Under what conditions does the inductance vary with frequency?

[Joe Gwinn]

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.

At audio frequencies, the shielding effect of non-ferromagnetic metals is partial, giving rise to tone shaping versus total exclusion. The human ear is very sensitive to such shaping. Resonance also affects tone, but this is independent, and both effects act at once.

One can vary the resonant peak without affecting eddy currents by putting capacitors in parallel with the coil. For measuring eddy current effects independent of resonance effects, it's helpful to do eddy current tests at one tenth of the resonant frequency, which is naturally the case if one measures a pickup that resonates at 10 KHz using a 1 KHz test signal.

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

The math was worked out during and before WW2, and the results were widely published after WW2. I would suggest reading Vance, which is short and fairly well written.

Actually, I may have some shielding experiment data as well. I recall doing this a few years ago. I'll look.

It's pretty simple to make such measurements with a signal generator, two coils, an oscilloscope, and a collection of metal sheets. Brass shimstock assortments are quite useful because they make varying the thickness easy.

[Possum]

...

Actually a tele baseplate LOWERS the inductance readings. So do covers. This is why I don't pay a huge amount of attention to Henry readings, AC resistance is a more logical thing to look at what is happening to the audio frequencies.

[RedHouse]

{whups, double posts}

[RedHouse]

...AC resistance is a more logical thing to look at what is happening to the audio frequencies....

What frequency(s) are you looking at?
(Extech freq's?)

[Mike Sulzer]

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.

The peak frequency went down; that is visible on my plot. If both types of effects, change in Q, and change in inductance are there, then the change in Q was the dominant effect.

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.

Let's look at this measurement with some skepticism. The Extech measures the complex impedance. (It interpreted that measurement as an inductance and resistance in series because you told it to.) There are an infinite number of circuits that have the complex impedance that it measured. A simplified model of the situation you have measured is a poorly coupled transformer, which can be represented as a perfectly coupled transformer with a different turns ratio with a leakage inductance in series with the secondary. A resistor is connected across the secondary. The series inductance and resistance can be transformed back to the primary so that we have a series resistance and inductance across the coil. If that resistance is very small and the inductance very large, then the parallel combination of the two inductors would be what you measured. This might be correct situation or maybe not.

In the case of the humbucker pickup that I modeled, this interpretation is certainly not correct. The value of the series resistance is much greater the the inductive reactance at lower frequencies, allowing the resistance to load the pickup. At higher frequencies, the inductance reactance increases and the coil is partially unloaded, allowing the resonant peak to occur.

Please think about this carefully; I believe you are missing the point of the measurements I have made and interpreted. Remember, you are doing what I am doing: assuming a model. That is what happens when you put the Extech in a particular mode. In the case of the pickup, I think you are assuming the wrong model.

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.

Yes, that is such an indirect method.

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

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.

But it is hard to separate the effects of coil loading from transmission loss, since both are frequency dependent.

[Mike Sulzer]

At audio frequencies, the shielding effect of non-ferromagnetic metals is partial, giving rise to tone shaping versus total exclusion. The human ear is very sensitive to such shaping. Resonance also affects tone, but this is independent, and both effects act at once.

Yes, but does one effect matter more than the other? Measurements or calculations are necessary. Both in agreement would be best.

[Joe Gwinn]

Yes, but does one effect matter more than the other? Measurements or calculations are necessary. Both in agreement would be best.

Models need to be made to agree with experiment. Models can do anything, but the real world is what it is. So I'd be making measurements.

[Joe Gwinn]

The peak frequency went down; that is visible on my plot. If both types of effects, change in Q, and change in inductance are there, then the change in Q was the dominant effect.

Let's look at this measurement with some skepticism. The Extech measures the complex impedance. (It interpreted that measurement as an inductance and resistance in series because you told it to.) There are an infinite number of circuits that have the complex impedance that it measured. A simplified model of the situation you have measured is a poorly coupled transformer, which can be represented as a perfectly coupled transformer with a different turns ratio with a leakage inductance in series with the secondary. A resistor is connected across the secondary. The series inductance and resistance can be transformed back to the primary so that we have a series resistance and inductance across the coil. If that resistance is very small and the inductance very large, then the parallel combination of the two inductors would be what you measured. This might be correct situation or maybe not.

In the case of the humbucker pickup that I modeled, this interpretation is certainly not correct. The value of the series resistance is much greater the the inductive reactance at lower frequencies, allowing the resistance to load the pickup. At higher frequencies, the inductance reactance increases and the coil is partially unloaded, allowing the resonant peak to occur.

Please think about this carefully; I believe you are missing the point of the measurements I have made and interpreted. Remember, you are doing what I am doing: assuming a model. That is what happens when you put the Extech in a particular mode. In the case of the pickup, I think you are assuming the wrong model.

Well, we've come full circle. Let me summarize it. I've been reading the relevant literature for thirty or forty years, and they all say than eddy current shielding reduces inductance, the Extech shows just that effect, and the pickup makers also report this effect. I also note that the national standards labs (like NBS and now NIST) for at least 100 years have modeled practical inductors as a series resistor with a parallel capacitor (for self-capacitance), and never add a parallel resistor, and yet the national standards labs are working to parts per million, far more precision than we will ever achieve with pickups.

So, I am presented with a choice: believe your model, or believe the industry and the standards labs and a century of experience.

But it is hard to separate the effects of coil loading from transmission loss, since both are frequency dependent.

I guess that that's true, but why does it matter?

[David Schwab]

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.

That's a very clear explanation! Thanks. I knew what it did, but not exactly why.

[Mike Sulzer]

So, I am presented with a choice: believe your model, or believe the industry and the standards labs and a century of experience.

That is a false choice.

In summary:
1. The complex impedance of a humbucker pickup versus frequency does not match that of a second order circuit (R, L, C). Additional element(s) are required. You cannot learn this with measurements at just a few frequencies. You actually need to look at impedance versus frequency to see this.
2. Unlike most iron cored coils, the humbucker uses solid, rather than laminated cores.
3. High permeability and moderate conductivity cause current to flow around the cores near the surface.
4. Each core thus behaves like a transformer secondary.
5. A transformer model is appropriate.
6. The secondary load reflects back on the primary in parallel. (This is why a transformer needs a large magnetizing inductance.)
7. The transformer model is poorly coupled, and so an inductance in series with the resistive load is required.
8. The frequency dependence of the skin effect means that the resistive load rises with frequency.

A model with these effects matches the measurements when the parameters are adjusted.

This does not disagree with "the industry and the standards labs and a century of experience". But you do have to measure the complex impedance as a function of frequency in order to relate model and measurements in a sensible way. A measurement of complex impedance at a couple of spot frequencies does not do it.

[Peter Naglitsch]

Sorry to interrupt this academic game of ping pong for something that I think is on topic although the complete other way around. It started with this statement from Possum:

Actually a tele baseplate LOWERS the inductance readings. So do covers.

As I am curious and like to back anything up with real life experience and measurements I took two randomly chosen Strat pickups, one made by me and one that came out of a customers ESP that I made new pickups for. I measured the inductance with and without a steel plate under the pickup. I even tried different pieces of steel to be 100% sure. This is what I got:
SC1;
Inductance w/o steel = 2.44H
Inductance with steel = 2.55H
SC2;
Inductance w/o steel = 2.93H
Inductance with steel = 3.09H
(Measurements taken with my cheepo Voltcraft LCR-9063)

So adding a steel plate beneath the pickup doesn't lower the inductance. Actually the other way around. I did the same thing with two humbuckers and a couple of different covers + one Tele neck pickup ripped out of a squire:
HB1;
Inductance w/o covers = 4.75H
Inductance with covers = 4.68H
HB2;
Inductance w/o covers = 4.45H
Inductance with covers = 4.34H
SC3;
Inductance w/o covers = 2.26H
Inductance with covers = 2.17H

So inductance does really go down on HBs and SCs using covers. HOWEVER I noticed one peculiar thing that really surprised me. I make a Gretsch lookalike pickup using these covers:

and when putting them on the same pickups the inductance didn't change much at all:
HB1;
Inductance w/o covers = 4.75H
Inductance with covers = 4.74H
HB2;
Inductance w/o covers = 4.45H
Inductance with covers = 4.46H

Conclusion:
Adding steel to the bottom of SC style pickups add to the inductance, traditional covers on HBs lower it and open type covers on HBs doesn't change it much. And from personal experiences (call it empirical knowledge if that makes anyone more comfortable) that I think most of us here share and can testify to: Adding a piece of steel under a SC type pickup add "bite" or treble to the sound, adding a cover removes a bit of treble or "dulls" the sound a bit and finally adding a top-less (no naughty thoughts now guys) or open cover like the ones pictured above or like this one:

doesn't change the sound much at all. So what does that tell us about inductance and how changes in inductance changes the frequency response of the pickup? Or how we can use that knowledge and adapt it to pickup design? This is more or less the total opposite of the origin of this discussion. Not "how does the inductance wary with frequency" but rather "how can we alter the inductance to get the frequencies that we want?"

Sorry if this is considered OT. Please continue as before...

[Mike Sulzer]

Sorry to interrupt this academic game of ping pong ...

Peter, how do you measure inductance?

Ping pong or not, it is real measurements and how to interpret them that we are discussing.

[David Schwab]

So adding a steel plate beneath the pickup doesn't lower the inductance. Actually the other way around.

I don't have an inductance meter, but I based my comment on an added steel plate increasing inductance, based on my experiments with pickups with low inductance, such as wound on a ceramic magnet with no steel poles. Adding a steel plate increases the output, which I attributed to an increase in inductance.

I did the same thing with two humbuckers and a couple of different covers + one Tele neck pickup ripped out of a squire...

So inductance does really go down on HBs and SCs using covers. HOWEVER I noticed one peculiar thing that really surprised me. I make a Gretsch lookalike pickup using these covers...
and when putting them on the same pickups the inductance didn't change much at all

And that makes sense because of eddy currents. The Gretsch style covers were made to reduce eddy currents. Rowe had a similar patent on a cover with a slit in it and an open front.

[Mike Sulzer]

Sorry, Peter, I did not see that that you said how you measure it..

[Joe Gwinn]

That is a false choice.

In summary:

[... a repeat of the questioned model ...]

A model with these effects matches the measurements when the parameters are adjusted.

This does not disagree with "the industry and the standards labs and a century of experience". But you do have to measure the complex impedance as a function of frequency in order to relate model and measurements in a sensible way. A measurement of complex impedance at a couple of spot frequencies does not do it.

It should be clear that I have some difficulty believing this model, for the reasons already explained at some length. And this model does disagree with that century of experience. You might wish to make some Maxwell-Wein Bridge measurements at various frequencies.