Pole Sensitivity to Moving Dipole Source on the String Path

[aquin43]

I constructed a probe with two single turn loops which had been wound round a 1mm drill.

The two loops are placed one above the other over the pickup. They are driven from the headphone channels of a Focusrite Scarlett 2i2 audio interface. The driving waveform is a sine wave alternately on each channel. The signal from the pickup is recovered via a Radford Noise meter used as a preamplifier driving channel 2 of the Scarlett 2i2. Signals are generated and measured using an Octave program on a Linux computer.

The idea is that the two loops represent the movement range of a dipole source within a vibrating string. The induced voltages represent that part of the flux coupled into the pickup that is capable of producing an output. The difference between the voltages induced by the two coils represents an approximation to the amount that this flux would change as the string moves vertically. The way that this difference changes as the probe is moved away from the pole at a fixed height along the string axis should relate directly to the sensitivity of the pickup to a vertically moving dipole at the probe position.

So far I have tried using this probe on a 4mm spacer above the pickup, which places the mid point of the coils at about 6mm above the pole. The pickup is a Tokai Strat Pickup, essentially the same as a Fender. Ideally one would move the probe with a micrometer drive and take a series of measurements. Failing that, I simply moved the probe by hand relative to the treble end pole to explore the general trend.

Readings on an arbitrary scale:

At edge of pole                         86
Half way from pole edge to cover edge  199
At cover edge                          202
6mm beyond cover edge                  139

This is width of sensitivity is not what I expected. In order to give the pole window, this pattern has to be multiplied by the string magnetisation pattern, which peaks just outside the pole.

There is the possibility that the eddy currents in the pole are expelling the flux that would go down there at lower frequencies. Strat pickups have low eddy current losses, however, and a similar pattern emerges when the test frequency is dropped to 425Hz (avoiding 50 Hz mains frequency). Measurements at a low frequency really need more drive power than the headphone output and, ideally, some analogue filtering of the signal.

Signal generation and measurement.

The tone burst sent to the loop is 3 times 2^N samples long at 48kHz, where N=14 in this case. The pickup output is amplified and sent to channel two of the 2i2.

The generated signal is created from an inverse FFT of the nearest frequency to the selected one (1.5kHz in this case) to fit exactly into the 2^N samples and exactly 2^N samples are retrieved from the reading. This ensures that the signal only appears in one bin of the subsequent FFT which is used to filter out interference.

Arthur

[ms]

If total flux through the pickup coil does not change so much as the driver coil is moved further away because the region with component through the axis of the pickup coil moves downward (and the coil has plenty of depth), then a similar argument applies to the gradient as well, but maybe not as much.

[ms]

Hers's my setup; doing a humbucker coil to see if it is different.


Once I realized the window is broad, I abandoned the two coil approach and just lifted up the retired drill press vice with a sheet of plastic to get the gradient.
I am working at 10900 HZ, and get about 60 db S/N using an fft with 1 Hz spacing and a Blackman window which broadens that to a few HZ, but gets the "trumpet" down better than 60 db very fast.






Here are relative voltage level differences:

Edge of core:                            .965
halfway from there to edge of coil: 1.
coil edge                                   .665
6 mm from edge of coil              .144

This is narrower than the strat you measured. Maybe this is from higher core permeability and shallower coil.

[aquin43]

May 21, 2020 9:31:50 GMT -5 ms said:

If total flux through the pickup coil does not change so much as the driver coil is moved further away because the region with component through the axis of the pickup coil moves downward (and the coil has plenty of depth), then a similar argument applies to the gradient as well, but maybe not as much.

Yes, the change in Z gradient is more or less reflecting the Y gradient, so the result should not be all that unexpected.

 

If the experiment is valid, that leaves the Strat window as having a peak just outside each edge of the pole with a rapid decay on each side caused mainly by the string magnetisation pattern.

Arthur

[antigua]

May 21, 2020 11:59:25 GMT -5 aquin43 said:

If the experiment is valid, that leaves the Strat window as having a peak just outside each edge of the pole with a rapid decay on each side caused mainly by the string magnetisation pattern.

I think the "rapid decay" is the game. Most of the window is defined by decay, with only the tiny area of space close to, and directly above the pole piece being homogeneous magnetic field (and it appeared to be especially wide only with the Quarter Pound). If the results are expressed as a rate of dB drop per distance, like  "-1.97dB / 1mm offset, up to 10mm offset at 5mm string/pole separation",  or "-0.88dB per 1mm offset, up to 10mm offset at 10mm string/pole separation", then the gradients of one testing method can be numerically compared to the gradients of another. 

[antigua]

If you put two loops/coils at right angles of each other (the tiny probe and the pickup), that's not unlike putting turns of wire on a toroid in order to guide flux in a loop, so I think it's to be expected that the mutual flux is greater when the loos are more perfectly at right angles, and less mutual when one loop is directly above, and perpendicular to the other loop. That would be true with or without a steel core, but the steel core probably serves to concentrate the flux change more centrally and maybe narrow the focus, in effect.

It seems to me that this sort of inference about the sensing width, which takes away the guitar string, forces you to conjecture about what would have happened had there been a guitar string, and it seems to me like that's the bigger mystery than the mutual flux path of wire loops at right angles. 

[ms]

May 24, 2020 4:42:50 GMT -5 antigua said:

If you put two loops/coils at right angles of each other (the tiny probe and the pickup), that's not unlike putting turns of wire on a toroid in order to guide flux in a loop, so I think it's to be expected that the mutual flux is greater when the loos are more perfectly at right angles, and less mutual when one loop is directly above, and perpendicular to the other loop. That would be true with or without a steel core, but the steel core probably serves to concentrate the flux change more centrally and maybe narrow the focus, in effect.

It seems to me that this sort of inference about the sensing width, which takes away the guitar string, forces you to conjecture about what would have happened had there been a guitar string, and it seems to me like that's the bigger mystery than the mutual flux path of wire loops at right angles. 

It is the other way around.  An analysis of the magnetization of the string suggests the topic of this discussion as a means of experimentally determining the effect of a small section of string as a function of where along the string it is located. 

In general, a loop of wire couples more tightly to a loop with the two axes pointing in the same direction, not perpendicular.  

The use of a toroid, especially with air core (unusual), usually is to confine self-generated fields and reject those externally generated.

[antigua]

May 24, 2020 6:57:51 GMT -5 ms said:

May 24, 2020 4:42:50 GMT -5 antigua said:

If you put two loops/coils at right angles of each other (the tiny probe and the pickup), that's not unlike putting turns of wire on a toroid in order to guide flux in a loop, so I think it's to be expected that the mutual flux is greater when the loos are more perfectly at right angles, and less mutual when one loop is directly above, and perpendicular to the other loop. That would be true with or without a steel core, but the steel core probably serves to concentrate the flux change more centrally and maybe narrow the focus, in effect.

It seems to me that this sort of inference about the sensing width, which takes away the guitar string, forces you to conjecture about what would have happened had there been a guitar string, and it seems to me like that's the bigger mystery than the mutual flux path of wire loops at right angles. 

It is the other way around.  An analysis of the magnetization of the string suggests the topic of this discussion as a means of experimentally determining the effect of a small section of string as a function of where along the string it is located. 

In general, a loop of wire couples more tightly to a loop with the two axes pointing in the same direction, not perpendicular.  

The use of a toroid, especially with air core (unusual), usually is to confine self-generated fields and reject those externally generated.

The flux lines are themselves loops around the physical loop itself, so if you have one loop perfectly perpendicular and above the other, on axis, the amount of flux mutual flux alignment is minimal, but if the two loops are on each other's edges like the letter "L", then the flux paths of each loop are complementary to one another. I think this sort of experiment would just serve to confirm which spatial orientation is beneficial two two loops and which aren't, but then at some point you have to factor back in the flux density of the guitar string in situ, because of course this experiment is supposing that the guitar string itself is a uniform magnet. In addition to uniformity of magnetic strength, it's also like modeling a transformer that would normally have cores in both coils, and instead having a one of them be an air core, that would change the coupling coefficient by some amount. Can the adjustment values that need to be accounted for empirically determined? What if instead of having air core test loops, you put some segment of guitar string through them?

[aquin43]

May 24, 2020 12:14:25 GMT -5 antigua said:

The flux lines are themselves loops around the physical loop itself, so if you have one loop perfectly perpendicular and above the other, on axis, the amount of flux mutual flux alignment is minimal, but if the two loops are on each other's edges like the letter "L", then the flux paths of each loop are complementary to one another. I think this sort of experiment would just serve to confirm which spatial orientation is beneficial two two loops and which aren't, but then at some point you have to factor back in the flux density of the guitar string in situ, because of course this experiment is supposing that the guitar string itself is a uniform magnet. In addition to uniformity of magnetic strength, it's also like modeling a transformer that would normally have cores in both coils, and instead having a one of them be an air core, that would change the coupling coefficient by some amount. Can the adjustment values that need to be accounted for empirically determined? What if instead of having air core test loops, you put some segment of guitar string through them?

I think that you are straying somewhat from the purpose of this experiment.

Here is a list of the assumptions made to justify the experiment in the first place and which were not made explicit.

1) The string is the source of magnetic flux for signal generation. *

2) The string is magnetised along its length with a pattern of flux density that can be determined.

3) Although the strength and detailed pattern of the flux within the string will alter as the string moves we can choose to neglect this and use a fixed pattern as an approximation if the string movement is small.

4) The string, so modelled, is weakly coupled to the pickup poles and coils so that the pickup output has no effect on the string magnetisation.

5) The axial flux pattern in the string can be modelled as an array of dipoles with their axes aligned with the string long axis.

6) A small circular coil carrying a current, in free space, produces a magnetic field that is similar to that of a dipole. This is a good approximation at distances of a few coil radii.

7) A small circular coil placed near to the pickup will be so weakly coupled to the pickup that it will behave as if it were in free space.

8) The coil, viewed as a dipole, can be used to represent a slice across the string and the response of the pickup to the coil will be the same as its response to that slice of the string.

9) In order to determine the amount of flux coupled into the pickup from the coil/dipole we can drive the coil with ac to produce a clear signal free from interference. This assumes that the modulated flux follows the same path as static flux.

10) The normal signal from the pickup depends not on the value of flux coupled from the string, but on how that value changes with movement of the string.

11) We can determine that rate of change either by moving our coil/dipole and measuring the difference in output or by using two coils in corresponding positions.

12) By combining the pattern of flux within the string and the pattern of sensitivity to the change in string position we can calculate the sensitivity to each slice of the string, or the pole window.

Arthur

* This is not literally true but it turns out that the perturbations in the much larger field of the pickup magnet that the string produces can be usefully modelled by adopting this point of view.

[antigua]

Thanks for typing that up in itemized format. It just seems to me that figuring out how to correct for the amount of standing magnetic flux at various points along the string would be very tricky, since the steel string is not like a non-permeable ceramic magnet, but instead is a self-supporting permeable network where every neighboring segment makes the flux of the next segment a little stronger than it would have been by itself. The issue I have is that the end result will be "a sensing window", but not "the sensing window", similar to your critique of aligning the pickup sideways with respect to the string. To get a measure of flux at a given point in space, the WT10A magnetometer prob could be carefully placed and used to record Gauss values. 

[ms]

May 25, 2020 13:23:16 GMT -5 antigua said:

Thanks for typing that up in itemized format. It just seems to me that figuring out how to correct for the amount of standing magnetic flux at various points along the string would be very tricky, since the steel string is not like a non-permeable ceramic magnet, but instead is a self-supporting permeable network where every neighboring segment makes the flux of the next segment a little stronger than it would have been by itself. The issue I have is that the end result will be "a sensing window", but not "the sensing window", similar to your critique of aligning the pickup sideways with respect to the string. To get a measure of flux at a given point in space, the WT10A magnetometer prob could be carefully placed and used to record Gauss values. 

That is why it is necessary to measure the flux inside the string.  Zollner's method  uses a moving coil surrounding the string.  This is a clever technique, but as he states, the resolution might be a bit limited. That is, the measurement might be "smeared" along the length of the string a bit.

[aquin43]

May 25, 2020 13:23:16 GMT -5 antigua said:

Thanks for typing that up in itemized format. It just seems to me that figuring out how to correct for the amount of standing magnetic flux at various points along the string would be very tricky, since the steel string is not like a non-permeable ceramic magnet, but instead is a self-supporting permeable network where every neighboring segment makes the flux of the next segment a little stronger than it would have been by itself. The issue I have is that the end result will be "a sensing window", but not "the sensing window", similar to your critique of aligning the pickup sideways with respect to the string. To get a measure of flux at a given point in space, the WT10A magnetometer prob could be carefully placed and used to record Gauss values. 

The effects of the permeability of the string and the interactions between adjacent segments are all taken care of by Nature when the magnetisation pattern within the string is formed in the first place. The conceptual array of dipoles has none of these interactions..

Arthur

[ms]

May 25, 2020 13:23:16 GMT -5 antigua said:

Thanks for typing that up in itemized format. It just seems to me that figuring out how to correct for the amount of standing magnetic flux at various points along the string would be very tricky, since the steel string is not like a non-permeable ceramic magnet, but instead is a self-supporting permeable network where every neighboring segment makes the flux of the next segment a little stronger than it would have been by itself. The issue I have is that the end result will be "a sensing window", but not "the sensing window", similar to your critique of aligning the pickup sideways with respect to the string. To get a measure of flux at a given point in space, the WT10A magnetometer prob could be carefully placed and used to record Gauss values. 

So you can see the importance of the "aha! moment" when aquin43 took the magnet out of the strat pickup and pointed it at the string from the side. Operation was not affected and since the magnetization of the string is many small dipoles and the field along the axis of a dipole points along its axis, then only this component matters. And we have it from Zollner's measurement with reasonable resolution.

Now, let's suppose you are having trouble believing that only the magnetization along the string is important right over the pole piece or magnet, where there is a B component pointing perpendicular to the string from the magnet or pole piece. It is certain that if you look at a place along the string many times the diameter of the high permeability string from the magnet, then it must be true since the direction of the field is almost completely determined by the mutual interactions of the dipoles. This is why we get at least a partially independent confirmation of acquin43's observation by putting a magnet close to the string (about 6 mm away from the pole piece, adjusted as necessary) and demonstrating that you can cancel out the pickup output using just this magnetization along the string (when it has the correct polarity). (This is the recent discussion on MEF: pickups:theory from just after the theory subform was created so that the one or two theoretical discussions per year that occurred there in the main forum would no longer bother the "real users".

[antigua]

So can the permeability of the string be safely neglected? Is the fact of the pseudo dipole being an air core a trivial distinction? Does the Kirk T McDonald paper assert that it can be neglected when it says "So long as the relative permeability is large compared to unity, the factor (μrel −1)/(μrel + 1) is essentially one, and the behavior of the electric guitar does not depend on the precise value of the permeability of the string" ?  A couple days ago I tuned a B string down to a low E, so it was very "floppy", and I was expecting it to be quieter than the low E because the B string is a lot less massive, but it seemed to me that the difference in mass didn't matter so much, what mattered was that the string had a much larger excursion, due to being very "floppy", and that the loudness was about equal, if not favoring the thin B string, because it was able to displace so much more being as slack as it was.

[ms]

May 26, 2020 10:55:24 GMT -5 antigua said:

So can the permeability of the string be safely neglected? Is the fact of the pseudo dipole being an air core a trivial distinction? Does the Kirk T McDonald paper assert that it can be neglected when it says "So long as the relative permeability is large compared to unity, the factor (μrel −1)/(μrel + 1) is essentially one, and the behavior of the electric guitar does not depend on the precise value of the permeability of the string" ?  A couple days ago I tuned a B string down to a low E, so it was very "floppy", and I was expecting it to be quieter than the low E because the B string is a lot less massive, but it seemed to me that the difference in mass didn't matter so much, what mattered was that the string had a much larger excursion, due to being very "floppy", and that the loudness was about equal, if not favoring the thin B string, because it was able to displace so much more being as slack as it was.

Zollner's measurements do not ignore the permeability of the string; they measure the flux with the effect of the permeability present.

KTM assumed a spherical cow so that he could show how a pickup works with a simple analytic solution.  His results tell you much of what you need to know, but nothing realistic about the pattern of magnetization of the string.  

[antigua]

May 26, 2020 11:38:50 GMT -5 ms said:

May 26, 2020 10:55:24 GMT -5 antigua said:

So can the permeability of the string be safely neglected? Is the fact of the pseudo dipole being an air core a trivial distinction? Does the Kirk T McDonald paper assert that it can be neglected when it says "So long as the relative permeability is large compared to unity, the factor (μrel −1)/(μrel + 1) is essentially one, and the behavior of the electric guitar does not depend on the precise value of the permeability of the string" ?  A couple days ago I tuned a B string down to a low E, so it was very "floppy", and I was expecting it to be quieter than the low E because the B string is a lot less massive, but it seemed to me that the difference in mass didn't matter so much, what mattered was that the string had a much larger excursion, due to being very "floppy", and that the loudness was about equal, if not favoring the thin B string, because it was able to displace so much more being as slack as it was.

Zollner's measurements do not ignore the permeability of the string; they measure the flux with the effect of the permeability present.

KTM assumed a spherical cow so that he could show how a pickup works with a simple analytic solution.  His results tell you much of what you need to know, but nothing realistic about the pattern of magnetization of the string.  

I'm referring to this experiment in regard to the air core. The two loops represent a dipole in space, but a point in space that is now air instead of steel, does that not matter much?

The McDonald assertion that permeability is not very important in the string so long as it's close to "1", that suggests to me that the guitar string might not be so important, that whether it's there or not in the testing rig doesn't affect the shape of the "window" by much.

[aquin43]

May 26, 2020 12:36:15 GMT -5 antigua said:

May 26, 2020 11:38:50 GMT -5 ms said:

Zollner's measurements do not ignore the permeability of the string; they measure the flux with the effect of the permeability present.

KTM assumed a spherical cow so that he could show how a pickup works with a simple analytic solution.  His results tell you much of what you need to know, but nothing realistic about the pattern of magnetization of the string.  

I'm referring to this experiment in regard to the air core. The two loops represent a dipole in space, but a point in space that is now air instead of steel, does that not matter much?

The McDonald assertion that permeability is not very important in the string so long as it's close to "1", that suggests to me that the guitar string might not be so important, that whether it's there or not in the testing rig doesn't affect the shape of the "window" by much.

The dipoles in the string are in free space too. All of the effects of permeability etc. were used up in establishing the magnetisation pattern in the first place. Nature "did the calculations" and set up the pattern which was measured and which we now represent as an array of dipoles of different moments.

Mc Donald's assertion relates to a different problem, that of establishing the flux within the string in the first place.

Arthur

[ms]

May 26, 2020 12:36:15 GMT -5 antigua said:

May 26, 2020 11:38:50 GMT -5 ms said:

Zollner's measurements do not ignore the permeability of the string; they measure the flux with the effect of the permeability present.

KTM assumed a spherical cow so that he could show how a pickup works with a simple analytic solution.  His results tell you much of what you need to know, but nothing realistic about the pattern of magnetization of the string.  

I'm referring to this experiment in regard to the air core. The two loops represent a dipole in space, but a point in space that is now air instead of steel, does that not matter much?

The McDonald assertion that permeability is not very important in the string so long as it's close to "1", that suggests to me that the guitar string might not be so important, that whether it's there or not in the testing rig doesn't affect the shape of the "window" by much.

What KTM showed is that the value of permeability is not important as long as it is much greater than one, such as steel.

The two loops emit test fields, and we want to compare the signal level as they are moved to different locations along the string.  They cannot include the effect of string permeability. That is contained in the measurement of the flux inside the string.

Edit: Sorry, I missed acquin43's reply.