cutting posts?

[Joe Gwinn]

Let's take this as a starting point. My interpretation of that statement is that the B field inside a slug should not decrease significantly as one looks inside the slug at greater distances from where it connects to the magnet. This plot:http://www.naic.edu/~sulzer/magWithRod1.png is the output from FEMM of a cylindrical magnet with a piece of steel (slug) attached. (The plot shows the right half only.) The field decreases a lot from the magnet to the other end of the slug. I think this means that the flux is not well confined, and this is what I expect from open rather than closed magnetic circuits. How do you interpret this?

As I recall, the original question was about screw versus slug poles in a humbucker magnetic circuit, whereas the FEMM plot given is that of some kind of notional singlecoil with heavy leakage. There will be leakage in a humbucker for sure, but it should be less than for a singlecoil. I think the real issue will be how symmetrical the leakage in a humbucker is, as a function of what the screw and slug poles look like and are made of.

While the flux would prefer steel, it has to get back to the magnet somehow, which forces part of the path to be in the air. Energy minimization requires some of the flux to exist stage left and right from the sides of the rod. One way to visualize it is to imagine the magnetic lines simultaneously trying to find the lowest-reluctance path while repelling one another.

By the way, it's a lot easier for the eye to comprehend the full picture, versus one side only.

[Mike Sulzer]

I think the real issue will be how symmetrical the leakage in a humbucker is, as a function of what the screw and slug poles look like and are made of.

But the point I am making is something else. The field decreases by several times from one end to the other. (A humbucker would be somewhat different, but I do not think that the effect coupling between the two coils is that large.) The flux is not confined, it is escaping. Therefore, can one say that the flux density is higher in the narrower core because the flux is constant? I do not think so.

[Joe Gwinn]

But the point I am making is something else. The field decreases by several times from one end to the other. (A humbucker would be somewhat different, but I do not think that the effect coupling between the two coils is that large.) The flux is not confined, it is escaping. Therefore, can one say that the flux density is higher in the narrower core because the flux is constant? I do not think so.

The magnetic circuit of a singlecoil is quite different from that of a humbucker, making generalizations from one dangerous to apply to the other. I think a FEMM study of a humbuucker magnetic circuit will get us home sooner.

[Mike Sulzer]

The magnetic circuit of a singlecoil is quite different from that of a humbucker, making generalizations from one dangerous to apply to the other. I think a FEMM study of a humbuucker magnetic circuit will get us home sooner.

FEMM is either cylindrical or 2D. The first is useless for six cores, or even two. A 2D model of an HB would way over estimate the interactions between the two modeled coils. (Think of the cylindrical pair of cores moving in and out of the page to form two long parallel strips.) I do not think the interactions are as high as you do, but we need a way to measure them.

[Joe Gwinn]

FEMM is either cylindrical or 2D. The first is useless for six cores, or even two. A 2D model of an HB would way over estimate the interactions between the two modeled coils. (Think of the cylindrical pair of cores moving in and out of the page to form two long parallel strips.) I do not think the interactions are as high as you do, but we need a way to measure them.

We can model the center of a two-blade humbucker in 2D, making the blade thicknesses different. This ought to be instructive, and may even be a good approximation to reality.

[Mike Sulzer]

Good idea. I have a water leak in my plumbing to track down tomorrow, and also the grocery shopping, but plan to watch the superbowl. If it gets dull, this will be more interesting.

We can model the center of a two-blade humbucker in 2D, making the blade thicknesses different. This ought to be instructive, and may even be a good approximation to reality.

[Mike Sulzer]

This post presents results of FEMM models of of a blade humbucker. As Joe suggested, the middle of a blade humbucker can be modeled accurately using FEMM's 2D (planar) mode. One has the freedom to arrange the material in the xy plane as one wishes, and the structure extends into and out of the page. Modeling a blade humbucker in this way is an example of a solution in search of a problem. In other words: the FEMM program has certain capabilities; what useful thing can we do with them?

The question under investigation is this: if the blades of the two coils have different widths, which one has the stronger field close to the blade where the string would be? There are two competing effects. First, if all the flux is confined to the steel near the magnet, the narrower blade would be expected to have the higher field because the flux density is higher. On the other hand, the flux can diverge from the steel with increasing distance from the magnet. If this happens more with the thinner blade, this could counteract the first effect. The answer could be different for different relative widths.

We would like to apply these results to humbuckers with circular pole pieces if possible. This is possible in a limited way only. The divergence would be expected to be greater with an additional dimension for the flux to move into. But how much greater?

A FEMM output plot is shown here: http://www.naic.edu/~sulzer/bladeHum.png . The blades are .5 inches high, .1 and .05 inches thick. Both effects are visible. The highest flux density is achieved in the narrower blade. (Close to the magnet, it is even higher than shown; the color scale is clipped off there so that the weaker intensities can be shown.) One also sees the flux diverge as distance from the magnet increases. This plot (http://www.naic.edu/~sulzer/bladeHumtcon.png) shows the vertical B field along a line 3/32 inches above the blades. The magnitude of the field is greater over the narrower blade, but it is not much greater, certainly not the factor one would expect if the field were not weakened by the divergence of the field lines.

This suggests looking at a case with an even narrower blade.

[Joe Gwinn]

The FEMM analysis in very nice. Thanks.

The question under investigation is this: if the blades of the two coils have different widths, which one has the stronger field close to the blade where the string would be?

The original question was not which has the stronger field at the poletip, it was which coil has the greater voltage induced by string motion. The strength of the field at the poletip was taken as a proxy for this voltage, which elicited the rejoinder that by Faraday's Law of Induction it is changes in total flux through the coil that matter, not the peak field, and that while the peak field would be higher for a narrower pole, the total flux would be about the same, so the induced voltage would also be the same.

http://en.wikipedia.org/wiki/Electromagnetic_induction

There are two competing effects. First, if all the flux is confined to the steel near the magnet, the narrower blade would be expected to have the higher field because the flux density is higher. On the other hand, the flux can diverge from the steel with increasing distance from the magnet. If this happens more with the thinner blade, this could counteract the first effect. The answer could be different for different relative widths.

The fact that the leakage flux lines between the blades are ~horizontal (parallel to the bar magnet) implies that despite the differences in blade thickness, the same total flux is carried by each blade. Said another way, by the conservation of flux, if the totals were not the same (as a function of distance from the magnet), the leakage flux lines would need to be tilted.

We would like to apply these results to humbuckers with circular pole pieces if possible. This is possible in a limited way only. The divergence would be expected to be greater with an additional dimension for the flux to move into. But how much greater?

I would expect that a slug or screw in the center of a humbucker would behave much as blades in the center of a blade humbucker, so the 2D approximation should apply to both cases. It won't be exact for sure, but it should nonetheless be very instructive.

A FEMM output plot is shown here: http://www.naic.edu/~sulzer/bladeHum.png. The blades are 0.5 inches high, 0.1 and 0.05 inches thick. Both effects are visible. The highest flux density is achieved in the narrower blade. (Close to the magnet, it is even higher than shown; the color scale is clipped off there so that the weaker intensities can be shown.) One also sees the flux diverge as distance from the magnet increases.

This plot is very clear. One can certainly see the flux crowding in the thinner blade, and the contest between flowing to the tip and leakage off to the side. If one covers the two blade poles with 0.125" wide pieces of black tape stuck to the FEMM plot, so one must look at the field in air only, it is very hard to tell the poles apart.

This plot (http://www.naic.edu/~sulzer/bladeHumtcon.png) shows the vertical B field along a line 3/32 inches above the blades. The magnitude of the field is greater over the narrower blade, but it is not much greater, certainly not the factor one would expect if the field were not weakened by the divergence of the field lines.

Even better is to introduce a thin music-wire steel rectangle above the humbucker to represent the string, and to see how the total flux varies as this "string" is moved a small distance up and down. The total flux in the blades can be determined at each of a small number of distances from the magnet.

This suggests looking at a case with an even narrower blade.

Yes. I would expect the crowding effect to become more intense as the blade thinned, with an increasing but slight tilt to the leakage lines between the poles, until saturation set in. The field intensity at the tip of the thinner pole will increase, but the total flux will not change that much. Until saturation sets in.

Which brings us to a question: What is the peak flux in the thinner blade? The max shown is above 8 millitesla, or 80 gauss, which is remote from saturation levels in mild steel (at least 10,000 gauss). In practice, we may not be able to make the blade thin enough for saturation to even happen.

[Mike Sulzer]

Joe,

Thanks for the comments; time is short at the moment, but I will try to get back to this tonight some time. One brief comment: I was primarily responding to David's and Peter's static field measurements. I agree that we want to look at the whole picture. If you have seen some of my modeling results from before, the idea is to divide the pickup physics into two parts:
1. The static field magnetizes the string.
2. Then replace the magnetized string with a small magnet, remove the strong static field, and look at the induction resulting from the small "string magnet".

This is because FEMM does not have enough accuracy to allow observing very small fluctuations in the presence of the strong field. So we sneak up on it. Comments invited.

[David Schwab]

Mike, wouldn't removing the permanant magnet from the pickup and using a small magnet in place of the string eliminate the entire magnetic circuit? Now you are looking at just the reaction of the small "string magnet' and the coils/cores, which is not the same magnet as the permanent magnet.

My experience shows that even small changes in the permeant magnet's flux path will alter the tone of the pickup. Others have done the same with designs that feature flux guides and things of that nature.

I'm using very strong magnets that throw a field pretty wide around the pickup, and I can still alter the tone by doing things like having the exit out behind the pickup or not, which is what the original question is about.

If you are only thinking of the string as a magnet, you are missing the permanent magnet's field shape and how the moving string interacts with the lines of flux. And that's one of the things that make different pickup design sound different, even using the exact same magnet in each test.

[Mike Sulzer]

If one covers the two blade poles with 0.125" wide pieces of black tape stuck to the FEMM plot, so one must look at the field in air only, it is very hard to tell the poles apart.

Yes and no. Farther from the poles, they must look the same, but not close up. This plot with more lines shows the differences:
http://www.naic.edu/~sulzer/bladeHum80lines.png

[Joe Gwinn]

Yes and no. Farther from the poles, they must look the same, but not close up. This plot with more lines shows the differences:
http://www.naic.edu/~sulzer/bladeHum80lines.png

They look the same to me outside of the black tape. What am I missing?

[Joe Gwinn]

Joe,

Thanks for the comments; time is short at the moment, but I will try to get back to this tonight some time. One brief comment: I was primarily responding to David's and Peter's static field measurements. I agree that we want to look at the whole picture. If you have seen some of my modeling results from before, the idea is to divide the pickup physics into two parts:
1. The static field magnetizes the string.
2. Then replace the magnetized string with a small magnet, remove the strong static field, and look at the induction resulting from the small "string magnet".

This is because FEMM does not have enough accuracy to allow observing very small fluctuations in the presence of the strong field. So we sneak up on it. Comments invited.

I'm not sure I buy this. Does Dr. Meeker agree?

[David Schwab]

Why is one blade thinner? If that's to simulate the screw vs. slug, it's missing the screw's head, which is the same diameter as the slug.

[Joe Gwinn]

Why is one blade thinner? If that's to simulate the screw vs. slug, it's missing the screw's head, which is the same diameter as the slug.

It's to make a simple test of the theory that the peak field over a pole isn't the key issue, that the key issue is the total flux in the pole, and that this total is largely insensitive to the pole thickness.

We went to modeling a blade pickup because FEMM is two-dimensional only, and it was not clear how best to model a 6-pole humbucker, making it harder to decide the basic physics issue.

There is no reason we cannot model a blade pickup where one blade is T-shaped, but this would be a subsequent effort.