Under what conditions does the inductance vary with frequency?

[Joe Gwinn]

Yes, that is the way I understand it. Therefore, I do not classify the skin depth-limited current flow in the coil of a high frequency inductor as an eddy current. I guess I misunderstood you when I thought you wrote above that it is an eddy current.

The cause of skin depth is eddy currents. In this case the variation of wire AC resistance with frequency is eddy currents in the wire itself.

In electromagnetics, all things that are possible are required, and all will happen to some degree. In most practical situations , only a few of the many possible effects are large enough to matter, and it is these few effects that each practical design concentrates on.

In guitar pickups, eddy currents in the very thin wire used for winding are not important, but eddy currents in nearby pieces of metal (like magnets, slugs, baseplates, and covers) are quite important.

So the AC resistance of a pickup coil is due to energy losses caused by eddy currents in that nearby metal, and is not due to eddy currents in the wire (which does however contribute its DC resistance).

[David Schwab]

So the AC resistance of a pickup coil is due to energy losses caused by eddy currents in that nearby metal, and is not due to eddy currents in the wire (which does however contribute its DC resistance).

I know you were talking to Mike but... That's what I thought.

But does that decrease inductance? I had never heard about that effect.

[Joe Gwinn]

So... do eddy current lower the inductance? And if so, is that due to the opposing magnetic field produced by the eddies?

Exactly. Yes to both.

Take an iron-cored coil. In the absence of eddy currents, the entire mass of iron would be available to increase the flux through the coil, yielding a proportionate increase in inductance. With eddy currents in that core, the AC magnetic field from the coil is to some degree pushed out of the core, so there is less field for a given coil current, and thus less inductance.

My understanding was that eddy currents affect the high frequencies more, which I assumed was due to AC resistance. I don't know how the magnetic field would tie into this.

The AC resistance is a consequence of the finite resistance of the core material through which the eddy current flows. This is best explained by comparing some extreme cases:

Iron core with superconducting lead plating, in liquid helium. The iron will not increase the magnetic flux because the eddy currents in the superconducting surface layer will totally exclude magnetic flux from the iron interior. The inductance will be much reduced, but the AC resistance will not change because eddy currents in a superconductor are lossless.

Ferrite core. No eddy currents so no flux expulsion, so inductance goes up (compared to air), and the AC resistance (excess over DC resistance of the coil) will only go up a tad, due to the magnetic hysteresis of the ferrite material.

Plain old iron core. The higher the frequency the larger the eddy currents in the iron, the greater the expulsion of flux from the core, the lower the inductance, and the greater the excess AC resistance due to eddy current losses in the core.

[RedHouse]

...In guitar pickups, eddy currents in the very thin wire used for winding are not important, but eddy currents in nearby pieces of metal (like magnets, slugs, baseplates, and covers) are quite important....

The tone, and attack changes slightly, this we can work around because we know it's there. Sometimes we are making a full-meal-deal out of eddy currents when they really should be more of a side-note.

We can use (or not) metal covers and back plates, a discussion of the types of metal used for covers and back plates seems much more useful area to the field of pickup making IMHO.

Speaking of back plates, isn't it funny how if we add a backplate to a Tele bridge pickup (or Jaguar s-c) it gets more treble, but when we cover a pickup with a metal cover between the pickup and strings it tends to loose some treble.

(yes I know, focusing the field etc.)

[Joe Gwinn]

Speaking of back plates, isn't it funny how if we add a backplate to a Tele bridge pickup (or Jaguar s-c) it gets more treble, but when we cover a pickup with a metal cover between the pickup and strings it tends to loose some treble.

(yes I know, focusing the field etc.)

It's actually not focusing, it's a form of electromagnetic shielding:

Consider a simple pickup without baseplate or cover. The motion of the strings generates an AC magnetic field, which then induces a AC voltage in the nearby pickup coil. Now, introduce a thin sheet of brass.

If we put the sheet between strings and coil, some part of the AC field will be reflected away from the coil, reducing the AC field at the coil and thus reducing the AC voltage from the coil.

If instead we put sheet behind coil, the reflection will increase the AC field at the coil.

In both cases, the amount of reflection increases with the square root of frequency.

If one has a coil between a thin cover and a thick baseplate, the net effect will be some complicated kind of balance between the above two effects.

If one uses nickel silver or stainless steel, eddy currents are much reduced over those in brass, so the reflections are all proportionately reduced.

[Mike Sulzer]

The cause of skin depth is eddy currents. In this case the variation of wire AC resistance with frequency is eddy currents in the wire itself.

Electromagnetic induction causes eddy currents. Electromagnetic induction causes skin depth. I think it is somewhat misleading to say that eddy currents are the cause of skin depth. I prefer:

"The effect is caused by electromagnetic induction in the metal which opposes the currents set up by the wave E-field..."
--http://www.fas.harvard.edu/~scdiroff/lds/ElectricityMagnetism/SkinDepth/SkinDepth.html

[Mike Sulzer]

If we put the sheet between strings and coil, some part of the AC field will be reflected away from the coil, reducing the AC field at the coil and thus reducing the AC voltage from the coil.

The amount that is reflected at audio frequencies is very small. If the reflection at audio frequencies were large enough to matter, electromagnetic effects would be large enough so that we would not need coils with 5000 or more turns. (High permeability cores help, too.)

[Joe Gwinn]

The amount that is reflected at audio frequencies is very small. If the reflection at audio frequencies were large enough to matter, electromagnetic effects would be large enough so that we would not need coils with 5000 or more turns. (High permeability cores help, too.)

It has the effect of shaping the tone, and this is exactly what people hear.

The theory of shielding is laid out in some detail in the literature, and I gave some references in Someone having fun with magnets thread. From posting #19, bottom:

The theory is clearly explained in Edward F. Vance, “Coupling to Shielded Cables”, Wiley 1978, 183 pages. Reprinted by Krieger in 1987. The same theory applies to metal boxes.

If this isn't deep enough, the fundamental source is "Electromagnetic Waves”, S.A. Schelkunoff, Van Nostrand 1943. The foundations of the theory of electromagnetic shields are set forth in §8.18 “Shielding Theory”. This is the basic reference, appears in almost all bibliographies of articles on shielding, and can be heavy going for those not having had a course in E&M Field Theory.

[Mike Sulzer]

What does the pickup cover do?

See here: http://www.naic.edu/~sulzer/coverEffects.png

It affects the pickup circuit. The effect shown in the figure is that it reduces the height of the peak. That is, losses from the eddy current induced in the cover from the current in the coil extract energy from the resonance, lowering the Q. Note that the peak frequency is also reduced a little bit. This is also consistent with lowering the Q.

The eddy currents do not lower the inductance. If they did, the resonant frequency would rise.

[Joe Gwinn]

See here: http://www.naic.edu/~sulzer/coverEffects.png

It affects the pickup circuit. The effect shown in the figure is that it reduces the height of the peak. That is, losses from the eddy current induced in the cover from the current in the coil extract energy from the resonance, lowering the Q. Note that the peak frequency is also reduced a little bit. This is also consistent with lowering the Q.

The eddy currents do not lower the inductance. If they did, the resonant frequency would rise.

How accurately can your setup measure inductance, and how do verify this?

What is the cover made of and how thick is it?

Try a thick piece of brass or copper.

[Mike Sulzer]

How accurately can your setup measure inductance, and how do verify this?

What is the cover made of and how thick is it?

Try a thick piece of brass or copper.

That was an old measurement before the I-V. Bit the effect of the loss dominates over the change in inductance. Otherwise the peak would rise.

We cannot directly measure the inductance at resonance anyway because of the capacitance. One must model the circuit. But the lack of rise in the resonant frequency is all we need to know.

It was thin; I do not remember the material.

I should do that; but it need not be much thicker than the skin depth.

[Mike Sulzer]

It has the effect of shaping the tone, and this is exactly what people hear.

You may be exaggerating how much conductors (as opposed to ferromagnetic materials) can shield out magnetic fields varying at audio frequencies. I think the tonal effects are adequately explained by losses at the high impedance resonance of the coil and cap.

Do you have calculations or measurements that unambiguously show that induced currents in thin conductors such as pickup covers can shield at audio frequencies?

[David Schwab]

The tone, and attack changes slightly, this we can work around because we know it's there. Sometimes we are making a full-meal-deal out of eddy currents when they really should be more of a side-note.

Where you really hear it is in the design of bass pickups. Eddy currents can kill the high end quickly. Modern bass pickups often have more high end than most guitar players would want.

We can use (or not) metal covers and back plates, a discussion of the types of metal used for covers and back plates seems much more useful area to the field of pickup making IMHO.

The less conductive the material, the better if you want to retain high end.

Speaking of back plates, isn't it funny how if we add a backplate to a Tele bridge pickup (or Jaguar s-c) it gets more treble, but when we cover a pickup with a metal cover between the pickup and strings it tends to loose some treble.

Tele and Jaguar pickups use steel back plates, which increase the inductance. It becomes part of the magnet circuit. You will hear the pickup get louder when you stick a piece of steel behind the magnets. This is especially true with non metallic magnets, like ceramic or neo.

Pickup covers are a different story, they aren't magnetic, and its the eddy currents in the cover that change the tone. Once again, the less conductive the material, the better if you want to retain high end.

[RedHouse]

....Modern bass pickups often have more high end than most guitar players would want....

This I agree with. I've been learning this lesson winding (and rewinding) pickups for my own bass. What works for guitar doesn't work so well for bass.

[Joe Gwinn]

That was an old measurement before the I-V. Bit the effect of the loss dominates over the change in inductance. Otherwise the peak would rise.

Resonant frequency varies as the square root of inductance, and the voltage peak of a low-Q resonator is quite broad, so it's likely that the apparatus was simply not sufficiently precise to detect the change. A Maxwell-Wein bridge can easily detect such changes, as can an Extech.

On 25 October 2005, having just wound a drive coil (575 turns of #32 wire on a StuMac pickup bobbin), I made a few Extech measurements:

Rdc= 46.36 ohms (measured with a TX3 DMM, not the Extech)

L1KHz(air)= 16.199 mH
R1KHz(air)= 46.18 ohms

The above in air, with no metal nearby. Then, I set the coil on a sheet of 0.090" thick aluminum (6061 alloy T6 temper) plate:

L1KHz(metal)= 14.254 mH
R1KHz(metal)= 55.12 ohms

So, the inductance change is 16.199/14.252= 1.1365:1, or 14%.

I've made other measurements, but have not found my notes yet. Copper is a better conductor than 6061T6 aluminum, and has a somewhat larger effect.

We cannot directly measure the inductance at resonance anyway because of the capacitance. One must model the circuit. But the lack of rise in the resonant frequency is all we need to know.

One certainly can measure the inductance at resonance. At zero phase, the capacitive reactance is equal to the inductive reactance. One measures the unknown self-capacitance of the coil by measuring zero-phase resonant frequency with a series of capacitors of known value in parallel with the coil. The method is in Terman.

It was thin; I do not remember the material.

Then it's probably nickel plated brass, maybe 0.020" thick.

I should do that; but it need not be much thicker than the skin depth.

At audio frequency, the skin depth is large, and the thickness of such things as covers is a fraction of the skin depth. If the covers were not thinner than the skin depth, no music would get through to the coil.

The skin depth is where the signal voltage is 1/e of the incident voltage. This is a 8.7 dB loss, which is easily audible.