot lines, but the added resistance made the exciter coil weaker, reducing the S/N ratio. So if the coupling is lower, the series inductance is higher, but apparently not high enough to interfere with measurements.

I cannot comment on your measurements. I gave you all the info necessary to make sure you have constant exciter current over frequency. When the exciter current falls with increasing frequency, so will your PU output voltage and thus frequency response will deviate. This effect can be seen in figure 5 of the document, where the responses show a pseudo plateau starting around 1kHz, just as predicted by the formula. In reality the PU bandpass response gets (increasingly) steeper towards resonance.

You may verify the frequency (in)dependance of the drive current by measuring the voltage over a series resistor, via the second channel of the Velleman. The effect of a decreasing drive may be partly masked by the resonance of the PU.