Eddy currents, and the orientation of the conductive metal

[antigua]

The test setup features a driver coil, a large aluminum heat sink, and a Strat pickup with no pole pieces in the bobbin (air core). 

I'm removing this test data on account of figuring out that the shape of the aluminum heat sink renders the test invalid. The heat sink is flat on one side with combs on the other, and so it's orientation makes a difference. I need to redo the test with a block of metal that is fully symmetrical. This is the bode plot "https://i.imgur.com/ KDyCQBi.png" without spaces, I don't want google images to pick it up and have it mislead people who stumble upon it. 



[removed]

[ms]

Starting with an air core was a good idea.  I will be interested to see if your prediction is true: that what I consider two different effects, attenuation of the signal and reduction of Q, are actually coupled  together.

[stratotarts]

I find it a little weird that the response with the aluminum in between the pickup, with equal distance between the pickup and the exciter coil, is greater than with the aluminum beside the exciter coil. Of course, I'm never surprised when things aren't the way I think they ought to be. Thinking about this, I was wondering about the 3D arrangement of the aluminum. It is possible for field lines to go around the aluminum by going around the block and through the test bench. Would those responses be the same if the exciter and pickup were positioned in the center of the block, rather than at the edge as it appears in this setup?

[antigua]

OK, here's a new and improved test, using the copper and aluminum blocks from this set www.amazon.com/gp/product/B00COQGA2U/ref=oh_aui_search_detailpage?ie=UTF8&psc=1 . It also contained some unknown grade of steel, and some unknown formulation of brass. 

The pickup and exciter coil are 50mm apart. The coils are taped down to make sure they don't move during the testing. 

The pickup has no pole pieces, so it's air core.




The test involves four scenarios: 1) no block 2) block beside exciter coil 3) block in between exciter coil and pickup 4) block beside the pickup.

Aluminum block; the highest peak is no block, the second highest peak is with the aluminum block in between the coils, and the two lower blocks are with the block either against the pickup or the exciter coil, and those peaks are about even, but when the block is beside the pickup, the inductance of the pickup is reduced slightly, as evidenced by the slightly higher resonant frequency in the green line. 



With a copper block, the results were nearly the same:



I also tried  putting the block behind the pickup, the curve was similar to the red plot line, or the result of placing the block in between the pickup and exciter coil.

The mystery steel block that came with the set only slightly reduced the Q factor and increased the inductance when it was beside the pickup, but was otherwise nearly inert. The brass block yielded curves very similar to the copper and aluminium.




The next thing to try was to see if placing steel slugs in the pickup made any difference with respect to eddy current interaction. 

This is how the pickup compares with and without the steel slugs. As can be seen, the steel slugs cause a higher inductance / lower peak frequency, and also cause eddy current losses by themselves:



This is the same four scenario test with the steel slugs in the pickup:



I was thinking that the steel slugs might enhance the losses when the metal block was closer to the pickup, but that doesn't seem to be the case. The four plots lines with the steel slugs in place matches the trends that are seen with the air core, including the drop in inductance when the block is beside the pickup.  

[ms]

Good test! (And I see that you still can get those blocks before Christmas.  A perfect gift for your loved one!)

So I think that you have shown that there are two effects of eddy currents that can be considered separately.

1. The first has to do with the total flux passing through the coil from external sources.  This includes the exciter coil and  high conductivity metal pieces that the coil excites in addition to the pickup.

2. The second is when current flows in the coil as a result of the induced flux.  Eddy currents then modify the parameters of the circuit, both the Q and the resonant frequency.

I think that the second is the dominant effect in most pickups.  The use of a brass cover or base plate could introduce some of the first.

[antigua]

Dec 3, 2018 7:07:55 GMT -5 ms said:

Good test! (And I see that you still can get those blocks before Christmas.  A perfect gift for your loved one!)

So I think that you have shown that there are two effects of eddy currents that can be considered separately.

1. The first has to do with the total flux passing through the coil from external sources.  This includes the exciter coil and  high conductivity metal pieces that the coil excites in addition to the pickup.

2. The second is when current flows in the coil as a result of the induced flux.  Eddy currents then modify the parameters of the circuit, both the Q and the resonant frequency.

I think that the second is the dominant effect in most pickups.  The use of a brass cover or base plate could introduce some of the first.

I agree, because going back to the transformer analogy, the shorted secondary is either coupling more strongly with the exciter, or it's coupling more strongly with the pickup, depending on which it's closer to, and in a typical pickup cover scenario, the coupling between cover and exciter is much smaller than the coupling between the pickup and the cover. 

This plot in particular shows what appears to be a lower Q factor when the block is coupling closely with the pickup, compared to when block is coupled with the exciter. So if eddy currents are manifesting as a parallel resistance across the coil it's coupling with, it would make sense that the Q factor is lower when it's acting as a parallel resistance in relation to the pickup. Also, when the block is beside the pickup, the inductance of the pickup drops slightly, which if I'm not mistaken, also fits with the analogy of a transformer that is seeing a higher coupling coefficient. 

I'm wondering if one of the newer models that are supposed to account for the relationship between the exciter and pickup can be made to duplicate these curves. 

[ms]

But remember that representing eddy currents with a transformer analogy requires using a transformer with a low coupling factor, that is, a lot of leakage flux. This means that there is an inductor in series with the resistor.  This adds an additional frequency dependence. (This effect is why it is difficult to design a very broad band output transformer for a tube amplifier.)

[aquin43]

Dec 4, 2018 1:14:21 GMT -5 antigua said:

Dec 3, 2018 7:07:55 GMT -5 ms said:

Good test! (And I see that you still can get those blocks before Christmas.  A perfect gift for your loved one!)

So I think that you have shown that there are two effects of eddy currents that can be considered separately.

1. The first has to do with the total flux passing through the coil from external sources.  This includes the exciter coil and  high conductivity metal pieces that the coil excites in addition to the pickup.

2. The second is when current flows in the coil as a result of the induced flux.  Eddy currents then modify the parameters of the circuit, both the Q and the resonant frequency.

I think that the second is the dominant effect in most pickups.  The use of a brass cover or base plate could introduce some of the first.

I agree, because going back to the transformer analogy, the shorted secondary is either coupling more strongly with the exciter, or it's coupling more strongly with the pickup, depending on which it's closer to, and in a typical pickup cover scenario, the coupling between cover and exciter is much smaller than the coupling between the pickup and the cover. 

This plot in particular shows what appears to be a lower Q factor when the block is coupling closely with the pickup, compared to when block is coupled with the exciter. So if eddy currents are manifesting as a parallel resistance across the coil it's coupling with, it would make sense that the Q factor is lower when it's acting as a parallel resistance in relation to the pickup. Also, when the block is beside the pickup, the inductance of the pickup drops slightly, which if I'm not mistaken, also fits with the analogy of a transformer that is seeing a higher coupling coefficient. 

I'm wondering if one of the newer models that are supposed to account for the relationship between the exciter and pickup can be made to duplicate these curves. 

The blocks will not effectively couple with a properly designed exciter. The exciter coil is in a circuit where the resistance is high compared to its reactance and consequently the driving voltage is high compared with any voltage that the reactive field from any passive coil or metal block can induce in it. The Ampere-Turns from the exciter, therefore, do not depend in any significant  way on the adjacent materials. It is like a "current source" of magnetic flux.

The blocks can alter the distribution of the magnetic field and absorb energy from it, but they will not alter the primary magneto motive flux from the exciter.

 

The position with the pickup coil is different. The small voltages induced by the field from the exciter are all it has and are profoundly influenced by the disturbances caused to the field by the metal blocks and, when the blocks are close, there is a strong coupling between the field due to the circulating current in the blocks and the voltage induced in the coil. Similarly, currents circulating in the coil via its distributed capacitance induce further currents in the blocks.

 

I think that you are seeing the two eddy current effects, shielding and coupling loss. The shielding effect is very wide band in this case I suppose because the blocks are so thick. They are also quite narrow so there is a ready path around them for the flux from the exciter.

Arthur

[antigua]

Dec 4, 2018 11:15:23 GMT -5 aquin43 said:

The blocks will not effectively couple with a properly designed exciter. The exciter coil is in a circuit where the resistance is high compared to its reactance and consequently the driving voltage is high compared with any voltage that the reactive field from any passive coil or metal block can induce in it. The Ampere-Turns from the exciter, therefore, do not depend in any significant  way on the adjacent materials. It is like a "current source" of magnetic flux.

The blocks can alter the distribution of the magnetic field and absorb energy from it, but they will not alter the primary magneto motive flux from the exciter.

When you say "effectively couple", do you mean the high resistance / low reactance of the exciter will literally result in a lower coupling coefficient, or is that coefficient the same, but it's effect upon the exciter coil's operation just very minimal?

Dec 4, 2018 11:15:23 GMT -5 aquin43 said:

I think that you are seeing the two eddy current effects, shielding and coupling loss. The shielding effect is very wide band in this case I suppose because the blocks are so thick. They are also quite narrow so there is a ready path around them for the flux from the exciter.

Arthur

That's a good point regarding penetration depth and frequency, if the metal is thin, there might be less attenuation in the lower frequnecies. I'll give that test a try, even though there's no much mystery to be solved there, it would be fun to see the theory at work. 

[aquin43]

Yes, while K between exciter and metal or coil might not be small, the voltage it induces in the exciter will always be negligible.

and the power dissipated by that voltage in the exciter drive circuit will also be negligible. This is one reason why the ideal exciter should have few turns and a self-resonant frequency well outside the audio band. Also, the drive resistor should be as high as possible compared with the exciter coil reactance at the highest frequency of interest. Otherwise there will be problems with the assumption that the drive voltage is a measure of the current in the coil and the coupling of the exciter to the pickup may become a source of error. Phase errors become significant long before the cut off frequency.

It would be interesting to see the effects of wide but thin metal sheets interposed between the exciter and the coil - maybe three to four times as wide as the coil and centred on it so that pretty much all of the flux would have to pass through the metal.

Arthur

[ms]

Dec 4, 2018 13:03:35 GMT -5 aquin43 said:

Yes, while K between exciter and metal or coil might not be small, the voltage it induces in the exciter will always be negligible.

That is not quite right.  If the current supplied to the exciter coil induces current in a piece of metal, the voltage across the exciter coil must change. Since the current in the exciter coil cannot change because the driving impedance is very high, the change in voltage across the exciter coil follows from the law of magnetic induction where the current in the piece of metal is the source of the flux.

[aquin43]

Dec 4, 2018 15:12:10 GMT -5 ms said:

Dec 4, 2018 13:03:35 GMT -5 aquin43 said:

Yes, while K between exciter and metal or coil might not be small, the voltage it induces in the exciter will always be negligible.

That is not quite right.  If the current supplied to the exciter coil induces current in a piece of metal, the voltage across the exciter coil must change. Since the current in the exciter coil cannot change because the driving impedance is very high, the change in voltage across the exciter coil follows from the law of magnetic induction where the current in the piece of metal is the source of the flux.

I have already agreed that a voltage is induced in the exciter by coupling from the eddy currents. The reason that this voltage is negligible is because the initial voltage across the exciter inductance is negligible by design and the induced voltage from a passive coupling will always be less than that - by a factor involving K^2 and the resistivity of the coupled metal.

Arthur

[ms]

Dec 4, 2018 16:38:14 GMT -5 aquin43 said:

Dec 4, 2018 15:12:10 GMT -5 ms said:

That is not quite right.  If the current supplied to the exciter coil induces current in a piece of metal, the voltage across the exciter coil must change. Since the current in the exciter coil cannot change because the driving impedance is very high, the change in voltage across the exciter coil follows from the law of magnetic induction where the current in the piece of metal is the source of the flux.

I have already agreed that a voltage is induced in the exciter by coupling from the eddy currents. The reason that this voltage is negligible is because the initial voltage across the exciter inductance is negligible by design and the induced voltage from a passive coupling will always be less than that - by a factor involving K^2 and the resistivity of the coupled metal.

Arthur

I see what you mean by negligible.  But I am not sure you and Antigua agree on what you mean by coupling.  He might just mean that the exciter coil causes current in the block, not that the current in the block has an effect on the current in the coil.

[stratotarts]

First, thanks Antigua for the revised test. It's a great reference post.

I would like to point out that any changes in current and voltage in the exciter coil due to the influence of the magnetic circuit are extremely easy to measure. So no great mystery about it should ever arise, in practice. I think the main difficulty would be to detect those with good accuracy because they are so small. I think it has already been pointed out that the current would be minimally affected because the exciter is effectively current driven. An almost constant current produces the effect of a very high impedance - even when translated through a loosely coupled transformer comprised of the exciter and device under test. Keeping the exciter drive current constant also keeps the test magnetic field constant. The small voltage that develops across the exciter coil at higher frequencies would only matter if it resulted in lower current due to a lower voltage across the exciter coil limiting resistor. Again, it's easy to measure and I predict that it will be too small to be important.

[aquin43]

Revisiting 'negligible' in this context. Phase is always the problem.

If the voltage across the exciter coil is 15% of the applied voltage, then the coil current will be down by about 0.1 dB, but the phase error will be over 8 degrees. At 50%, the loss is still only 1 dB but the phase error is 27 degrees.

That is why I use a coil with only 20 turns in series with 100 Ohms. Even then it needs phase compensation at 20kHz.

Arthur

[ms]

Dec 5, 2018 18:44:01 GMT -5 aquin43 said:

Revisiting 'negligible' in this context. Phase is always the problem.

If the voltage across the exciter coil is 15% of the applied voltage, then the coil current will be down by about 0.1 dB, but the phase error will be over 8 degrees. At 50%, the loss is still only 1 dB but the phase error is 27 degrees.

That is why I use a coil with only 20 turns in series with 100 Ohms. Even then it needs phase compensation at 20kHz.

Arthur

I use three turns, a diameter about the same as a pole piece, and drive it with an ampere, using a power amp,  through an 8 ohm resistor.  For a while I had a power amp set up with a 20 ohm output impedance using feedback, but I do not have that any more.

[antigua]

Here is a test using a flattened out brass Tele neck pickup cover.

I magnified it since the peaks were  hard to see otherwise. The result is similar, with a lesser degree of variance between the amplitude of the peaks. The most noticeable difference is that where as the large aluminium block caused "block by the exciter" and "block by the pickup" to be about the same height, in this case the "plate by the pickup" is definitely lower than "plate by the exciter". Also as before, when the eddy current cause is very close to the pickup, the inductance appears to drop slightly. 

It's hard to tell due to the noise level, but I believe the shallower depth of the eddy currents causes the attenuation to occur more gradually as the frequency rises. 

The damping is very mild compared to when a brass Tele neck pickup over is placed entirely over pickup, which is probably due to the fact that it's not encompassing as much of the coil's flux path, but also might be partly due to the 5cm distance between the pickup and the exciter. 

[ms]

It looks like the blue (beside the exciter) shows the most attenuation at high frequencies because it is almost all "shielding" effect. That is,  the exciter coil induces current in the brass, and the sum of the flux from this current and the flux from the current through the exciter coil tend to cancel a bit, reducing the total flux through the pickup coil.  The effect increases gradually with frequency.

It looks like the green (beside the pickup) is mostly from altering the circuit parameters since it shows a large effect at the peak where the impedance is highest and so most easily affected.  There has to be some shielding effect as well, but I think what you hear is mostly from modifying the peak.

The cable capacitance towers the resonance, increasing the relative importance of altering the circuit parameters compared to the shielding effect.

[antigua]

Here is a test using a sheet of brass, roughly 4x10 inches. The overall result is the same, but even more minor, probably due to the brass sheet being about half as thick as the brass Tele neck over. As with the flattened cover, the biggest effect happens when the brass is beside the pickup. Only with the thick aluminum block was the effect as dramatic when beside either the exciter, or the pickup. 

[antigua]

Using the "Tuscon Model" made up by Tele Tucson on TDPRI, featuring three coupled coils, where one is the pickup, another is an eddy current causing agent, and the third the exciter (or maybe even a moving, magnetized guitar string), I was able to reproduce this trend by adjusting the coupling coefficients to correspond with the eddy current coil (conductive block) coupling more strongly with either the exciter, or the pickup, but leaving the coupling coefficient the same between the pickup and the exciter, since in the experiment the pickup and the exciter were  held at a fixed 50mm distance apart.

Here is the experimental data:




and here is the LtSpice model. I have matched the colors to be the same in both plots (white replacing black). The tallest peak, white, corresponds to there being no eddy currents, which is modeled by making the coupling coefficient a very tiny number. Next comes red, the eddy current is loosely but equally coupled with both the exciter and the pickup in order to represent the conductive block being in between the pickup and exciter. The comes the blue line, corresponding to the eddy current causing block being strongly coupled with the exciter, but weakly with the pickup. Finally, the green line corresponds to the the eddy current causing conductive block being beside the pickup, and shows the same drop of inductance, or increased resonant peak, in modeling as is observed in the practical experiment.

I didn't go for perfect curve matching of course, so the values are all somewhat arbitrary. My goal was just to see if the same trend would emerge when the coupling coefficients were set up to vary in the same manner they had in the practical demo, and it appears it did.




Knowing that this model appears to reflect reality, it should be possible to derive some equivalent values for the eddy current resistance and coupling coefficient by curve matching pickups with and without metal covers. 

[ms]

Why is coupling to the exciter coil an issue?  It is so easy to drive the coil with a high enough impedance so that there is no significant coupling.  The danger is that if you do not do that then you have an extra degree of freedom that can be used to get a better match between data and model than there actually is.

[antigua]

Dec 14, 2018 6:46:25 GMT -5 ms said:

Why is coupling to the exciter coil an issue?  It is so easy to drive the coil with a high enough impedance so that there is no significant coupling.  The danger is that if you do not do that then you have an extra degree of freedom that can be used to get a better match between data and model than there actually is.

I'm not sure what you mean, but having the conductive block beside the exciter coil had a noticeable impact on the response curve, so I thought it was important to see that bear out in the model in order to further establish its congruence with reality. 

[ms]

Dec 14, 2018 11:53:19 GMT -5 antigua said:

Dec 14, 2018 6:46:25 GMT -5 ms said:

Why is coupling to the exciter coil an issue?  It is so easy to drive the coil with a high enough impedance so that there is no significant coupling.  The danger is that if you do not do that then you have an extra degree of freedom that can be used to get a better match between data and model than there actually is.

I'm not sure what you mean, but having the conductive block beside the exciter coil had a noticeable impact on the response curve, so I thought it was important to see that bear out in the model in order to further establish its congruence with reality. 

Sorry, I think I am confusing two meanings of "coupling".

1. Current from circuit ABC causes a voltage to be induced in circuit XYZ.

2. Circuits ABC and XYZ mutually affect each other's operation.

I am not a Spice user but I believe that you are driving the exciter coil with a fixed 1 ampere current.  Therefore #1 applies and there is no mutual effect since the current through the exciter (and therefore the B it produces) cannot be affected by the circuit it is supplying flux to.

[antigua]

Dec 14, 2018 12:10:44 GMT -5 ms said:

Dec 14, 2018 11:53:19 GMT -5 antigua said:

I'm not sure what you mean, but having the conductive block beside the exciter coil had a noticeable impact on the response curve, so I thought it was important to see that bear out in the model in order to further establish its congruence with reality. 

Sorry, I think I am confusing two meanings of "coupling".

1. Current from circuit ABC causes a voltage to be induced in circuit XYZ.

2. Circuits ABC and XYZ mutually affect each other's operation.

I am not a Spice user but I believe that you are driving the exciter coil with a fixed 1 ampere current.  Therefore #1 applies and there is no mutual effect since the current through the exciter (and therefore the B it produces) cannot be affected by the circuit it is supplying flux to.

By coupling I always mean "mutual coupling coefficient" in the spice transformer directives("Ksomething CoilA CoilB couplingCoefficient"), which are the variables "CE" "SE" and the static 0.1 in the LtSpice model, or the real world analog where if one of the three "coils" is closer together, a greater portion of flux lines intersect, and so the coupling coefficient inches closer to 1. 

I think in practice I shouldn't be placing the exciter directly up against the pickup's cover, I should make sure there is a few millimeters distance so that the exciter isn't coupling with the cover, but I think overall you're right, it probably makes little or no difference. It took a substantial chunk of aluminum and an unloaded pickup to even produce an observable effect. With the flattened out Tele cover there was less than 1dB attenuation when the exciter was beside the cover. 

The significant thing about the Tuscon model is that it appears to be able to produce deep curves as seen in Filter'trons and the TriSonic, and I can input real values for the pickup, and the (irrelevant) exciter coil, but I'm not sure what realistic values should be used for the mutual coupling coefficient and the resistance in the eddy current circuit. The model created by Tele Tuscon had inputted values, but I'm not sure how realistic they are. 

[straylight]

Thanks so much for this, I was trying to work out how to model this. Next up for me will have to be taking a parametric spice run and plotting against real data.