Laminated Core

[Joe Gwinn]

Are we suggesting laminating parallel to the long or short dimension of the pole bar (as viewed from above) for optimum effect?

The loading effect effect varies with something like the square of the thickness. The strips can be long way or short way, so long as the thickness dimension is perpendicular to the axis of the coil. Long way is a lot less work. Kinman has a patent on doing it the short way, but he isn't building a blade pickup.

Cutting transverse slits in a thick blade won't work - it's the smallest dimension that's perpendicular to the coil axis that counts.

[Mike Sulzer]

The issue is to get the desired amount of eddy current loading, to get a desired sound.

That's not the issue fieldwrangler brought up, the one I was addressing. On the other hand, if you do want to get a controlled reduction in eddy currents over a solid blade, say 2, 3, 4, 5... times less, why use laminations? That is difficult. Just cut the blade into pieces in the obvious way along the axis of the pickup, and make sure that they are insulated from each other.

[David King]

That's basically what Bartolini does.

[Mike Sulzer]

That's not the issue fieldwrangler brought up, the one I was addressing. On the other hand, if you do want to get a controlled reduction in eddy currents over a solid blade, say 2, 3, 4, 5... times less, why use laminations? That is difficult. Just cut the blade into pieces in the obvious way along the axis of the pickup, and make sure that they are insulated from each other.

I see now; what I am suggesting would only be good for fine tuning; if you want to reduce it a few times, laminations in the usual way are easier.

[Mike Sulzer]

The loading effect effect varies with something like the square of the thickness. The strips can be long way or short way, so long as the thickness dimension is perpendicular to the axis of the coil. Long way is a lot less work. Kinman has a patent on doing it the short way, but he isn't building a blade pickup.

Cutting transverse slits in a thick blade won't work - it's the smallest dimension that's perpendicular to the coil axis that counts.

Maybe I am still confused. If you make thin laminations twice as thin (and thus have twice as many), the resistance of each stays almost the same, and the voltage around the loop is half as much. So the power dissipated in each drops by a factor of four (p = (v^2)/R). But you have twice as many laminations, and so the total power has been reduced by half. That makes the variation look linear.

[Joe Gwinn]

Maybe I am still confused. If you make thin laminations twice as thin (and thus have twice as many), the resistance of each stays almost the same, and the voltage around the loop is half as much. So the power dissipated in each drops by a factor of four (p = (v^2)/R). But you have twice as many laminations, and so the total power has been reduced by half. That makes the variation look linear.

I was speaking of individual laminations. If you have more than one lamination, their effects will add, as you note.

The shape of the loss versus frequency will follow the thickness of the individual laminations, not the number of laminations, so one adjusts both individual thickness and number to suit.

[Mike Sulzer]

The shape of the loss versus frequency will follow the thickness of the individual laminations, not the number of laminations,

I think if you pull out half the laminations, the frequency at which 3db is lost would rise. In a pickup, the onset of skin effect in the individual laminations might also be a complicating issue.

[Joe Gwinn]

I think if you pull out half the laminations, the frequency at which 3db is lost would rise. In a pickup, the onset of skin effect in the individual laminations might also be a complicating issue.

No, the height of the peak will also change, preserving the shape.

[Mike Sulzer]

No, the height of the peak will also change, preserving the shape.

This is complicated; for exact results, one must consider a specific situation, but consider this somewhat specific situation: an air coil into which one can insert one or two identical laminations, thin enough so that they do not affect the inductance significantly. We apply changng flux to induce a voltage. The voltage across the coil is determined by a voltage divider in which the coil inductance (+ resistance) is the series element and the shunt element is the impedance resulting from the loading due to the lamination. This impedance as a function of frequency can be determined by the theory described elsewhere, but never mind, it is what it is. One lamination results in a certain attenuation versus frequency. Two laminations halves the shunt impedance. If the shunt impedance were purely resistive, this would cut the 3 db frequency in half, assuming the coil is purely inductive at this frequency. The shunt impedance is not purely resistive, while the series impedance is not purely inductive, and so it will not do that, but if the former is partly resistive and the latter mostly inductive, I expect the frequency to drop, how much depending on the specifics.

[Joe Gwinn]

This is complicated; for exact results, one must consider a specific situation, but consider this somewhat specific situation: an air coil into which one can insert one or two identical laminations, thin enough so that they do not affect the inductance significantly. We apply changng flux to induce a voltage. The voltage across the coil is determined by a voltage divider in which the coil inductance (+ resistance) is the series element and the shunt element is the impedance resulting from the loading due to the lamination. This impedance as a function of frequency can be determined by the theory described elsewhere, but never mind, it is what it is. One lamination results in a certain attenuation versus frequency. Two laminations halves the shunt impedance. If the shunt impedance were purely resistive, this would cut the 3 db frequency in half, assuming the coil is purely inductive at this frequency. The shunt impedance is not purely resistive, while the series impedance is not purely inductive, and so it will not do that, but if the former is partly resistive and the latter mostly inductive, I expect the frequency to drop, how much depending on the specifics.

I have no idea if your proposed model circuit is an adequate representation for what's actually going on. I'd start with trying it in a test coil, and then fit the math to the experimental results.

[Mike Sulzer]

I have no idea if your proposed model circuit is an adequate representation for what's actually going on. I'd start with trying it in a test coil, and then fit the math to the experimental results.

What circuit model were you basing your statement ("No, the height of the peak...") on, if any? Clearly, the coil capacitance effect is explained by the series-shunt divider model, coil in series, shunt capacitor. Why would the impedance from eddy currents be different? The loading from eddy currents appears across the coil in the same way; it is like the secondary of a transformer.

Fitting to experimental results is what I have been doing in that other discussion. But also, starting with the experimental impedance measurements, it is possible to "unparallel" the coil inductance and construct the series-shunt circuit model. Preliminary results for steel show the small dip in the middle like some humbucker response measurements, but before I show this I want to get frequency response measurements from the same coil-core combinations (using a test exciter coil), but this requires some slightly different software that I need to write.

[Joe Gwinn]

What circuit model were you basing your statement ("No, the height of the peak...") on, if any? Clearly, the coil capacitance effect is explained by the series-shunt divider model, coil in series, shunt capacitor. Why would the impedance from eddy currents be different? The loading from eddy currents appears across the coil in the same way; it is like the secondary of a transformer.

It's based on physics reasoning, which may or may not translate well to lumped-parameter circuit designs, although approximations are often good enough to be useful.

The reasoning is that if a single lamination of thickness t produces a given eddy-current loss curve (with respect to frequency), two such laminations next to one another will produce the same curve, only with twice the loss at each and every frequency. In other words, the curve goes up and down, but does not change shape.

By contrast, if a pair of laminations of thickness t is replaced by a single lamination of thickness 2t, one will get a different frequency response than the lamination of thickness t.

Now, it must be noted that the above rule applies only when the skin depth is no less than t and 2t or so. If the skin depth is far less than t, varying the lamination thickness will have little effect.

Fitting to experimental results is what I have been doing in that other discussion.

True, and a very useful thing to do.

But also, starting with the experimental impedance measurements, it is possible to "unparallel" the coil inductance and construct the series-shunt circuit model. Preliminary results for steel show the small dip in the middle like some humbucker response measurements, but before I show this I want to get frequency response measurements from the same coil-core combinations (using a test exciter coil), but this requires some slightly different software that I need to write.

This is the part I'm less sure of, as it seems to have cart before horse. The issue is that the physics of eddy current is not fully expressible by networks of lumped-parameter components. Although one can come up with useful approximations, one usually starts with measurements on the system in question, and then back-fits a circuit diagram that yields and adequate approximation, where "adequate" is decided in the context of what one will use the system in question for.

[Mike Sulzer]

It's based on physics reasoning, which may or may not translate well to lumped-parameter circuit designs, although approximations are often good enough to be useful.

True, physics reasoning is more general, but this statement of the physics does not describe the situation completely:

The reasoning is that if a single lamination of thickness t produces a given eddy-current loss curve (with respect to frequency), two such laminations next to one another will produce the same curve, only with twice the loss at each and every frequency. In other words, the curve goes up and down, but does not change shape.

By contrast, if a pair of laminations of thickness t is replaced by a single lamination of thickness 2t, one will get a different frequency response than the lamination of thickness t.

The effect of the coil inductance is missing, and it is necessary for determining the losses in the pickup and its response.

This is the part I'm less sure of, as it seems to have cart before horse. The issue is that the physics of eddy current is not fully expressible by networks of lumped-parameter components. Although one can come up with useful approximations, one usually starts with measurements on the system in question, and then back-fits a circuit diagram that yields and adequate approximation, where "adequate" is decided in the context of what one will use the system in question for.

The concept of impedance is more general than that of lumped elements restricted to Rs, Ls and Cs. Equation 8 in the pdf file referred to in the current pickup measurement discussion is for impedance, but you cannot represent that impedance exactly by such lumped elements except in certain limiting cases. However, that impedance is exact in a case where the stated conditions are met. Then the question is, how closely are these conditions met in a real pickup? This is why I measured an artificial case, shorted turn, and showed that it compares well, and two pickups, one that compares well and another for which the model is of some use, but clearly not fully accurate.

I do not think that representing the eddy current losses as an impedance across the coil is perfectly accurate, but I doubt that it is any less accurate that saying that a coil has "capacitance", when the reality is much more complicated. To the extent that this is true, one can take out the coil impedance, leaving that due to eddy currents. The accuracy of this can be checked by measuring the frequency response of the pickups by use of an exciter coil and comparing that to predictions using the impedance concept just described. I doubt that they will agree perfectly, but we shall see.

[Joe Gwinn]

True, physics reasoning is more general, but this statement of the physics does not describe the situation completely.

Well, it is certainly a back-of-the-envelop kind of analysis, but I don't understand your point.

The effect of the coil inductance is missing, and it is necessary for determining the losses in the pickup and its response.

Yes, there will be an effect, but how big? Earlier, you had in effect concluded it would be minimal: "This is complicated; for exact results, one must consider a specific situation, but consider this somewhat specific situation: an air coil into which one can insert one or two identical laminations, thin enough so that they do not affect the inductance significantly." In any event, this assumption deserves a direct test.

In a pickup with one coil and two laminations, currents in the two laminations can and will interact with one another.

The concept of impedance is more general than that of lumped elements restricted to Rs, Ls and Cs. Equation 8 in the pdf file referred to in the current pickup measurement discussion is for impedance, but you cannot represent that impedance exactly by such lumped elements except in certain limiting cases. However, that impedance is exact in a case where the stated conditions are met. Then the question is, how closely are these conditions met in a real pickup? This is why I measured an artificial case, shorted turn, and showed that it compares well, and two pickups, one that compares well and another for which the model is of some use, but clearly not fully accurate.

I think you are restating my point, and it's true that one always has impedance, even if there are no lumped-parameter elements.

For the audience: A lumped-parameter circuit is one where there are things like recognizable inductors, capacitors, and resistors, each being a object one can hold in the hand, and each being a fairly pure representative of the breeds L, R, or C. A common example of a non-lumped parameter is the stray capacitance of an inductance coil.

I do not think that representing the eddy current losses as an impedance across the coil is perfectly accurate, but I doubt that it is any less accurate that saying that a coil has "capacitance", when the reality is much more complicated. To the extent that this is true, one can take out the coil impedance, leaving that due to eddy currents. The accuracy of this can be checked by measuring the frequency response of the pickups by use of an exciter coil and comparing that to predictions using the impedance concept just described. I doubt that they will agree perfectly, but we shall see.

I agree, but submit that it can get pretty complicated, which is why one normally starts with measurements and the simplest plausible lumped-parameter circuit that emulates the measured behaviour, adding components only when and where the approximation is insufficient for the intended use. There is a whole literature on such things, and many a researcher has become famous for finding a nice approximating model. where nice means simpler (more tractable mathematically) than anything else that accurate.

[Mike Sulzer]

If you want to know the change in the frequency response of a pickup from adding a laminated core, you must include the effect of the coil inductance because it is an important part of the circuit. I did not conclude that the effect the inductance would be negligible, as you said I did. All I did was consider a case where the effect of the laminations on the inductance would be small, just for simplicity. Read my statement (that you quoted) again. I do not think that there is any point in commenting on the rest of what you wrote until this misunderstanding is cleared up.