Humbuckers... well, duuuh...

[R.G.]

... the foregoing as I slap my forehead. Don't know why I didn't think of this before.

A humbucker is two single coils, arranged to be electrically additive for signal and cancelling for common mode. The hum is cancelled by the arrangement...

and signal components add depending on the characteristics of the individual coils.

It's not one pickup, it's two, added together. And it's built in a way that's magnetically asymmetrical, even if the coils are identical - which is usually not true.

Of course there is a huge variation and everything affects everything - it's not one pickup it's two. Each with its own inductance, resistance, coil capcitance and other fibbles and foibles, and then you add the two together.

For instance, the measured inductance (for instance) of a humbucker as a unit is a number that's actually the sum of two independent inductances, which each have their own effect on their half of the electrical sum. Likewise number of turns, likewise potting saturation, likewise coil scatter, likewise area fill of the winding window, likewise position along the string, and so on to all details.

Isolation of effects is important. Assume that a coil has a notch or peak in its response - not necessarily that it does have that, but assume that it does. Now take two non-identical coils and add their responses together. The response of the two added is more even than either separately, because they each fill in the opposite coil's peaks and valleys. Two response quirks that happen to fall on the same frequency reinforce.

You have to know the responses of each single coil before you can tease out the contribution of what you're doing to the whole pickup.

Sorry for my public epiphany. You guys probably already realized this all along, and use the non-identicality to tune pickups. It just took me a while to catch up.

[Zhangliqun]

Don't forget that each coil also sees a different piece of each string and thus picks up a different harmonic flavor. So even if the two coils were somehow 100% identical, the string itself makes them different.

[R.G.]

Yeah, that's what

likewise position along the string

meant.

[Zhangliqun]

Oops, never mind...

[R.G.]

'S'OK. I had to go back and reread what I wrote to be sure. I thought I typed that, but sometimes my composer queue overruns my output buffer...

[David Schwab]

R.G., there a lot of good information in some of the patents on pickups out there.

Two of my favorites are the Bartolini patents; 3983777 and 3983778. He actually used pole piece shape to alter the field shape, and thus change the harmonic content of the pickup.

DiMarzio has a ton also. They have a one on mis-matched coils.

5111728
4442749
4295404
4133243
5811710
5399802
4320681
4501185
5530199
5908998
5945632

Another is Bill Lawrence

3902394 (tbird pu)
3915048 (circuit)
4151776 (S3)
5376754(closed circuit coil)
4364295 (L-500)
5789691(stack)
3916751 (ripper)
3711619 (coax coils)

Lots of good technical reading!

[R.G.]

Patents are an interesting concept. A patent is not a reward for genius. It's a bribe to get geniuses to reveal their successes. One version of that description is in the enabling legislation for patents.

The bribe is the government agreeing to ...er... let you sue someone for copying your stuff, and telling the courts to rule for you if you make a very convincing case. The government gets your full disclosure of how to do the magic you thought up, and your agreement that it's public knowledge after the term.

The interesting thing is that substantially all of the patents from the guitar-and-amplifier Golden Age have expired. We're encouraged to use that stuff freely. It's why the government runs the patent racket. So every patent issued before September 11, 1987 is something your government wants you to have for free. Patents are issued in numerical order. Patents with a number less than 4692950 are now expired.

It's also why we have the raft of million-angels-on-the-head-of-a-pin patents, certainly in amplifiers, probably in pickups. Obtaining a patent on some minutely different aspect is another way to slow your competition down.

In the end, the only good way to win the innovation game is to outrun them, not fence them out.

[Possum]

Uh actually you missed the fact that they both share the same magnet so its not really two different pickups added together unless they both had their own magnet. Also the slug coil and the screw pole are radically different in how they sense the string and that the screw poles go well below the magnet while the slugs do not. when I started making pickups I hated humbuckers, I made one set and called it a day. Little did I know how simple yet how complex they are, way more than single coils. A good single coil is probably harder to make than an acceptible humbucker, so I am very glad I didn't try to tackle humbuckers in the beginning; alot of these Ebay genius winders put together a couple stewmac kits and think they know it all when basically they know zero. One of the weirdest things I ever tried with a humbucker was a very short magnet. I got this weird tone that was bright but somehow sounded just wrong. I discovered that the magnetic polarity was somehow getting reversed in the circuit in some areas and was blowing back into the other coil is nearest I can describe it, very strange and very bad :-)

[R.G.]

Originally Posted by Possum

Uh actually you missed the fact that they both share the same magnet so its not really two different pickups added together unless they both had their own magnet.

Yeah, it's an oversimplification. However, having a common magnet merely muddies it up a bit, not quite the same as the same magnet.

In a variable reluctance setup (and pickups are that), the magnet forces a set of flux density times pole face area out of the magnet. Changing the reluctance doesn't change the field inside the magnet - no external coercivity to counteract the Br. What changes is the way the field is distributed outside the magnet. So, as you point out...

Originally Posted by Possum

Also the slug coil and the screw pole are radically different in how they sense the string and that the screw poles go well below the magnet while the slugs do not.

... the two coils each have a different fraction of the M-field and how the local reluctance change affects the part of the field that cuts them.

So while there may be only one magnet, the field distribution in each coil is different enough that they may as well have similar but different magnets. The field in each coil is different, as each coil gets a similar but different portion of the M-field out of the forcing magnet.

The only place where you would have to take two coils together into account instead of two coils independently added together is in the mutual inductance of the two coils. Like a very inefficient transformer, some of the signal induced in one coil will be picked up in the other, and vice versa. Then that mutual signal plus each of the separate components get added to make the external signal voltage - ignoring in-phase, out-of-phase, series/parallel, etc. connections.

Originally Posted by Possum

... One of the weirdest things I ever tried with a humbucker was a very short magnet. I got this weird tone that was bright but somehow sounded just wrong. I discovered that the magnetic polarity was somehow getting reversed in the circuit in some areas and was blowing back into the other coil is nearest I can describe it, very strange and very bad

That would be that mutual inductance thing. Here's a working hypothesis: the shorter the real magnet is as part of the structure, the more leakage outside the pole pieces you get. The more leakage, the more shared fringe flux and the bigger the percentage of the total signal the mutual coupling signal is - probably because the total signal goes down while the mutual sensing drops less.

At least that's where I'd start looking.

[Joe Gwinn]

Originally Posted by R.G.

That would be that mutual inductance thing. Here's a working hypothesis: the shorter the real magnet is as part of the structure, the more leakage outside the pole pieces you get. The more leakage, the more shared fringe flux and the bigger the percentage of the total signal the mutual coupling signal is - probably because the total signal goes down while the mutual sensing drops less.

Mutual inductance between coils does not depend on the static magnetic field at all. The magnets act as bits of slightly permeable material in linking the coils.

I've measured the coupling coefficient k of the coils of a number of humbuckers (having side-by-side coils), and the values all seem to be about 0.17. (k=Lmutual/Sqrt[La*Lb])

[R.G.]

Originally Posted by Joe Gwinn

Mutual inductance between coils does not depend on the static magnetic field at all. The magnets act as bits of slightly permeable material in linking the coils.

I sure didn't express myself well, did I?

What I was thinking was that the effective permeability of the magnet itself is low - it's sitting at the top corner of a squarish BH curve. I opined in my head that the pole structure was higher permeability than the permanent magnet length of the path, and so shorter magnets did two things:
- less total field, hence less signal overall in both single signals and mutual.
- more high permeability metal in the path, so greater mutual coupling.

I'll have to go look this up, 'cause I have not messed with it for a few decades. No, the mutual inductance doesn't depend on the magnetic field through the coils, but doesn't it depend on how much of the path is high permeability? For instance, two coils with parallel axes 1" apart have some value of k. Insert two U cores to make a high permeability path and the value of k goes up because the cores shunt fields more effectively through the coils and let less flux couple one coil but not the other.

Originally Posted by Joe Gwinn

I've measured the coupling coefficient k of the coils of a number of humbuckers (having side-by-side coils), and the values all seem to be about 0.17. (k=Lmutual/Sqrt[La*Lb])

Yep, that last was the formula for k, all right. I got out my old motors book.

It would be interesting to replace magnets with a varying length of magnet plus steel slug to make up the same length of path and measure k. That should make k vary, shouldn't it?

But it's possible that I flat got the mutual signal part wrong.

[Joe Gwinn]

Originally Posted by R.G.

What I was thinking was that the effective permeability of the magnet itself is low - it's sitting at the top corner of a squarish BH curve. I opined in my head that the pole structure was higher permeability than the permanent magnet length of the path, and so shorter magnets did two things:
- less total field, hence less signal overall in both single signals and mutual.
- more high permeability metal in the path, so greater mutual coupling.

I'll have to go look this up, 'cause I have not messed with it for a few decades. No, the mutual inductance doesn't depend on the magnetic field through the coils, but doesn't it depend on how much of the path is high permeability? For instance, two coils with parallel axes 1" apart have some value of k. Insert two U cores to make a high permeability path and the value of k goes up because the cores shunt fields more effectively through the coils and let less flux couple one coil but not the other.

The more high-permeability material in a ring linking the coils, the higher the coupling coefficient/

It would be interesting to replace magnets with a varying length of magnet plus steel slug to make up the same length of path and measure k. That should make k vary, shouldn't it?

Alnico seems to have an incremental permeability of 3 or 4, while for mild steel it's more like 2000. And for air it's exactly one. So, the coupling between coils of a humbucker will largely depend on the ratio of air to steel in a ring linking both coils.

[R.G.]

Joe - am I missing something? I thought

"the mutual inductance doesn't depend on the magnetic field through the coils, but doesn't it depend on how much of the path is high permeability?"
was the same as

Originally Posted by Joe Gwinn

The more high-permeability material in a ring linking the coils, the higher the coupling coefficient/

Where I think of "path" as "ring linking the coils" - that is, where the magnetic flux goes.

And I thought
"What I was thinking was that the effective permeability of the magnet itself is low - it's sitting at the top corner of a squarish BH curve. I opined in my head that the pole structure was higher permeability than the permanent magnet length of the path,"
was the same as:

Originally Posted by Joe Gwinn

Alnico seems to have an incremental permeability of 3 or 4, while for mild steel it's more like 2000. And for air it's exactly one. So, the coupling between coils of a humbucker will largely depend on the ratio of air to steel in a ring linking both coils.

again substituting path or "where the flux goes" for "ring linking the coils".

Flux does follow a ring - if it's not distorted by a high permeability "ditch" to run in.

[Joe Gwinn]

Originally Posted by R.G.

Joe - am I missing something? I thought ....
Flux does follow a ring - if it's not distorted by a high permeability "ditch" to run in.

Reset. The issue in pickups is that the air gaps are very large, to the point of dominating the distribution of magnetic fields. We have three materials of interest: mild steel, alnico, and nonmagnetic (air, copper, plastic, stainless steel, brass, et al). The incremental permeabilities are ~2000, ~3, and 1.000 respectively. The 2000 will generally win all disputes, but it takes very little nonmagnetic material to effectively isolate the steel. The dominance of nonmagnetic materials, especially air, in pickups is why the exact shape of the magnetic components matters so little in practice.

A number of people explore magnetic fields using the shareware program FEMM http://femm.neil.williamsleesmill.me.uk/.

[Dave Kerr]

Originally Posted by Joe Gwinn

A number of people explore magnetic fields using the shareware program FEMM http://femm.neil.williamsleesmill.me.uk/.

Yeah, Steve Kersting's site has some cool stuff
here

[David Schwab]

Originally Posted by Joe Gwinn

A number of people explore magnetic fields using the shareware program FEMM http://femm.neil.williamsleesmill.me.uk/.

I've not used this program myself, but from what I've seen it seems too show the field extending way too far above the pickup. Since the field drops off with the square of the distance (it's early but you know what I mean), I doubt the field extends that far above a pickup. Not in a usable way.

[Joe Gwinn]

Originally Posted by David Schwab

I've not used this program myself, but from what I've seen it seems too show the field extending way too far above the pickup. Since the field drops off with the square of the distance (it's early but you know what I mean), I doubt the field extends that far above a pickup. Not in a usable way.

Actually, the fields go to infinity. But they become auditorially insignificant pretty fast, which isn't obvious from a field plot.

By the way, the inverse square law is for isolated poles. If one has N and S poles near one another (such as in a humbucker), the effect falls off with the inverse cube of distance. This is another reason that strings must be close.

But, there is another twist. The inverse square and cube laws above are for 3D space. Think little spherical poles. If one has an extended structure of constant cross-section, like a pickup (which is much longer than it is wide or tall), near the center the fields are confined to be ~2D, and the laws become inverse and inverse square respectively. But near the ends it looks more like isolated poles. And so on.

In FEMM, one specifies a cross-section, and must specify if one is solving a 2D or a 3D problem. This is why.

[David Schwab]

Originally Posted by Joe Gwinn

Actually, the fields go to infinity.

Same as gravity... Good thing Jupiter is so damn far away.

Then of course everything is a magnet due to electron spin, but the domains aren't lined up and cancel out...