Someone having fun with magnets

[Joe Gwinn]

"skin depth, which varies in inverse proportion to the square root of frequency": Exactly, this means that as the frequency goes up, the skin depth goes down and the resistance goes up. If this resistance is driven by a voltage source through some impedance, then less energy is dissipated as the frequency goes up. In the case of a humbucker pickup core, the skin depth is small enough so that we can think of the voltage induced around the core by the current flow in the pickup coil as resulting in a current around the outer layer of the core, that is, its "skin". This current decreases at higher frequencies because the skin depth decreases, increasing the resistance of the path.

The complicating factor is that the flux leakage due to the open core means that there is a "leakage inductance" appearing in series with this resistance. The impedance of this inductance also increases with frequency, meaning that the energy dissipated in the core decreases with frequency faster than from the increasing resistance alone.

This was included in the last discussion on modeling a humbucker pickup. Both effects have to be included to in the circuit model in order to get good agreement with the measured results.

This all implies that one can use 60 Hz power transformers at 400 Hz, or even as output transformers for audio power amplifiers. We know that this is not the case, so something is wrong with the analysis.

Another thing we know is that the AC resistance of a pickup is higher at 1000 Hz than at 120 Hz. At 120 Hz, the AC resistance is very close to the DC resistance. For example, using an Extech LCR meter, an old single-coil I have (six alnico magnets, forbon bobbin, copper-plated baseplate) measures 6.286 Kohms and 2.562 H at 120 Hz, and 7.311 Kohms and 2.508 H at 1000 Hz. (Rdc is 6.255 ohms.)

Now, I've always wondered if eddy currents in the cover had the same effect as the same currents in the baseplate or the magnets or the slugs, the physical difference being that the music signal must pass through the cover but not the other components. But I never gathered enough energy to chase this issue down.

[David Schwab]

Under what conditions? I think I have shown that that is not the case for humbucker pickups. The pickup magnetic circuit with its open pole pieces is nothing like the closed core of a transformer or many other types of magnetic circuits. There is no reason why eddy currents shouold have the same behavior.

Transformers don't have permanent magnets as part of the circuit. I'm sure there is a stronger magnetic field around most pickups than transformers.

[Mike Sulzer]

This all implies that one can use 60 Hz power transformers at 400 Hz, or even as output transformers for audio power amplifiers. We know that this is not the case, so something is wrong with the analysis.

I do not think what I wrote has any such implications. Eddy current loss in power transformers is complicated. For example, this reference:Transformer - Wikipedia, the free encyclopedia, says: "The eddy current loss is a complex function of the square of supply frequency and inverse square of the material thickness." This is different from what you have been saying, and it is not clear to me how broad is the applicability of the frequency variation that you have stated.

Another thing we know is that the AC resistance of a pickup is higher at 1000 Hz than at 120 Hz. At 120 Hz, the AC resistance is very close to the DC resistance. For example, using an Extech LCR meter, an old single-coil I have (six alnico magnets, forbon bobbin, copper-plated baseplate) measures 6.286 Kohms and 2.562 H at 120 Hz, and 7.311 Kohms and 2.508 H at 1000 Hz. (Rdc is 6.255 ohms.)

The loss due to the dc resistance appears in series with the coil inductance. The loss due to eddy currents appears in parallel. How can a meter that measures the amplitude and phase of the impedance at spot frequencies sort out those two effects and give you a meaningful number describing the total losses? I do not think it can, but maybe I am wrong.

This is why I have gone to the trouble to put together an instrument that measures essentially continuously in frequency. Then one can check against an hypothesized model.

Now, I've always wondered if eddy currents in the cover had the same effect as the same currents in the baseplate or the magnets or the slugs, the physical difference being that the music signal must pass through the cover but not the other components. But I never gathered enough energy to chase this issue down.

The total flux through the cover is composed mostly of the flux from the cores responding to the changing field from the string. So there really is not any reason to be concerned that the signal from the string passing through the cover would be a different effect.

[Joe Gwinn]

I do not think what I wrote has any such implications. Eddy current loss in power transformers is complicated. For example, this reference:Transformer - Wikipedia, the free encyclopedia, says: "The eddy current loss is a complex function of the square of supply frequency and inverse square of the material thickness." This is different from what you have been saying, and it is not clear to me how broad is the applicability of the frequency variation that you have stated.

The loss due to the dc resistance appears in series with the coil inductance. The loss due to eddy currents appears in parallel. How can a meter that measures the amplitude and phase of the impedance at spot frequencies sort out those two effects and give you a meaningful number describing the total losses? I do not think it can, but maybe I am wrong.

The original assertion was that eddy currents had the same effect on both low and high frequencies. Square or square root, both vary with frequency, so the assertion of equal effect cannot be right. This was my original point.

As for Square versus Square Root, it's interesting that these are the mathematical inverses of one another. This has to be the result of looking at the same basic phenomena from different directions.

This is why I have gone to the trouble to put together an instrument that measures essentially continuously in frequency. Then one can check against an hypothesized model.

Lab tests are always worthwhile.

The total flux through the cover is composed mostly of the flux from the cores responding to the changing field from the string. So there really is not any reason to be concerned that the signal from the string passing through the cover would be a different effect.

I'm not so sure. It's a reflected versus transmitted kind of issue, and this is a big issue in the mathematical theory of electromagnetic shields.

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.

[madialex]

This is the point where the engineer types go at it and I sit and skim over because they left my intellect level several paragraphs back LOL.

[Mike Sulzer]

The original assertion was that eddy currents had the same effect on both low and high frequencies. Square or square root, both vary with frequency, so the assertion of equal effect cannot be right. This was my original point.

My assertion has two parts.

1. Resistance due to eddy currents rises with the square root of frequency. I think you agree with this.

2. The effect of eddy currents on a pickup goes down as the "eddy resistance" rises because the loading on the pickup decreases.

Example: If I remove the cover from a humbucker, the impedance at the resonance rises. That is, with that metal part removed, the overall eddy resistance has gone up and there is less loading effect on the peak.

Example 2: If I measure the impedance of a particular humbucker I get a resonant peak at about 12 KHz. If the eddy resistance remained constant with frequency from its value at 1 KHz rather than rising, that peak would be lower and broader. That is, the effect of eddy currents is less because the resistance rises with frequency.

Lab tests are always worthwhile.

Lab tests are worthwhile when the measured parameters can be properly analyzed to give useful information about the device under test. I do not think that you have shown that to be the case for measurements with the Extech when there are two sources of loss in a pickup, one appearing to be in series, the other in parallel. It might be the case, but it needs to be shown.

I'm not so sure. It's a reflected versus transmitted kind of issue, and this is a big issue in the mathematical theory of electromagnetic shields.

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.

The pickup cover is non-magnetic, or very slightly magnetic, and thin. Such materials do not cause significant magnetic shielding. Generally one needs a material with high permeability.

[Joe Gwinn]

My assertion has two parts.

1. Resistance due to eddy currents rises with the square root of frequency. I think you agree with this.

2. The effect of eddy currents on a pickup goes down as the "eddy resistance" rises because the loading on the pickup decreases.

Example: If I remove the cover from a humbucker, the impedance at the resonance rises. That is, with that metal part removed, the overall eddy resistance has gone up and there is less loading effect on the peak.

Example 2: If I measure the impedance of a particular humbucker I get a resonant peak at about 12 KHz. If the eddy resistance remained constant with frequency from its value at 1 KHz rather than rising, that peak would be lower and broader. That is, the effect of eddy currents is less because the resistance rises with frequency.

All LCR meters and impedance bridges are measuring the complex impedance of a two-terminal device of unknown internal construction. One can use a given measured complex impedance to fit any number of proposed equivalent circuits. The Extech PAR/SER button allows one to choose between two such equivalent circuits, one with resistor in series, the other with resistor in parallel. As one pushes the button, one can see both resistance values. But they say the same thing, as they are both derived from the same physical measurement. Varying the frequency can allow one to tell the true parallel from the true series contributions, as they most often arise from different physics effects that do not necessarily vary the same with frequency.

But to come back to a more basic issue, the original claim was that eddy currents have the same audible effect at high and low frequencies, but this claim is directly contradicted by the everyday experience the the more nearby metal the less the highs one hears. So, one is led to question any analysis claiming the contrary. Something is surely missing.

Lab tests are worthwhile when the measured parameters can be properly analyzed to give useful information about the device under test. I do not think that you have shown that to be the case for measurements with the Extech when there are two sources of loss in a pickup, one appearing to be in series, the other in parallel. It might be the case, but it needs to be shown.

Huh? I agree that the Extech is what it is, as described above, but what has that got to do with my agreeing that experiments are a good way to settle technical debates?

The pickup cover is non-magnetic, or very slightly magnetic, and thin. Such materials do not cause significant magnetic shielding. Generally one needs a material with high permeability.

True enough, but I said electromagnetic shielding, not just magnetic shielding. At audio frequencies, most of the shielding effect comes from the large impedance mismatch between free space (377 ohms) and the metal (milliohms). This works even with totally non-magnetic materials. The impedance mismatch causes the incident electromagnetic field to be reflected.

[David Schwab]

But to come back to a more basic issue, the original claim was that eddy currents have the same audible effect at high and low frequencies, but this claim is directly contradicted by the everyday experience the the more nearby metal the less the highs one hears. So, one is led to question any analysis claiming the contrary. Something is surely missing.

I have to agree here.

Here's an interesting photo of a broken DiMarzio bass pickup. Even though the pickup has a metal cover, you can see that they added a sheet of brass to the top, under the cover. I'm assuming this was to use eddy currents to roll some top end off the pickup.

A few non scientific observations. Eddy currents produce their own magnetic field that opposes the field that produced them. We know from practical experience that weaker magnets produce a darker tone than stronger magnets. So it would seem this opposing field could be making the magnetic circuit less efficient at higher frequencies.

It certainly never reduces the low frequencies, but then not much does.

[Mike Sulzer]

But to come back to a more basic issue, the original claim was that eddy currents have the same audible effect at high and low frequencies.

I did not make that claim. I explained what I am claiming in my previous post. Would you please respond that?

In a resonse to David S. above I discussed why the most audible effect is at the high frequencies.

Huh? I agree that the Extech is what it is, as described above, but what has that got to do with my agreeing that experiments are a good way to settle technical debates?

You wrote "Lab tests are always worthwhile." I think some lab tests are not worthwhile. I do not think that the Extech gives you enough frequencies to sort out what is happening in a humbucker.

True enough, but I said electromagnetic shielding, not just magnetic shielding. At audio frequencies, most of the shielding effect comes from the large impedance mismatch between free space (377 ohms) and the metal (milliohms). This works even with totally non-magnetic materials. The impedance mismatch causes the incident electromagnetic field to be reflected.

Yes you did, but I thought you were referring to the possible shielding of the string signal from the pickup by the cover as in a previous post. That would involve the magnetic field only.

[Joe Gwinn]

I did not make that claim. I explained what I am claiming in my previous post. Would you please respond that?

In a resonse to David S. above I discussed why the most audible effect is at the high frequencies.

See next (from 05-06-2009 11:56 AM):

The currents induced in the cores of humbucker are considered eddy currents. They do not affect the highs more than the lows, as I explained in my previous post.

This seems to say that highs and lows are equally affected.

You wrote "Lab tests are always worthwhile." I think some lab tests are not worthwhile. I do not think that the Extech gives you enough frequencies to sort out what is happening in a humbucker.

It is what it is, and two frequencies tells only part of the story, and with only one frequency one has no idea.

One reason I build a Maxwell-Wein bridge is that it allows impedance measurements to be made at any audio frequency.

Yes you did, but I thought you were referring to the possible shielding of the string signal from the pickup by the cover as in a previous post. That would involve the magnetic field only.

OK.

[Mike Sulzer]

See next (from 05-06-2009 11:56 AM):

This seems to say that highs and lows are equally affected.

Taken alone, it could so seem.

But anyway, let us look at eddy loses in an iron core coil. Terman, Radio Engineer's Handbook, 1943 Edition:

"A coil having hysteresis and eddy-current losses can be represented by postulating series resistance Rh and Re, respectively, in series with an inductance having no losses, together with a resistance Rc representing copper losses, as shown in Fig. 64b. In many cases, it is found convenient to represent the eddy-current lossesas a resistance Rsh shunted across the coil as in Fig. 64c, instead of as a series resistance. When the eddy current losses are small, this shunting resistance is independent of frequency, whereas the series resistance is proportional to the square of the frequency."

This equation is from Fig. 64c: Rsh = (omega*L)^2/Re.

Following this are two equations for Re. For a laminated coil, Re depends upon the square of the lamination thickness. For a powdered iron core, it depends on the square of the magnetic particle size. There is no skin depth in these equations. It is stated that it is assumed that the core is already sufficiently subdivided that the magnetic skin effect is not a factor. Thus it would seem that in many practical cases, dividing the core into thin enough slabs, or small enough particles, so that the flux enclosed by each loop is small enough to reduce the total eddy current to an acceptable level, also makes the skin effect negligible.

The humbucker pickup core is not such a case because it is not laminated or powdered. Therefore, one must consider the skin effect. The model I made uses a shunt resistor because this is suggested by the physics. So the only frequency dependence of this resistor is from the skin effect. I will discuss more about this model in a post later.

[Mike Sulzer]

Let's look at how the properties of eddy current effects discussed in the previous post can be applied to modeling the impedance of a humbucker pickup. This was discussed in the thread "A new model the impedance of a humbucker, compared to measurements". This post here is a brief summary.

That thread presented a simple model (using a concept very much like the one discussed in Terman [previous post in this thread]), a better model involving an imperfect transformer, and then with Joe's suggestion involving the skin effect, the final model.

In the simple model, the effect of eddy currents is represented by a parallel resistor, with no variation in frequency. A comparison of the impedance of this model with measurements is given in that thread,
Post 9:
http://www.naic.edu/~sulzer/hbAmplitude.png
http://www.naic.edu/~sulzer/hbPhase.png

The comparison is not very good. If the parameters are adjusted for the correct peak frequency and magnitude at the peak, the width of the model is too wide.

A good model is found.
Post 26:
http://www.naic.edu/~sulzer/hbAmpSD.png
http://www.naic.edu/~sulzer/hbPhaseSD.png

Leakage flux in the imperfect transformer is accounted for with an inductor in series with the "eddy resistor". This partially "unloads" the pickup at the higher frequencies, allowing a narrower width. But it is not good enough. The final step is to include the variation of the value of the "eddy resistor" due to the skin effect.

This is the first time that I know of that the impedance of a humbucker has been adequately modeled.

[Joe Gwinn]

This is the first time that I know of that the impedance of a humbucker has been adequately modeled.

It sure is a whole lot better than before. But adequately modeled?

Why don't the curves lay one on top of the other? Unless one can make a case for inaudible difference.

At least this isn't a Hi Fi Golden Ear forum.

[Mike Sulzer]

It sure is a whole lot better than before. But adequately modeled?

Why don't the curves lay one on top of the other? Unless one can make a case for inaudible difference.

At least this isn't a Hi Fi Golden Ear forum.

Yes, adequately modeled. Do you have any idea how hard it is to adjust four patitally interacting parameters simultaneousy by hand for a good fit? This really needs to be done by the usual minimization procedure one uses with non-linear least squares fitting by computer. But that is a lot of work to implement.

And there are bound to be some additional small physical effects that are not accounted for.

But how much do the two effects found in this work matter? When the pickup is loaded by the cable capacitance, the peak comes way down in frequency. How bad is the simple model in this case? It would be interesting if part of the difference in the sound between pickups using steel cores and those using alnico magnets as cores is the differences in the shapes of the frequeny response curves due to differences in these subtle eddy current effects. But this is certainly not obvious, and it would not be so easy to show that it is true.

[Joe Gwinn]

Yes you did, but I thought you were referring to the possible shielding of the string signal from the pickup by the cover as in a previous post. That would involve the magnetic field only.

Yes, I was talking about the changing magnetic field from the vibrating string. I know that the word electromagnetic makes one think only of radio waves, but there is more to it than that. The referenced theory is complete in that it handles all three limiting cases (magnetic, electric, and radio waves) with a single mathematical framework, and everything in between.