Using Femm To Model Pickups

[erikbojerik]

Aha...I think we're talking about different surfaces when thinking about the flux.

For flux, think of dividing the surface inside the loop into small patches. Multiply the area of each patch by the strength of the component of the field pointing perpendicular to the area and add them all up. If the field is changing through the area; the largest contribution to the changing flux is where the field is changing the most. If we move the string magnet closer to or further from the pickup, the relevant component of the field strength changes most through the pole piece.

I agree up to this point; yes, if you define a surface area within the pole piece, that's where the field strength changes the most. No question.

So it makes the most contribution.

Here is where I disagree; in order for the changing magnetic flux to generate current in the coil, the relevant surface is the surface of the wire itself that makes up the coil. You won't generate current in the coil by changing the flux through an arbitrary surface that has no relationship to the strands of wire that make up the coil, no matter how strong. The coil wire itself is the "antenna" that picks up the changing flux.

Everywhere on the surface counts; the major contribution comes from where the field changes most rapidly, and that is generally where the field is strongest.

I don't think so; I think you need magnetic flux changing through the metal of the wire itself in order to generate current (emf). That's why I've paid all my attention to the area outside the pole.

Your "at home" experiment is not completely specified until you describe the field. If you specify a field that does not change in space where the loop moves, then you get no voltage no matter how you move the loop. This is because the total flux through the loop does not change. If the field does change significantly with location, then you do get a voltage when the loop moves because the total flux changes. (integral of B(dot)da is different at diferent times)

Agreed.

"Here's the key...wherever those moving contours cross the turns of the coil, you have a changing magnetic flux across a conductor, and you'll make current."

How can you predict a numerical value from that? It does not work. You must look at the change in the integral of B(dot)da. You can have contours moving across conductors and get nothing; the effects on different parts of the surface can cancel.

I can't predict a numerical value, but it IS the phenomenon that is causing current to move in the conductor. Sure it can be set up to cancel, but in 3D that is a very special geometrical situation.

Try this; instead of loops of wire, make the "coil" be a single straight strand of wire, one end at ground the other connected to a meter. Now what is the relevant surface across which the flux is changing? It is the wire's skin. Same for a coil. Think of B*da as the field crossing the surface defined by the insulation of 4000 turns of wire.

Edited October 13, 2007 by erikbojerik

[Mike Sulzer]

"Here is where I disagree; in order for the changing magnetic flux to generate current in the coil, the relevant surface is the surface of the wire itself that makes up the coil."

No, it certainly is not. See pages 208-209 of the latest version of Jackson, or apply Stoke's theorem to the differential version of the relevant one of Maxwell's equations.

[erikbojerik]

See pages 208-209 of the latest version of Jackson, or apply Stoke's theorem to the differential version of the relevant one of Maxwell's equations.

Mike, do you have the full Jackson ref?

If you could do a Stokes-Maxwell tutorial, that would be great and probably educational for all the people following this discussion (the "Stoke's" that I have in my head is a sphere sinking through a fluid).

[Mike Sulzer]

See pages 208-209 of the latest version of Jackson, or apply Stoke's theorem to the differential version of the relevant one of Maxwell's equations.

Mike, do you have the full Jackson ref?

If you could do a Stokes-Maxwell tutorial, that would be great and probably educational for all the people following this discussion (the "Stoke's" that I have in my head is a sphere sinking through a fluid).

Sure, the first part is easy:

Jackson, John David, Classical Electrodynamics, Wiley (1999, 3rd Edition) ISBN 0-471-30932-X.

This classic on the subject is not easy. I am sure there is something as good for magnetic induction, but easier to read and more up to date. I am not familiar with what it might be, but a look at some E&M 101 type course at your favorite university would probably give a title.

Let me think about the second part.

Mike

[Mike Sulzer]

I did this test:

I had available this bobbin with pole pieces:

GuitarUSA strat type bobbin with high permeability (non-permanent magnet) ferrite pole pieces, 7/8 inches long, flush with the top of the bobbin, and sticking out the bottom. There was about 3/8 inches of pole piece below the bottom of the coil.

The test is to position this over the pole pieces of a pickup in the guitar. Thus the string is already magnetized. Do this with top or bottom facing the strings and compare the voltage. I accepted the inaccuracy of picking and casual positioning, used the #1 string open, and looked at the second harmonic on the FFT analyzer.

I got about three times the voltage with the top of the bobbin (pole pieces flush with the top) facing the strings than with the bottom of the bobbin (with the pole pieces extending from the bobbin) facing the strings.

[SwedishLuthier]

This is very interesting in at least two fields.

1. This totally contradicts my experiment! I can live with that As I mentioned I will repeat my experiment during the week with an E-bow as a driver to eliminate picking variations. My first thought on this result is that I think that you need to have a real magnet in there to show how a real life pickup works. To be continued...

2. This is a very good proof for the thesis that the string is magnetized. Period!

Great experiment Mike. It gave us some important information.

EDIT/UPDATE

I got the E-bow today and used it to replicate Mikes test with a “real” pickup (my test pickup) with a magnetic rod and “in between” two pickups, meaning as little as possible influence from the surrounding magnetic fields.

The result? Somewhere in between my first experiment and Mikes resent. I tested on all four “middle” strings.(resting the e-bow on the surrounding strings to eliminate hand pressure etc) to se if there were any frequency dependencies in the usable spectra. This is what I got (numbers in Volt):

String coil towards strings coil away from strings

A .87 .46

D .55 .37

G .47 .27

B .37 .18

So, this is a definite proof for that the top part of the coil contributes more than the bottom part. Mikes experiment was very much in line with his predictions about the 1:3 ratio. My experiment (with a “real” pickup) gave us the ratio 1:2. Now how can that be? I dunno. But I know for sure that 1/3 of the output is coming from the bottom part of the coil. So I will not take that part away. Now I will have to repeat the same test with a P90 shaped coil…

Well, that is not going to happen for a few days. I’m going away on another, shorter, business trip. Se ya guys.

NEWS FLASH (meaning a second edit if someone still cares…)

I repeated the last test but added a Tele steel base plate, still flipping my test coil (not moving the steel plate that remained as far away from the strings as possible as in a Tele).

New result (rig recalibrated due to the distance change caused by adding the steelplate):

String coil towards strings coil away from strings

A .80 .40

D .83 .42

G 1.12 ..51

B .79 .30

The difference in absolute numbers can be a result of finding a “sweeter spot” for the E-bow in this test series. Please note that the difference between the top and bottom coil gets bigger with higher frequency when the plate is added (almost the 1:3 ratio Mike got for the B-string). Compare that to the very consistent 1:2 ratio of the first test. Anyone care to try to explain?

Now I really have to go packing…

Edited October 15, 2007 by SwedishLuthier

[erikbojerik]

Great experiments guys! You guys should post this over on the ampage forum.

If only I could decide which is more important; the magnetic flux through the poles (strong field, small surface area), or the magnetic flux through the turns of the coil (weak field, large surface area). I've not yet had a chance to track down the Jackson book (too busy resawing backs & sides ), but I can see how there would be contributions from both...along the lines of Rick Turner's "everything affects everything" mantra.

Peter, when you get back maybe you could repeat your eBow experiment in the following way (your bobbin with a single pole piece):

1) polepiece in the middle position (3rd or 4th string)

2) polepiece in the end position (1st or 6th string)

You'll have to do the test with one string, and move it on the guitar to follow the polepiece, but if my idea about the coil's wire turns is correct, then there should be more output at the end of the bobbin than in the middle (same inner coil aperture, more wire in a stronger field at the end compared with the middle).

[Mike Sulzer]

The FEMM plots at the beginning of this discussion show the magnitude of B. What we really want to look at, for applying the law of induction, is the change in B when the string moves. This is harder to do; you have to subtract two cases with the string magnet at different heights. This requires writing out data from FEMM. It is possible to do this for B on a single contour, a line or curve on the image plot. You also have a choice as to what to write out; for example it can be the component of B along the contour.

I have been saying that the magnitude of B is a good indicator how how big the change is. Of course the shape of the curve matters also. It is possible to show how accurate those magnitude plots are at showing the change by using the capabilities of FEMM described above .

The plot linked to below has three curves. The blue one is the component of B parallel to the pole piece at a distance of .04 inches from the center (axis) of the pole piece. (This is inside the pole piece.) That is, this contour is .04 inches from the left side of the plot linked to in the first post of this discussion. (The scale is like the second plot where I knocked down the coercivity by a factor of 1000.)

The red line is this component of B for a vertical contour just outside the pole piece. It is very small and negative (points in the other direction).

The green line is the result of subtracting the blue from a similar one with the string magnet lowered by .005 inches. It decreases with increased distance from the string, as expected, but the shape is different from the blue line.

Notice that the green line is "noisy". This is due to the finite accuracy of the computation in the simulation. It shows up on the difference because the magnitude has been reduced quite a bit by the subtraction (and scaled back up, notice the right hand scale).

It is this noise that limits how much we can do. If you magnetize the pole piece from below and use a piece of steel for the string, you can see that it becomes magnetized. But if you move the "string" down, and look at the difference (analogous to the green line) it is too noisy. This is because the difference is very small, and the computation noise dominates. So it looks tough to do the full simulation that I want to do, but I will play some more.

http://www.naic.edu/~sulzer/BalongContours.png

[JoeAArthur]

The FEMM plots at the beginning of this discussion show the magnitude of B. What we really want to look at, for applying the law of induction, is the change in B when the string moves. This is harder to do; you have to subtract two cases with the string magnet at different heights. This requires writing out data from FEMM. It is possible to do this for B on a single contour, a line or curve on the image plot. You also have a choice as to what to write out; for example it can be the component of B along the contour.

I have been saying that the magnitude of B is a good indicator how how big the change is. Of course the shape of the curve matters also. It is possible to show how accurate those magnitude plots are at showing the change by using the capabilities of FEMM described above .

The plot linked to below has three curves. The blue one is the component of B parallel to the pole piece at a distance of .04 inches from the center (axis) of the pole piece. (This is inside the pole piece.) That is, this contour is .04 inches from the left side of the plot linked to in the first post of this discussion. (The scale is like the second plot where I knocked down the coercivity by a factor of 1000.)

The red line is this component of B for a vertical contour just outside the pole piece. It is very small and negative (points in the other direction).

The green line is the result of subtracting the blue from a similar one with the string magnet lowered by .005 inches. It decreases with increased distance from the string, as expected, but the shape is different from the blue line.

Notice that the green line is "noisy". This is due to the finite accuracy of the computation in the simulation. It shows up on the difference because the magnitude has been reduced quite a bit by the subtraction (and scaled back up, notice the right hand scale).

It is this noise that limits how much we can do. If you magnetize the pole piece from below and use a piece of steel for the string, you can see that it becomes magnetized. But if you move the "string" down, and look at the difference (analogous to the green line) it is too noisy. This is because the difference is very small, and the computation noise dominates. So it looks tough to do the full simulation that I want to do, but I will play some more.

http://www.naic.edu/~sulzer/BalongContours.png

So, if I get this correctly... more BS + more BS = more BS?

Ain't this what you were trying to prove didn't exist all along?

[erikbojerik]

[Diatonick]

This is very interesting in at least two fields.

1. This totally contradicts my experiment! I can live with that As I mentioned I will repeat my experiment during the week with an E-bow as a driver to eliminate picking variations. My first thought on this result is that I think that you need to have a real magnet in there to show how a real life pickup works. To be continued...

2. This is a very good proof for the thesis that the string is magnetized. Period!

Great experiment Mike. It gave us some important information.

EDIT/UPDATE

I got the E-bow today and used it to replicate Mikes test with a “real” pickup (my test pickup) with a magnetic rod and “in between” two pickups, meaning as little as possible influence from the surrounding magnetic fields.

The result? Somewhere in between my first experiment and Mikes resent. I tested on all four “middle” strings.(resting the e-bow on the surrounding strings to eliminate hand pressure etc) to se if there were any frequency dependencies in the usable spectra. This is what I got (numbers in Volt):

String coil towards strings coil away from strings

A .87 .46

D .55 .37

G .47 .27

B .37 .18

So, this is a definite proof for that the top part of the coil contributes more than the bottom part. Mikes experiment was very much in line with his predictions about the 1:3 ratio. My experiment (with a “real” pickup) gave us the ratio 1:2. Now how can that be? I dunno. But I know for sure that 1/3 of the output is coming from the bottom part of the coil. So I will not take that part away. Now I will have to repeat the same test with a P90 shaped coil…

Well, that is not going to happen for a few days. I’m going away on another, shorter, business trip. Se ya guys.

NEWS FLASH (meaning a second edit if someone still cares…)

I repeated the last test but added a Tele steel base plate, still flipping my test coil (not moving the steel plate that remained as far away from the strings as possible as in a Tele).

New result (rig recalibrated due to the distance change caused by adding the steelplate):

String coil towards strings coil away from strings

A .80 .40

D .83 .42

G 1.12 ..51

B .79 .30

The difference in absolute numbers can be a result of finding a “sweeter spot” for the E-bow in this test series. Please note that the difference between the top and bottom coil gets bigger with higher frequency when the plate is added (almost the 1:3 ratio Mike got for the B-string). Compare that to the very consistent 1:2 ratio of the first test. Anyone care to try to explain?

Now I really have to go packing…

WOW!!!

What a powerpacked information.

Very educative thread.

-diatonick

[Mike Sulzer]

This is very interesting in at least two fields.

1. This totally contradicts my experiment! I can live with that As I mentioned I will repeat my experiment during the week with an E-bow as a driver to eliminate picking variations. My first thought on this result is that I think that you need to have a real magnet in there to show how a real life pickup works. To be continued...

2. This is a very good proof for the thesis that the string is magnetized. Period!

Great experiment Mike. It gave us some important information.

EDIT/UPDATE

I got the E-bow today and used it to replicate Mikes test with a “real” pickup (my test pickup) with a magnetic rod and “in between” two pickups, meaning as little as possible influence from the surrounding magnetic fields.

The result? Somewhere in between my first experiment and Mikes resent. I tested on all four “middle” strings.(resting the e-bow on the surrounding strings to eliminate hand pressure etc) to se if there were any frequency dependencies in the usable spectra. This is what I got (numbers in Volt):

String coil towards strings coil away from strings

A .87 .46

D .55 .37

G .47 .27

B .37 .18

So, this is a definite proof for that the top part of the coil contributes more than the bottom part. Mikes experiment was very much in line with his predictions about the 1:3 ratio. My experiment (with a “real” pickup) gave us the ratio 1:2. Now how can that be? I dunno. But I know for sure that 1/3 of the output is coming from the bottom part of the coil. So I will not take that part away. Now I will have to repeat the same test with a P90 shaped coil…

Well, that is not going to happen for a few days. I’m going away on another, shorter, business trip. Se ya guys.

NEWS FLASH (meaning a second edit if someone still cares…)

I repeated the last test but added a Tele steel base plate, still flipping my test coil (not moving the steel plate that remained as far away from the strings as possible as in a Tele).

New result (rig recalibrated due to the distance change caused by adding the steelplate):

String coil towards strings coil away from strings

A .80 .40

D .83 .42

G 1.12 ..51

B .79 .30

The difference in absolute numbers can be a result of finding a “sweeter spot” for the E-bow in this test series. Please note that the difference between the top and bottom coil gets bigger with higher frequency when the plate is added (almost the 1:3 ratio Mike got for the B-string). Compare that to the very consistent 1:2 ratio of the first test. Anyone care to try to explain?

Now I really have to go packing…

Very interesting Peter. Our test pickups are very different, so I do not think it is a big deal about the factor of 2 or 3. When you do the steel plate test, the steel plate is close to the strings in one of the test positions? I wonder what that does?

Mike

[Mike Sulzer]

Peter,

I misread your post and missed that you said that the steel plate remains far from the strings in both positions. So if I understand, in one case the coil is close the the plate, and in the other case it is not. Since the inductance of the coil could be affected by how close the plate is to the coil, it could be that the high frequency effects are due to the inductance changes. But that is only a possibility. Maybe we can devise an experiment to tell.

[SwedishLuthier]

Peter, when you get back maybe you could repeat your eBow experiment in the following way (your bobbin with a single pole piece):

1) polepiece in the middle position (3rd or 4th string)

2) polepiece in the end position (1st or 6th string)

You'll have to do the test with one string, and move it on the guitar to follow the polepiece, but if my idea about the coil's wire turns is correct, then there should be more output at the end of the bobbin than in the middle (same inner coil aperture, more wire in a stronger field at the end compared with the middle).

I think that I understand the first part. Unfortunately the coil cant slide around on the magnet. It is fixed at one end. I flipped the hole thing around. I can of cause repeat the test with the outer strings but I will have to get some type of resting surface for the E-bow. Unfortunately I have too little time to experiment with those things in the next week and a half (this last month have been a nightmare) as I will have to prepare for a guitar show (the great Scandinavian guitarshow), finishing/polishing the exhibition guitars and wind a couple of pickups. Sorry guys (maybe, maybe during the weekend).

So, if I get this correctly... more BS + more BS = more BS?

Ain't this what you were trying to prove didn't exist all along?

And you base this on? Please Joe, argue with us, add fact, thoughts, theories of whatever. Be specific on what you think Mike is missing/contradicting himself/whatever. But please do no call other peoples posts BS. That’s not very mature

WOW!!!

What a powerpacked information.

Very educative thread.

-diatonick

Tnx diatonick. Feel free to contribute or ask.

Peter,

I misread your post and missed that you said that the steel plate remains far from the strings in both positions. So if I understand, in one case the coil is close the the plate, and in the other case it is not. Since the inductance of the coil could be affected by how close the plate is to the coil, it could be that the high frequency effects are due to the inductance changes. But that is only a possibility. Maybe we can devise an experiment to tell.

Yup, you got it right. More experiments might be very interesting. But As I wrote earlier I might not find the time the next couple of days. But If you guys think something out I might be able to squeeze an extra experimental coil (if necessary) into the production run I will do this weekend.

[Mike Sulzer]

So it looks as though modeling a pickup with FEMM has to be a two step process:

1. Model a magnet/polepiece and have that illuminate a peice of steel representing the string.

2. Replace the steel "string" with a hard ferromagnet, that results in the same total field as in step one.

3. Remove the permanent magnetization from the pole piece, keeping the permeability the same.

4. Model the fluctuating field through the pole piece.

This is pretty much a continuation of the same procedure, except the idea in step two is to get the field right, not just have approximately the right form. It is also necessary to see how much the magnetizatoin of the "string" changes as a function of the string position when the string vibrates. It appears that this is very little, since this effect should make the pickup non-linear (and pickups are quite linear). I will try to have some results soon on the linearity of pickups.

[David Schwab]

I'm coming in very late to this discussion, and I haven't read everything yet... but I wanted to comment on this...

All of you:

If you put another pickup in series to change the inductance, you will double the resistance.

That's one way to increase the inductance, but another way is to use more ferromagnetic material within the body of the bobbin. If you have a big steel bar for a core, you have increased the inductance. You can then use less wire so the resistance is not increased. This is the common arrangement of some recent stacked pickup designs. The bottom coils have high inductance and low resistance as compared to the upper coil.

But an update on the “upper part of the coil contribute more” issue.

I made a test pickup. One magnet (A5 and symmetrically charged with 15 Gauss at each end)). Wire wound like “half a strat” on that magnet (or half a stacked strat HB but with one magnet). 4000 turns (equal to half of a beefy strat, AWG42) I then put it in my test rig I have for measuring frequency response of the pickups I wind., first with the coil “at the bottom”, then at the top. This way I have eliminated all factors I can think of. It is the same magnet, the same windings the same lead wires the same measurement amplifier (my sound card) and what more…nope cant think of anything.

I then measured the output of the coil when “flipped” and “unflipped” keeping a close eye on the positioning so I hit the same spot in the rig (this rig isn’t made for this type of “pickup”). The result (drum roll please): The ration between the upper and lower part of the coil isn’t 1:2 as an earlier educated guess. It is 1:1! Exactly! There was a difference in less than 2%! So maybe we can put the hole “upper versus lower part of the coil debate behind us as this proves in real life that the hol pickup contributes equally to the output.

I made a stacked Tele lead pickup last year. My intention was to wind it on the hot side since it was replacing a newer LawrenceUSA pickup, which was on the thin side. I made it with an 1/8" steel blade for a core, and used to ceramic magnets on the bottom arraigned in the same manner as a P-90.

I wound it with 43 gauge wire, to about 12K total. I probably wound both coils in the same direction, but I don't remember. I wired it with 4 conductor cable.

The resulting tone was far different than I would expect for a pickup wound to this resistance. It was very bright and clean, and at about the same level as the two original Bill Lawrence L-250's in the neck and middle positions. It makes a nice sounding vintage Tele pickup, but that wasn't my intention!

I decided to try a few things, so the first was to listen to each coil separately. The top coil sounded like you would expect, bright clean and punchy, and of course it hummed. The bottom coil was a real surprise, it was dark and mellow sounding. So clearly that half of the coil is not sensing what the top half is. Keep in mind that with this pickup the magnets are on the bottom.

Lastly I wired it in phase, and got a big loud P-90 type roar. This is what Seymour Duncan calls the boost switch wiring. I wired a push-pull volume pot to accomplish this.

So, the question is why do stacked pickups of this type sound thin? I think it's clearly phase cancelation, since the highs were intact, but the low end suffered.

Obviously this is not a standard stack configuration. And the older style stacks always have over wound coils to compensate for the thin tone. The original Duncan stacks have the magnets running through both coils, so at least the opposite poles are kind of far from each other. The original Dimarzio stacks have dummy bottom coils, and a magnetic shield. Both coils are wound close to the same resistance (12.51 top, 13.06 bottom).

The newer DiMarzio stacks, like the Virtual Vintage Solo Pro, have a fairly normal top coil, wound to 8.53K with Alnico II rods. Beneath that is a U shaped magnetic shield. The bottom coil is different. It has 10 steel slugs, 6 where the magnets would go, and 4 between them. In the middle is a steel screw to hold the top and bottom coil together. The bottom coil is wound to 2.447K. The coil appears to be full, so the inside of the bobbin might be a larger diameter than what one would expect. The two coils are wired in series.

This has to be the best stacked pickup I've heard so far. So by increasing the inductance of the bottom coil, it can be wound to a lower resistance, and this prevents the low frequency cancelation.

Edited October 26, 2007 by David Schwab

[SwedishLuthier]

Were nice info Dave. As you read on in this thread you will find an update on this experiment, were the ratio 1:2 from the top vs bottom part of the coil were measured.

What I really need to figure out is a way of

1 measuring the inductance with what I have available (digital multimeter, oscilloscope soundgenerator)

2 find a way of altering the inductance for a coil without changing anything else

As soon as I know this I have offered to go on making tests like the on already done.

[R.G.]

1 measuring the inductance with what I have available (digital multimeter, oscilloscope soundgenerator)

2 find a way of altering the inductance for a coil without changing anything else

To measure the inductance,

Measure the resistance so you can later subtract it out.

Set up a test jig, with a 1M pot in series with a 10K resistor to ground, and the pickup in series with a 10K resistor to ground.

Drive the top of the 1M and the top of the pickup with a 1kHz sine wave. Measure the voltage across the 10K under the pickup, then adjust the 1M resistor to give the same voltage across its 10K resistor.

Measure the setting on the 1M pot. This value is the magnitude of the AC impedance of the pickup.

The AC impedance of the pickup is Zp = Rp +jwL. The magnitude of Zp = square root of the sum of the squares of Rp and jwL. Solve Zp = SQRT(Rp^2 +(jwL)^2) for L.

Note that I've ignored C. Generally you should be able to do this at 1kHz. If L is bigger than 3-4H, you may not be able to do this and you may have to look at phase angle on the scope.

I think that will work.

For 2 you're out of luck. You can't change only the inductance of a coil. You must change at least two things about it to get the same inductance. More/fewer turns needs less/more core area or less/more gap to compensate, and you probably have to change the wire diameter to keep the same resistance. All you can do is design a new coil with a different inductance keeping one thing constant that you care about - constant turns, constant area, constant gap, constant resistance, constant wire size, etc. But you can only have one.

[R.G.]

Here's a thought - if what the lower coil does is mostly to get rid of hum, and it's not as effective at highs anyway, can it be designed so its natural rolloff is way low, just above power line. Kill the hum only, not the signal, and let the signal pass through.

Maybe dinking with added capacitance can do something like that. Hmmmm...

Then a bit later it strikes me that this is getting very, very abstract to avoid putting a battery inside a guitar. One possibility is to buffer the pickup right on the pickup, make the buffer be low current, and make it work from one or two hearing aid batteries out of a magazine of about six. Batteries don't have to be as big as PP3s. The voltage can be up-verted to as much voltage as you like to run the buffer from.

[JoeAArthur]

Here's a thought - if what the lower coil does is mostly to get rid of hum, and it's not as effective at highs anyway, can it be designed so its natural rolloff is way low, just above power line. Kill the hum only, not the signal, and let the signal pass through.

Maybe dinking with added capacitance can do something like that. Hmmmm...

Then a bit later it strikes me that this is getting very, very abstract to avoid putting a battery inside a guitar. One possibility is to buffer the pickup right on the pickup, make the buffer be low current, and make it work from one or two hearing aid batteries out of a magazine of about six. Batteries don't have to be as big as PP3s. The voltage can be up-verted to as much voltage as you like to run the buffer from.

Actually, using a cap to split a humbucker is a technique that dates back to the 1970s. It gives a single coil sound as expected by splitting the humbucker, but keeps most of the humbucking effect.

It goes in and out of style every 10 years or so.

[SwedishLuthier]

Thanks for trying to help me R.G. Unfortunately this :

The AC impedance of the pickup is Zp = Rp +jwL. The magnitude of Zp = square root of the sum of the squares of Rp and jwL. Solve Zp = SQRT(Rp^2 +(jwL)^2) for L.

makes me a bit unsure. We are probably using different term but If I remember correctly (probably not) jw is the same as ω = the “angle frequency” (translating the Swedish terms here…) and equals 2∏f were f is the frequency (1khz). At least the old book I still have says Z = √(®2 + (ωL-1/ωC)2) and if we neglect C that would be Z = √(®2 + (ωL)2) or Z = √(®2 + (2∏fL)2)

Meaning

L=(√(Z)2-®2)/2∏fL

Have I understood/remembered things correctly?

[Mike Sulzer]

Peter,

Here is some more info on the way I measure inductance:

1. Make a parallel resonant circuit with the pickup coil and a cap of say 1000pf. (Coill might have 100

or 200 additional C).

2. Feed with random noise from computer random noise generator through 1 Mohm.

3. Look across the coil with computer scope.

4. Use the FFT analyzer mode. Average for a long time to get good results.

Here is an example. It is a guitar parts SC bobbin with high permeability ferrite pole peices; about 2000 turns on the coil. This the blue curve. From the peak frequency I get about 1 H. (L = 1/((2*pi*f)^2)*C). (Wikipedia, LC_circuit) That is the blue curve. The red is same coil, air core, about .3 H. I also show the effect of putting a steel bar against the coil.

http://www.naic.edu/~sulzer/inductanceMeas.png

[David Schwab]

Here's a thought - if what the lower coil does is mostly to get rid of hum, and it's not as effective at highs anyway, can it be designed so its natural rolloff is way low, just above power line. Kill the hum only, not the signal, and let the signal pass through.

The latest stacked designs use a smaller lower coil with no magnets and high inductance, as with the DiMarzio example I posted. As Mike points out with the high permeability ferrite pole pieces, you are getting a high inductance with a small number of turns.

And with the bottom coil shielded from the magnets it doesn't really pick up too much of the strings, while the top coil is shielded from the hum. So the top coil is the string sensing coil, and the bottom is being used to pick up noise.

Kevin Beller from Duncan has an interesting design where the top coil's shield extends into the core of the bottom coil, thus bringing the noise flux with it.

After my experiment I'm convinced that identical coils is not the way to do it. My pickup doesn't sound bad, but it wasn't the sound I was going for. I'm going to start on a new design this week for the Tele and a Strat style guitar I'm making.

Maybe dinking with added capacitance can do something like that. Hmmmm...

There have been designs where the one coil is bypassed with a cap, and some have trim pots across the bottom coil.

Then a bit later it strikes me that this is getting very, very abstract to avoid putting a battery inside a guitar. One possibility is to buffer the pickup right on the pickup, make the buffer be low current, and make it work from one or two hearing aid batteries out of a magazine of about six. Batteries don't have to be as big as PP3s. The voltage can be up-verted to as much voltage as you like to run the buffer from.

I agree... using battery powered circuits would simplify the whole thing immensely. EMG make a bouzouki pickup that uses two hearing aid or camera batteries. EMG-B

Well of course pickups like EMG's are buffered right in the pickup. They are running each coil into the differential inputs of an op amp, with the other end of the coils grounded. Doing it actively is probably the best way to go. Some people don't care for the tone of buffered pickups because they can sound brighter, and guitar players seem to dig the warmer tone of having the pickup loaded down a bit, and even weaker magnets, like Alnico II.

But you can of course make a buffer with the right load to simulate a passive pickup, and then actively sum the dummy coil to buck the hum. EMG's sound pretty passive, and they use a whole butt load of wire on them there coils! Plus a brass screen shield. They are very quiet, but I think what's lacking in them is the design of the pickup itself.

Seymour Duncan seem to have a new active pickup design. With the "Blackouts" they write:

The "other" USA-made active humbuckers use unbalanced inputs in a differential preamp. The problem is, an unbalanced differential preamp is not very effective at cancelling hum.

They also claim they offer reduced hum around fluorescent lighting and computer monitors. Hope they apply for a patent! I'm curious to see what they are doing.

I've been working on a balanced DC coupled buffer design myself. Hope they didn't do the same thing!

[Mike Sulzer]

The purpose of this post is to start the process of showing that a magnetic pickup is non-linear. This means that if one were to move a string in a perfect sinusoid, the output of the pickup would consist of the fundamental and some harmonics. Since real string motion already has harmonics, the non-linearity modifies the harmonics, and thus alters the sound. In his article "The Secrets of Electric Guitar pickups", (http://buildyourguitar.com/resources/lemme/), Helmuth Lemme briefly discusses the non-linear distortion of a guitar pickup due to the hyperbolic relationship between the distance of the string from the pole piece the flux through it. The idea here is to show a simplified guitar waveform resulting from this non-linearity.

In this post we look at how a small piece of steel (representing the string) at various distances over the pole piece is magnetized to produce a perturbation the the total field. A later post will look at how the field from the "string" produces magnetic flux through the pole piece. Then it is necessary to show how to put these two things together to get the simplified waveform from the pickup.

Non-linear effects are amplitude sensitive; therefore it is important to measure how far the string moves from its equilibrium position. At mimf.com, Bill Machrome suggested making a mini strobe light from a white LED. Driving it very near the vibration frequency almost freezes the motion, and a rule can be used to determine the peak vibration amplitude. This turns out to be just under 1/16 inch (#1 E string, .011"), and so I have used +/-.03 inches as a maximum.

The pickup modeled here is a single steel pole piece with a small neo magnet on the bottom. A small piece of steel (the "string"), is located .1 inches above this pole piece, and can move up and down. The "string": is actually a small ring, .010 inch thick and .1 inch in diameter. This is what I can model in FEMM using the mode with cylindrical symmetry.

This figure (http://www.naic.edu/~sulzer/nlmPickupResp.png) shows the result discussed this post (and part of the next) . First consider the set of curves near the top of the plot. The five peaked plots show the magnetic field with the string located at five different heights above the pole piece. (We are looking at the field along a vertical contour extending up from the pole piece .05 inches from its center. This contour passes through the "string".) Also, one line (dark blue) shows the field with no "string". It is the baseline that the other fields approach as the distance from the string is increased.

The lowest set of curves is like the upper set, but with the baseline subtracted. The green line running along the peaks of the curves is the the field with no string, scaled by 40% in order to show that the variation with distance of the intensity of the magnetization of the string is very nearly the same as the field that causes it. We would expect this to be true because the string has very little material compared to the pole piece. But we would not necessarily expect such a simple result if we put a much larger piece of steel over the pole piece. Magnetic problems can be quite complicated, and it is good to find a simple result!

This simple result means that a single application of FEMM determines all we need to know about the magnetization of the string as the string varies in height. Remember, the magnetization of the string is essentially instantaneous: it varies with the field as the string moves up and down. This is similar to how an iron core audio inductor works: as the current in the audio wave form varies, the magnetization of the core varies along with the current.

There is a middle set of two curves and five black points. They will be discussed later.

[Mike Sulzer]

This subject of this post is what happens to the magnetic flux through the pole piece when the magnetized "string" moves up and down. Errors (noise) in the FEMM simulations prevent us from looking directly at the magnetic field perturbations in the pole piece due to the B field produced when the string is magnetized by the permanent field. Therefore, we use the field at the string as a measure of the magnetization that is produced, remove the permanent magnet, and replace the string with a permanent magnet that generates the same field. This figure shows how this works: http://www.naic.edu/~sulzer/nlmAsmVsIndMag.png. The red line is like one of the curves from the set at the bottom of the plot described in the previous post. It is shown here on a larger scale, and the simulation noise is clearly visible. The simulation tries to compute the additional field from the string as induced by the permanent magnet at the bottom of the pole piece. It has limited accuracy. The blue line shows the field from a permanent magnet replacing the string, with the permanent magnet at the bottom of the pole piece removed. This field is in good, but not perfect, agreement with the induced field and it has no visible noise right through the pole piece.

This figure, http://www.naic.edu/~sulzer/FieldThroughPP.png, shows how the field through the pole piece varies for five different positions of the string magnet. The plot uses a log scale so that the entire range can be seen. The peaks look wider because of the log scale. It shows the field through a single contour in the pole piece. It would be good to know the field along all possible contours to determine the flux through the pole piece, but the relative changes in flux are not much affected by just looking at one. So as a proxy for the total flux, we just add up the field along the contour for each string position. These five numbers then represent the flux. They are shown on the plot from the previous post, http://www.naic.edu/~sulzer/nlmPickupResp.png, in the middle set along with two lines. The light blue curve is a scaled version of the green line below (or the dark blue above). The fact that the points do not fit the light blue line shows that a different function describes the variation of flux with distance (with the magnetization constant). A good fit (purple line) is easily obtained by steepening the slope a bit.

So the purple curve determines the relative variation of flux with distance if the string magnetization remains constant. But we know that it does not. So it is necessary to multiply the two variations together to get the total response. That will be the subject of the next post.