Capacitance measurements above 20KHz: helpful for measuring eddy current effects

[Mike Sulzer]

This discussion is suggested by the recent one on the Hantek 1833c, a meter that can measure using frequencies as high as 100 KHz, and it is about making use of the ability to measure impedance versus frequency above 20KHz, especially capacitance. This first post describes why I want to measure pickup capacitance, and then evaluates my measurement technique for measuring impedance (Z) versus frequency (f) well beyond 20KZ. Finally it shows that the method for extracting C from Z (a method to be described in a later post) allows the goals of the measurement to be met, a characterization of the effects of eddy currents.

I agree with Helmholtz comments in that other discussion that the the player has little need to know the C of a pickup; it is swamped by cable capacitance and the guitar sound can be varied easily by cable selection. I also agree with Joe Gwinn, who said that the purpose of measuring C is related to pickup design. In particular, I want to rate pickups according eddy current effects as a function of frequency. My method for accomplishing this needs a good measurement of C. I have done this before by making a mathematical model of eddy current loss and including it with the other parameters and fitting everything at once. What I want now is a way of measuring C (not perfectly, but with sufficient accuracy) to reveal the effects of the eddy currents without having to model them. This is possible with higher frequency measurements that reveal more information about C without so much contamination from the inductance.

The first attachment shows the impedance up to a frequency of 80 KHz (based at a sampling rate of 192 KHz) of a humbucker screw coil with very short leads and removed from the base plate. This is a brand X pickup made in Japan some years ago. It is not possible to say much about eddy current effects from looking at this plot, and so there is some way to go to meet the goals of the project!.

Now it is necessary to determine how well the instrument (an Apogee Element 24 and computer) works for measuring capacitance. The second attachment shows the admittance of a test measurement. (Admittance (Y) is the reciprocal of Z, Y = 1/Z. It is a straight line with positive slope for a capacitor. It is good to display Y rather than Z for a capacitor since it is easy to see deviations from a straight line.) The measurement looks good up to a bit beyond 70KHz. The line starts bending down beyond that. The derived C value agrees well with the Extech. This value is determined by fitting a function to the measured data as a function of frequency. The description of this is coming in a later post.

Eddy currents reduce the apparent inductance of the pickup coil, more with with increasing frequency. The imaginary part of Z for an inductor is a straight line with positive slope. When eddy currents are present, their effects increase with frequency and the line bends a bit in the downward direction. We expect the effect to be present in the data displayed in the first attachment, but obscured by the effect of the capacitance. But if we know the capacitance, we can remove its effect on the measured impedance. The pickup is an L in series with an R all in parallel with a C. Admittances add for devices in parallel, also we have Ypm = 1./(j *w*L + R) + j*w*C. We use w for omega = 2*pi*f. Ypm is just 1/Zpm, the measured data. From that we subtract j*w*C, using the measured value of C. This leaves the first term; take its reciprocal to get an impedance, easiest for viewing an inductance, and we get R + j*w*L where both L and R might vary with frequency. If there are no eddy currents the imaginary part of this should be a straight line, and this line should match the line found by taking the low frequency inductance, call it Lcoil, and making j*w*Lcoil. If there are eddy currents, the measured data as a function of frequency should bend downward from j*w*Lcoil.

To begin testing this, we take the screws out of the humbucker coil (to remove the eddy current loss), measure the impedance, and do the calculations described in the previous paragraph. The results are shown in the next attached plot. The good agreement of the dashed and colored line over the entire audio range suggests the the measured value for C is good, that is, as good as we need it to be. (The determination of C used measurements between 20KHz and 40KHz only; use of higher frequencies will be investigated later.)

Repeat the measurements and calculation with the screws installed, and we get the the last attached plot. The measured C is very nearly the same. This probably means (subject to additional verification) that C changes little or not at all when eddy currents are introduced and that the position of the vertical line below the dashed line is a measure of the eddy current effect as a function of frequency.

The next post will describe how C is found from the measured Z, or actually Y.

[Mike Sulzer]

I got side tracked from what I intended to do. Here is a surprising effect on the impedance above 20KHz when using AlNiCo magnets. First look at the first attachment, the admittance for a coil with steel screw cores. No Alnico, this is for reference only; notice that the curves are smooth. The second plot is for a strat pickup I wound a few days ago from some old Stew Mac parts I have had for years. The jumbo in the imaginary part is large enough so that you cannot use the data above 40KHz to measure capacitance. The third plot is for an under wound tele bridge ;pickup. DIfferent type of AlNiCo?






You have to be careful what data to use in determining capacitance. It appears that the permeability of AlNiCo can be a function of frequency.

[Helmholtz]

I think that HF irregularities in the impedance response are caused by non-uniform winding, resulting in non-uniformly distributed capacitance.
This could happen when larger coil voids are filled up during winding.

[Mike Sulzer]

I think that HF irregularities in the impedance response are caused by non-uniform winding, resulting in non-uniformly distributed capacitance.
This could happen when larger coil voids are filled up during winding.

Interesting idea! I will see if I can find some way to test it.

[Joe Gwinn]

I'd compute the Arc Tangent of the imaginary impedance divided by the real part. This may show all the resonances clearly.

[Mike Sulzer]

I think that HF irregularities in the impedance response are caused by non-uniform winding, resulting in non-uniformly distributed capacitance.
This could happen when larger coil voids are filled up during winding.

The results of the test indicate that, as Helmholtz wrote, it is how the pickup is wound that determines the high frequency characteristics of the impedance or admittance. The effects show up with an air core coil, and adding cores of alnico or steel changes the results in small, but surprising ways.

The test coil uses a plastic bobbin intended to make a strat pickup. IMO, it is not good for pickups since you cannot get enough wire on, but it is OK for this test. The spool of wire ran out during winding, and the wind continued with another. So this winding has a significant “irregularity”.

The attachment shows the admittance for three cases: air, AlNiCo, and steel. For the imaginary part, the orange is air, the red is AlNiCo, and the brown is steel. (Remember, ideally, the high frequency part of the admittance would just be a straight line, and the slope determines the capacitance. The line should pass through the origin when extrapolated to lower frequencies. The negative low frequency part is inductive, and the resonant frequency is at the zero crossing.)

The three inductances are different, as they should be, but I do not understand why the rest of the curves look as they do.

[Mike Sulzer]

I'd compute the Arc Tangent of the imaginary impedance divided by the real part. This may show all the resonances clearly.

[Helmholtz]

The attachment shows the admittance for three cases: air, AlNiCo, and steel. For the imaginary part, the orange is air, the red is AlNiCo, and the brown is steel. (Remember, ideally, the high frequency part of the admittance would just be a straight line, and the slope determines the capacitance. The line should pass through the origin when extrapolated to lower frequencies. The negative low frequency part is inductive, and the resonant frequency is at the zero crossing.)

I see a piecewise linear imaginary admittance curve. The slope is decreasing in 2 steps. Capacitance is given as slope divided by 2pi.
From the highest frequency part I calculate a capacitance of 150pF.
Question is, what "switches off" parts of the capacitance with increasing frequency? And which is the capacitance that matters for the PU's main resonance?

Do you consider winding a tapped PU coil that allows adding small capacitance to part of the winding?

I think a model could be additional, smaller parallel capacitances having some inductance in series.

[Joe Gwinn]

Well, that's pretty clear. The main resonance is at about 8 KHz (where phase crosses zero). There are little parasitic resonators causing for instance the bump between 50 KHz and 60 KHz, but this does not involve the main parallel LCR resonance.

I have to think about this, but there may be a trick with differences that will show the parasitic resonances more clearly.

[Mike Sulzer]

Yes sir, that is the same main resonance already well defined by the zero crossing of the imaginary part of the admittance (or impedance). I do not know what range of phenomena is covered by the term "parasitic resonance", but it is the physics that we need to understand. For example, on the "st. bob." (strat bobbin) plot above, differences induced by the different cores return at the highest frequencies after disappearing at the intermediate frequencies. Why?

Well, that's pretty clear. The main resonance is at about 8 KHz (where phase crosses zero). There are little parasitic resonators causing for instance the bump between 50 KHz and 60 KHz, but this does not involve the main parallel LCR resonance.

I have to think about this, but there may be a trick with differences that will show the parasitic resonances more clearly.

[Helmholtz]

For example, on the "st. bob." (strat bobbin) plot above, differences induced by the different cores return at the highest frequencies after disappearing at the intermediate frequencies. Why?

I wouldn't be surprized if all conductive cores increased capacitance by a few pF, as they might slightly change the distribution of the electric field for the inner layer.

[Joe Gwinn]

Yes sir, that is the same main resonance already well defined by the zero crossing of the imaginary part of the admittance (or impedance).

Yes, mathematically true for sure. But I like the phase view as well. For one example, on the resonances of crystal resonators, one will see the modes one after another.

I do not know what range of phenomena is covered by the term "parasitic resonance", but it is the physics that we need to understand. For example, on the "st. bob." (strat bobbin) plot above, differences induced by the different cores return at the highest frequencies after disappearing at the intermediate frequencies. Why?

Hard to say without more details. Eddy currents vary with all of the following: magnetic permeability, electric permittivity, physical dimensions, geometric relation between coil and conductive material, ...

Helmholtz's earlier point about increased capacitance is one example.

[Mike Sulzer]

I wouldn't be surprized if all conductive cores increased capacitance by a few pF, as they might slightly change the distribution of the electric field for the inner layer.

Yes, I can see that the core could have some charge separation end to end.

To me the real mystery is why the effect of the cores becomes almost all the same between 35 and 55 KHz on "St. Bob.". But the circuit is not entirely capacitive in that range since the extrapolation of the "linear" imaginary part does not pass through the origin.

[Mike Sulzer]

Yes, mathematically true for sure. But I like the phase view as well. For one example, on the resonances of crystal resonators, one will see the modes one after another.




Hard to say without more details. Eddy currents vary with all of the following: magnetic permeability, electric permittivity, physical dimensions, geometric relation between coil and conductive material, ...

Helmholtz's earlier point about increased capacitance is one example.

Actually, it seems that we do not even know how much eddy currents are involved. The basic effect (bumps at about 35 and 60 KHz on st. Bob.)) occurs with an air core coil. No eddy currents! It seems to do with how the coil is wound, as Helmholtz said. The cores modify the effect in a strange way, but maybe that is due to permeability but not conductivity. Who knows?

[Helmholtz]

I think the main inductance has essentially lost its influence on the admittance above 30kHz.
But I could imagine that the effective permeability of the cores has some effect on the "transformer" coupling between coil partitions.