Measuring the capacitance of an inductor or Inductors

[Mike Sulzer]

Permanent magnets produce eddy currents in nearby conductors.

As you said: moving magnets. They produce a field that changes in time at a fixed point in space.

So in a pickup, when the magnetic field is disturbed, eddy currents will be produced in any metal parts on the pickup.

The idea that pickups work because something disturbs the permanent field is probably the biggest impediment to understanding anyone ever thought up. It is true in a sense; but to understand how it is true, you need to understand how E&M really works.

[David Schwab]

The idea that pickups work because something disturbs the permanent field is probably the biggest impediment to understanding anyone ever thought up. It is true in a sense; but to understand how it is true, you need to understand how E&M really works.

And if you put some conductive metal near your pickup, and there goes the high end. If not from eddy currents, than what?

The consensus is eddy currents, and pickup designers over the years have done things like make slits in covers to combat that effect. And it works.

Even using a more conductive metal like aluminum for a baseplate will drastically alter the tone. Pickup makers say this is due to eddy currents. If the magnet is not moving, and you claim that's needed, what causes the loss of high end when conductive metal is in the close proximity of the coils?

[Mike Sulzer]

And if you put some conductive metal near your pickup, and there goes the high end. If not from eddy currents, than what?

The consensus is eddy currents, and pickup designers over the years have done things like make slits in covers to combat that effect. And it works.

Even using a more conductive metal like aluminum for a baseplate will drastically alter the tone. Pickup makers say this is due to eddy currents. If the magnet is not moving, and you claim that's needed, what causes the loss of high end when conductive metal is in the close proximity of the coils?

Really? We have discussed the effects of eddy currents such as in a cover or base plate several times, and I have even shown plots showing the reduction in the high frequencies, especially at the resonance. Obviously it is currents in the conductor.

But does it have anything to do with the permanent magnet? Not directly. Any ac current in the coil induces currents in nearby conductors (the law of electromagnetic induction). This happens with or without any permanent magnets. The process is enhanced by higher permeability cores. The permeability can be a function of the strength of the permanent field; so in this sense this field plays a role. But that is not what you should concentrate on.

Here are some key questions and answers:

1. What causes the magnetic field that induces the currents in the pickup cover?

Answer: ac current flowing in the coil. Any currents, whether resulting from the vibration of the string, or a signal you injected in to test the pickup.

2. What does the permanent magnet in the pickup do?

Answer: It establishes a permanent field which only matters at the location of the string. It produces magnetic polarization in the string. That is, it magnetizes it.

3. How does the vibrating string cause currents in the cover?

Answer: Indirectly. A voltage is induced in the coil by the time varying magnetic flux (field times area) through the coil. The field varies because the string is moving, but it is the varying field that matters, not why it is varying. Current flows in the coil because there is a load connected to it and because the coil's self-inductance and capacitance make a resonant circuit in which current flows. This ac current then makes a varying magnetic field, possibly enhanced by high permeability cores. The varying field induces a voltage around some path in the cover and then current flows because the cover conducts.

Let's forget this "disturbance in the force" (I mean field) crap. That is for star wars. Pickups work according to Maxwell's equations, one of which is the law of magnetic induction.

[David Schwab]

Let's forget this "disturbance in the force" (I mean field) crap. That is for star wars.

The moving string changes the reluctance of the magnetic circuit. The magnetic circuit is made up of closed paths of magnetic flux. So the moving strings modulate the magnetic flux linking the coil, inducing current to flow.

So maybe saying the string is "disturbing the field" is not the best words to use, but thats the gist of it. It's variable reluctance.

Pickups work according to Maxwell's equations, one of which is the law of magnetic induction.

And that would be Faraday's law of induction (Lorentz force law).

[Mike Sulzer]

The moving string changes the reluctance of the magnetic circuit. The magnetic circuit is made up of closed paths of magnetic flux. So the moving strings modulate the magnetic flux linking the coil, inducing current to flow.

So maybe saying the string is "disturbing the field" is not the best words to use, but thats the gist of it. It's variable reluctance.



And that would be Faraday's law of induction (Lorentz force law).

Variable reluctance is a computational method. It does not replace understanding the basic physics, and you cannot use it in place of such an understanding. If you want to understand this stuff, pretend you never heard of variable reluctance and start over from the basics.

The law of induction is not the Lorentz force law. There is an interesting relationship for sure. It helped Einstein discover special relativity.

[Mike Sulzer]

Your cores in a pickup should be grounded, and in a typical humbucker they are.

But they were not in my measurement. That is what I was describing.

[Joe Gwinn]

Variable reluctance is a computational method. It does not replace understanding the basic physics, and you cannot use it in place of such an understanding. If you want to understand this stuff, pretend you never heard of variable reluctance and start over from the basics.

Now hold on. There are multiple mathematically equivalent ways to approach the actual pickup situation, and variable reluctance is a major one.

Nor is there any sin in using multiple methods to understand a physical system.

And direct application of Maxwell's Equations most often yields results too complex to be of any practical use, or even to be solved except by numerical methods, so one must approximate in practice.

[Joe Gwinn]

I would think that increasing the space between coil and shield would be better. Using an insulating material should increase the capacitance if its dielectric constant is greater than that of air.

True enough, but mechanical considerations intrude, so people use a thick layer of low-index (dielectric index that is) material instead of air.

[Joe Gwinn]

On the subject of cores causing a change in capacitance:

A grounded shield is different from ungrounded cores. If the part of the coil closest to the shield has an oscillating voltage that differs from ground, then charge must flow.

And in a flat plate air capacitor, inserting an ungrounded metal plate between the capacitor plates will increase the capacitance since it is now equivalent to two capacitors with smaller spacing in series.

But, how much charge has to flow as a result of ungrounded cores? The potential across the inner winding is a small fraction of the total, and so the fact that the potential on the surface of the core must be the same everywhere has only a small effect on the flow of charge in the coil.

If one end of the coil is grounded, often the situation, even a grounded core will increase self capacitance. And so on.

In practice, metallic objects near a coil increase its capacitance. There are multiple reasons.

[Possum]

....

Belwar I think you may end up getting screwy results, if you read the link I posted, those guys had I think 3 different buffers they were using to isolate all the possible interferences from instruments etc. and even put the pickup in a Mu metal tube during measurements. Also if you go here there is an excellent Excel sheet of pickups they tested including capacitance:
UIUC Physics 498POM Guitar Pickup Measurements

I doubt you can duplicate what they did with simple instruments. You'll notice they said capacitance is very hard to measure, they used a special HP machine to do that, its worth reading even if the math is way out of my league :-)

[Mike Sulzer]

Now hold on. There are multiple mathematically equivalent ways to approach the actual pickup situation, and variable reluctance is a major one.

Fine. But VR is not equivalent to the law of induction, except in some circumstances where it applies almost exactly and others where it is a good approximation.

I agree that it can be useful. In fact I used it in that other thread, noting, I believe, its approximate applicability. You did not agree and called for more measurements.
But you cannot turn it around and use it as a replacement for understanding induction. The all too common misunderstanding that the value of the permanent field is important every where is an example.

Nor is there any sin in using multiple methods to understand a physical system.

Of course. But that does not describe what happens when VR is used to understand pickups.

And direct application of Maxwell's Equations most often yields results too complex to be of any practical use, or even to be solved except by numerical methods, so one must approximate in practice.

You are making my case for me. Exactly. One applies the appropriate approximations and computational methods that get the job done. But one does not then turn it around and claim that one has gained a better intuitive understanding of the general problem.


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.

[Mike Sulzer]

True enough, but mechanical considerations intrude, so people use a thick layer of low-index (dielectric index that is) material instead of air.

Right. To increase or maintain the spacing. That was my point.

[Joe Gwinn]

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

Reduced to its essentials, in VR models, one assumes that magnetic field changes propagate at infinite speed (compared to the rate at which the ferromagnetic bodies move). So, there are no lagged-potential or radiation effects to consider, and the voltage output is that due to the relatively slow rate of change of flux through the coil versus time. The size of the air gap is irrelevant to the applicability of VR models.

[Mike Sulzer]

If one end of the coil is grounded, often the situation, even a grounded core will increase self capacitance. And so on.

Yes, a grounded core is where one would expect the most effect because charge is free to flow. My point was that even an ungrounded core can have some effect.

In practice, metallic objects near a coil increase its capacitance. There are multiple reasons.

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

[Mike Sulzer]

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

Reduced to its essentials, in VR models, one assumes that magnetic field changes propagate at infinite speed (compared to the rate at which the ferromagnetic bodies move). So, there are no lagged-potential or radiation effects to consider, and the voltage output is that due to the relatively slow rate of change of flux through the coil versus time. The size of the air gap is irrelevant to the applicability of VR models.

But it is relevant to how easy it is to solve the problem. Classic simple case: A piece of magnetic material moves in and out of a gap in a high permeability closed core.

If you have an open core or large gap, you will need to solve a differential equation to find out exactly what is going on. Of course, once you do that, you should be able to model certain changes to the system very easily with VR.