Measuring the capacitance of an inductor or Inductors

[Joe Gwinn]

Yes. But in the case of ungrounded pickup cores, I think the differences between cores in/out is probably due to the magnetic properties.

Magnetic properties are not relevant. The easiest way to see this is to consider a single-layer solenoid with various cores, including no core at all.

One can approximate the self capacitance of the cored single-layer solenoid using a bunch of little capacitor between turns and from each turn to the core. With a DC voltage on the coil, one can work out all the voltages, and the energy stored in each little capacitor. By the conservation of energy, the sum of the energy values and the overall DC voltage can be used to solve for the total self capacitance using the classic equation Energy=1/2*Capacitance*(Voltage squared).

While the number of little capacitors is very large, one can handle them by classes: between adjacent turns, between turns once removed, turns twice removerd, and so on; between turn and core, between core and ground, and so on. It will quickly become apparent which classes are the largest contributors to the overall stored energy and thus self capacitance.

But one does need to make the measurements.

Yes. A slitted brass tube core compared to a slitted mild steel tube core will tell the tale.

Mild steel tubing may be bought from auto parts stores as brake line.

[bbsailor]

Joe, Mike, Dave, and all,

Distributed capacitance is very difficult to calculate because of the variation in how the wire lays in relation the capacitive-adding surfaces.

Wind a simple bobbin coil with no core and measure the coil's self resonance.

Use a piece of thin aluminum foil gum wrapper as a capacitance plate (the same size as a pickup base plate) to represent what a thicker plate would look like except the gum wrapper has very, very low eddy currents. Measure the capacitance between the gum wrapper and the two coil leads. You will get slightly different readings depending on which coil lead wires you are using due to how the wire lays in relation the the gum wrapper. Measure the new coil self resonance with the added capacitance of the gum wrapper.

Guess what? The pickup coil-to-gum wrapper foil capacitance is not fully imposed on lowering the pickup coil self resonant point. Only a fraction, about 20%, is imposed on lowering the resonance. Now replace the gum wrapper with a metal base plate which will have higher eddy currents and do the same measurement. The capacitive effects will be the same but the eddy currents effects can now be independently seen.

Now, add thin foil around a sanded 3/16 wood dowel (to make a little thinner) and ground the foil inserts to the aluminum base foils and take additional measurements. Change the foil inserts to metal slugs which have a higher eddy current effect and see more self resonance differences.

This is a classic case of trying to isolate variables. I discoverd this when doing research on making fast pulse induction metal detector coils and it applies to all coils where shielding is used in close proximity.

This effect is most evident as the resonant shifts in guitar pickups are in the middle of the highest human hearing sensitivity range where various guitar harmonics, vice primary frequencies, are emphasized.

I hope this adds a little more lab-based perspective on this issue.

Joseph Rogowski

[Possum]

....

Here's some of what was on that link I posted:

If the electric guitar’s pickup resonant frequency is 1 KHz < fres < 10 KHz, where the pickup
impedance, Z(f = fres) is a maximum in this frequency range, then no measurement of the
inductance, L(f) at f = 10 KHz is possible with the HP 4262A, due to the measurement technique
used by the HP 4262A (one form of AC bridge). However, one can instead measure the
capacitance, C(f) of the pickup at f = 10 KHz with the HP 4262A, analyzing the electric guitar
pickup as a lumped, parallel C-R circuit, because the reactance, χ(f) on the high side of the
resonance of the pickup, i.e. f > fres has negative slope (i.e. dχ(f)/df < 0), due to the dominance of
the pickup’s capacitance, C over the pickup’s inductance, L in this frequency region, i.e. χC(f) >
χL(f) when f > fres (conversely, χC(f) < χL(f) when f < fres). Again, we can also simultaneously
obtain a measurement of the dissipation, DC(f), which is again related to the quality factor, QC(f)
= 1/DC(f), or DC(f) = 1/QC(f). The mathematical formula for the dissipation, DC(f) can again be
used to calculate the resistive/dissipative (real/in-phase) component, RD(f) of the complex
impedance of the pickup, Z(f) at the frequency, f, so analyzed by this device.
For a series C-R network: RDs(f) = χCs(f) DCs(f) = [1/(2πf Cs(f))] DLs(f).
For a parallel C-R network: RDp(f) = χCp(f)/DCp(f) = [1/(2πf Cp(f))]/DLp(f).
In reality, an electric guitar pickup is considerably more complicated than the simple, very
crude model of a pickup consisting of a lumped series L-R in parallel with a lumped C, because
the actual L, R and C are distributed over the many thousands of turns of the pickup coil.
Furthermore, the pickup inductance, L is not a constant, independent of frequency due to
frequency-dependence of the magnetization, M (magnetic dipole moment per unit volume) of the
permanent magnet(s) used in the pickup, how fully the magnets are charged (i.e. where the
permanent magnets reside on the B-H hysteresis curve) as well as the frequency-dependent
properties of the magnetically permeable material(s) used in the construction of the electric
guitar pickup – soft iron pole pieces, booster plates, even frequency-dependent eddy current
effects in nonmagnetic metal components associated with the pickup – booster plates, mounting
brackets, screws, etc. Thus, L = L(f). In addition to these effects, even the pickup resistance at
finite frequency, R(f) differs from that at zero frequency, i.e. R(f) ≠ RDC = R(f = 0) due to
frequency-dependent magnetic dissipation processes extant in the electric guitar pickup
associated with the permanent magnets and the magnetically permeable materials of the pickup,
the effects of eddy currents induced in conducting materials used in the construction of the
pickup (and/or in proximity to the pickup) and also frequency-dependent resistivity effects
associated with the fine-gauge pickup wire (immersed in the magnetic field of the pickup) of the
pickup coil. Nevertheless, the measured pickup capacitance C(f = 10 KHz), and corresponding
DC(f = 10 KHz) info obtained is useful. We also compute RC(f) from this data.

[David Schwab]

Here's the good stuff™ from that (made more legible):

In reality, an electric guitar pickup is considerably more complicated than the simple, very crude model of a pickup consisting of a lumped series L-R in parallel with a lumped C, because the actual L, R and C are distributed over the many thousands of turns of the pickup coil.

Furthermore, the pickup inductance, L is not a constant, independent of frequency due to frequency-dependence of the magnetization, M (magnetic dipole moment per unit volume) of the permanent magnet(s) used in the pickup, how fully the magnets are charged (i.e. where the permanent magnets reside on the B-H hysteresis curve) as well as the frequency-dependent properties of the magnetically permeable material(s) used in the construction of the electric guitar pickup – soft iron pole pieces, booster plates, even frequency-dependent eddy current effects in nonmagnetic metal components associated with the pickup – booster plates, mounting brackets, screws, etc.

[Possum]

....

The rest of that is on the link I posted further back, I see that no one read it. It is worth reading the full text and how they set up their measuring instruments and many buffers to isolate interference from the instruments themselves. They said they were in a building several stories up and had to isolate the pickup in a Mu metal cylinder because the pickup would hear trucks and car electrical interference way out on the street. If you also go the second link I posted there is a very large Excel document of a ton of pickups they measured including alot of vintage ones, no PAFs unfortunately. Still what they did doesn't mean its the only way to do things, but neither is it alot of theory, I pointed it out because this is actual work being done and very clearly thought out and applied in a real life lab. Thought maybe you could pick up some pointers from it. That stuff has been there for at least 8 years since I started, the Excel file keeps getting added to, I believe there are some bass pickups in there too maybe...

[Mike Sulzer]

Here's some of what was on that link .....

You know Possum, for a relatively senior man of the world, you sure are impressed by a lot of talk about fancy equipment. The method for measuring the capacitance that Joe described (from Terman and other sources) is more accurate than what the professor proposes. He is making a simplifying assumption that he has not bothered to justify. Terman's method eliminates the need for such an assumption and even provides a way (through multiple measurements) to obtain an accurate measurement with simple equipment, effectively averaging together several independent measurements (by drawing a line through the points) in order to reduce random errors.

In that article you referred to, you have an intelligent educated guy throwing down a lot of ideas about guitar pickups. He has not really checked out what he says. (Does he show how much the variation with frequency of magnetic properties of the materials affects the inductance? Joe and I have been working on that for a while here.)

His results are some impedance plots. That is what everyone makes.

[Mike Sulzer]

Magnetic properties are not relevant.

You are right, of course. I was referring to potential inaccuracies in the capacitance measurement due to the complicated nature of the properties of the coil.

[Mike Sulzer]

Joe, Mike, Dave, and all,

...Measure the new coil self resonance with the added capacitance of the gum wrapper. ....

What was the gum wrapper connected to in this measurement?

[David Schwab]

(Does he show how much the variation with frequency of magnetic properties of the materials affects the inductance? Joe and I have been working on that for a while here.)

I think it's more accurate to say that you have been disagreeing with Joe over this, and his ideas on the subject are more closely related to the article mentioned, as well as the general experience of many pickup makers. And you can't make assumptions about what that professor knows or doesn't about pickups.

Mike, you seem to think everything you say is correct, but I can think of at least one thing which was that stacking magnets does not add up their power, when clearly it does, and can be shown on a gauss meter. And that seems like a really obvious thing.

So lighten up a little, because your approach on this is not yielding any useful results, is it? You can't keep saying this and that effect doesn't exist, when clearly they do. I think it would be safe to say that Possum knows more about pickups than a lot of people here, even if he doesn't know the math behind it.

[bbsailor]

What was the gum wrapper connected to in this measurement?

Mike,

I just placed the coil on the gum wrapper foil and first measured the capacitance between one coil winding and the foil and then the other coil winding and the foil.

Then I connected the coil to ground one coil lead with an alligator clip. Try each lead separately as it will changes the resonance slightly due to how the wire lays in the coil form.

I take self resonance measurements each way and note the results.

Then replace the foil with a typical bottom plate and do the same resonance measurements. Any difference will be due to eddy currents because the capacitance effects will the the same.

When putting in the gum wrapper around 3/16 wood dowels just let some extra foil stick out of the bottom and press the 6 foil inserts against the bottom foil piece to ground them. The resonance should be a little lower with this added capacitance.

You should use a scope probe with a 10X setting for less probe loading on the pickup coil. You can even add a few pf capacitor in series with a probe to reduce the pickup coil loading. I use a digital display function generator to obtain an accurate frequency reading of the resonant peak. If you have access to a digital scope, all the better for more accurate measurements.

Once you do this experiment you will separate the capacitive effects from the eddy current effects.

The typical guitar pickup coax lead (12" long) can add up to 1/3 of the total pickup capacitance measured at self resonance. Try doing the experiment with naked humbucker wound pickup slug bobbin without the coax lead.

This is a very enlightning experiment.

Joseph Rogowski

[Mike Sulzer]

I think it's more accurate to say that you have been disagreeing with Joe over this, and his ideas on the subject are more closely related to the article mentioned, as well as the general experience of many pickup makers. And you can't make assumptions about what that professor knows or doesn't about pickups.

Mike, you seem to think everything you say is correct, but I can think of at least one thing which was that stacking magnets does not add up their power, when clearly it does, and can be shown on a gauss meter. And that seems like a really obvious thing.

So lighten up a little, because your approach on this is not yielding any useful results, is it? You can't keep saying this and that effect doesn't exist, when clearly they do. I think it would be safe to say that Possum knows more about pickups than a lot of people here, even if he doesn't know the math behind it.

Go somewhere quiet and examine your motives for writing what you just did.

Why do you assume that Joe is right and I am wrong? I justify what I write with both theory and measurements. Why do you not say that Joe is disagreeing with me?

I did not make assumptions about what "that professor" knows; he has done some measurements, yes. He is assuming that the variation of permeability with frequency results in a variation of inductance in a pickup. He has not shown this nor has he thought it all the way through. (By the way, Professor Errede is a somewhat well known guy; look him up if you want to see what he has done. But this does not mean he has looked at pickups in depth.)

Stacking magnets? What I told you was that as the stack gets really long, making even longer does not add much strength at one end of the stack. It is what happens when I do it.

Useful results? Yes, a model for a humbucker coil that shows the effects of leakage inductance. I think that is quite useful. Theory (model) and measurement agree; what other model does that? I realize that the contention that the series and parallel losses in a pickup place limitations on the accuracy of a measurement at a single frequency is not popular, but has anyone shown me wrong? And it is important to understand the reasons why a pickup core does not cause the inductance to vary very much with frequency.

Disagreement in science is important. Disagreement without research is useless. Is that what you think I am doing?

And what does what Possum knows have anything to do with this? Do you think I am insulting Possum because I am giving him a little bit of a hard time for referring to this article repeatedly? Let him defend himself if he feels it is necessary. He was looking for a response, and he got it.

I think what Joe and I have been discussing on this forum goes well beyond what Professor Errede has done.

[David Schwab]

Go somewhere quiet and examine your motives for writing what you just did.

I am somewhere quiet. You disagree with everyone here. You are even disagreeing with someone else's research. It's annoying. That's my motivation. It's a repeat of MIMF.

I'll take the variable reluctance thing. That's what guitar pickups are, variable reluctance transducers. There are also other kinds variable reluctance sensors, which are not much different from guitar pickups in their function. They sense a piece of moving metal with a permanent magnet and a coil.

You said:

VR works really well when you have a high permeability nearly closed magnetic path. As a result flux lines are nearly perfectly contained in the material, and flow in a simple way across the gap, or whatever. A guitar pickup is the opposite situation. The problem is dominated by the free space, not the material.

And then Joe rightly pointed out:

Umm. Variable reluctance models are widely used to analyze industrial variable-reluctance position sensors, which also have very large air gaps.

A humbucker is a perfect example of having an air gap, but it is still a relatively compact closed magnetic circuit over the pickup. The two poles are not that far from each other.

I don't give much credance to Wikipedia, but just to illustrate a point, their definition is:

A variable reluctance sensor (VRS) is used to measure position and speed of moving metal components. This sensor consists of a permanent magnet, a ferromagnetic pole piece, a pickup coil, and a rotating toothed wheel.

Just replace the rotating toothed wheel with a moving string.

You have a right to say what ever you want here, and so do I. But I don't have to agree with you, and I can say so. I think you are sometimes missing the forest for the trees.

[Mike Sulzer]

Joseph,

Thanks for the clarification. I am puzzled as to why the resonant frequency does not go down as much as one might expect. Probably I am misunderstanding something.

[Mike Sulzer]

Where have I disagreed with the professor's research results? He showed some impedance plots; they look OK. I disagreed with a statement he made, but I do not think it was one of his results, just a general statement he made.

Nor have I said that you cannot analyze a pickup with the VR method. I do not see any good reason for doing so as it is not simpler than other methods in this case and it does not lead one to a good physical understanding. What does the permanent magnet do? I think you are confused and your reliance on an understanding based only on VR is the reason why.

By a closed magnetic circuit, I mean one like a toroid or typical transformer core. A pickup is certainly not that.

[David Schwab]

Where have I disagreed with the professor's research results? He showed some impedance plots; they look OK. I disagreed with a statement he made, but I do not think it was one of his results, just a general statement he made.

I was referring to:

The method for measuring the capacitance that Joe described (from Terman and other sources) is more accurate than what the professor proposes. He is making a simplifying assumption that he has not bothered to justify.
...
In that article you referred to, you have an intelligent educated guy throwing down a lot of ideas about guitar pickups. He has not really checked out what he says. (Does he show how much the variation with frequency of magnetic properties of the materials affects the inductance? Joe and I have been working on that for a while here.)

His results are some impedance plots. That is what everyone makes.

Yes, science needs to be checked. But in my opinion a lot of what he is saying is commonly known to the art. I'm all for you dissecting the physics behind this stuff, but I keep seeing you dismissing certain things because they don't fit into certain formulas. And that's probably why I also have an issue with simplified models of things like pickups, because they aren't all that simple. Lots of stuff going on there. How does one go about tweezing them apart?

It reminds me of the time I told some people from EMG that their pickups sounded better with 100K pots. The guy dismissed it, and said to me "that doesn't make sense. It can't happen". But it did, and was very easy to demonstrate. Of course he was thinking about the output impedance, etc., and it made no sense to him. So sometimes, even though something shouldn't be, it is. Then you have to find out why. And then later I saw their specs that the output impedance of that pickup was about 100K, and they were using 25K pots.

Nor have I said that you cannot analyze a pickup with the VR method. I do not see any good reason for doing so as it is not simpler than other methods in this case and it does not lead one to a good physical understanding. What does the permanent magnet do? I think you are confused and your reliance on an understanding based only on VR is the reason why.

I was not talking about analyzing a pickup with VR. I was saying VR is pretty much how pickups work. It was in reference to the "disturbing the field" thing.

By a closed magnetic circuit, I mean one like a toroid or typical transformer core. A pickup is certainly not that.

And neither is a VR sensor. Transformers are not transducers. They aren't made to sense moving metal objects in the gap between the poles. They don't have permanent magnets. But sure, they have cores and coils, and all the inductance rules apply, but I feel if you are using a transformer as a model, you are missing things that go on in pickups. Like VR.