Designing A Pickup

[Geo]

I know I want something P90 style for my next project. Rather than spending a ton on the best P90's available, I'd like to expirement. The standard P90 seems about as complex as a humbucker (minus 1 bobbin of course). I'd like to try making a "P90", but constructing the bobbin like a Strat bobbin--two plates held together by fixed magnetic polepieces. No baseplate, bar magnets, spacers, etc.

I would probably design it to fit inside a standard P90 cover. Another thought is to use the top plate of the bobbin to mount the pickups "dogear-style". I.e., no pickup covers. The top plate would have dogears extending beyond the dimensions of the pickup hole and would be mounted with screws and springs. I would wrap the coil in black pickup tape like a coverless humbucker. Any thoughts on that? Is it a bad idea?

And has anyone ever tried a pickup like this? Just wondering...

[Mike Sulzer]

I know I want something P90 style for my next project. Rather than spending a ton on the best P90's available, I'd like to expirement. The standard P90 seems about as complex as a humbucker (minus 1 bobbin of course). I'd like to try making a "P90", but constructing the bobbin like a Strat bobbin--two plates held together by fixed magnetic polepieces. No baseplate, bar magnets, spacers, etc.

I would probably design it to fit inside a standard P90 cover. Another thought is to use the top plate of the bobbin to mount the pickups "dogear-style". I.e., no pickup covers. The top plate would have dogears extending beyond the dimensions of the pickup hole and would be mounted with screws and springs. I would wrap the coil in black pickup tape like a coverless humbucker. Any thoughts on that? Is it a bad idea?

And has anyone ever tried a pickup like this? Just wondering...

The only physical problem that I can think of is that available magnets of the strat type might be a bit too long for P-90 case. But since you are not using a base plate this would just be a matter letting them stick out the back a bit and making sure you rout the body properly.

If you want a P-90 sound you need to get the resonant frequency right. I am not sure about the relative effective permeabilities of alnico magnets and the screws. I am guessing they are close enough so that you just have to make the coil with the same number of turns as a P-90 coil to get good results.

[Geo]

Thanks for the reply, Mike.

The length of the magnets shouldn't be a problem. This guitar will be semi-hollow, so there will be plenty of space below.

Does anyone have any thoughts on the "coverless" option? I.e., is it enough protection to wrap the coil with tape? That would make things so pleasantly simple!

Another option is to use a standard P90 cover. I would enlarge the polepiece holes in the cover to fit Strat magnets. I would also make a simple baseplate with the necessary holes, to allow use of the cover. This might look better.

Edited September 11, 2007 by Geo

[psw]

The P-90 sound is created not only by a wider flatter coil, but also a wider magnetic field "shape" that is created by the two magnets below pointing like poles to the core.

What you are proposing may end up a little more like Jazzmaster pickups. It could have an interesting sound, but as is often debated, it wont be a P-90...

Try it and see, it is unlikely to sound "bad"...

pete

[Geo]

The P-90 sound is created not only by a wider flatter coil, but also a wider magnetic field "shape" that is created by the two magnets below pointing like poles to the core.

Mm, I was wondering about that too. I have played a Jazzmaster once or twice and didn't really like it. Hm...

[SwedishLuthier]

I have made that type of pickups a couple of times. They have an interesting mix in sound between the strat type of sound and the P90 type of sound. Compared to the S90/T90 type of pickup, that is another cross between a P90 and strat/tele (strat/tele bobbin, screw pole pieces, sometime a retainer bar and magnets placed like in a P90) the sound is quite different. The S90/T90 have more of the “compressed” sound of a P90 while a R90 (my name for a P90 with alnico poles) have a more "open" sound but with less treble and more mid and bass, like a massively over wound Strat/Tele.

There will be no problem with using a P90 cover. All you have to do is to let the magnets protrude a bit out of the top flange and enlarge the holes in the cover. It looks a bit like the Burnes pickup made famous by Brian May (skinnier but similar). If you let the mags stick out on the back it will change the magnetic field pattern and direct the field away from the lower parts of the coil (compared to the standard P90). Also have a look at what PSW wrote. An advantage with the R90 design and keeping the mags flush with the lower flange is that you can add a steel base plate a la Tele bridge. It adds quite a bit of bite/twang to the pickup.

Regarding your thoughts that the standard P90 design is as complex as the HB it is not really so. The P90 is only a tad more complex (in the making that is) compared to a SC. Try buying ready made P90 bobbins from allparts and all you need to do is adding the screws and the magnets (and the wire of cause) and you are done. To my knowledge no base plate is used in a traditional P90 pickup. My Gibson P90s (got them way before I started to wind myself) came without baseplates. The pickup is screwed into the guitar either through the dog ears or through the pickup itself (soapbar).

Making your pickup without cover and screwing the top flange into the top of the guitar is probably going to make the distance to the strings too high. Especially as the pole pieces are non-adjustable. But all that depend on your guitar design.

Does anyone have any thoughts on the "coverless" option? I.e., is it enough protection to wrap the coil with tape?

Probably. As you mentioned most HBs are made that way nowadays.

it wont be a P-90...

Try it and see, it is unlikely to sound "bad"...

So true

[Mike Sulzer]

What do the magnets in a pickup do? They (temporarily) magnetize the strings, either directly, as in the case of a Fender type SC, or indirectly, by first magnetizing a pole piece (screw, slug, or whatever) as in a HB or P-90. In either case it is the magnetic material close to the string that does the work. The shape of the field down below away from the string has essentially no effect. That is, the permanent magnetic field passing through the coil is not the issue at all.

The other thing the pickup does is to sense the time-varying magnetic field that is produced when the magnetized string vibrates. Of course the coil is essential for this, but the pole pieces also play an essential role. This is because whether they are permanent magets or a temporarily magnetizable material like soft steel, they increase the tiny field fluctuations from the string that pass through the coil.

Try this some time: wrap several hundred turns of wire around a humbucker slug and connect it to an amp. Hold it over a pickup and string. See how much signal you get. Then try the same think with a plastic rod. The slug gives more signal because it amplifies the field from the vibrating string.

The third aspect of the pickup is the circuit it is in. The pickup has inductance, capacitance, and resistance, and other circuits, especially the cable capacitance affect its operation. Much of the diferences in pickup sound have to do with the frequency response of this circuit. In particular, a broad resonance is formed, and the location of the peak frequency and the width of this peak matter. This response is measurable. If you want to understand how much difference in sound between pickups is due to more subtle effects, you must first look at the frequency response.

[SwedishLuthier]

The shape of the field down below away from the string has essentially no effect. That is, the permanent magnetic field passing through the coil is not the issue at all.

Slightly off topic but that is not what I believe Mike. The electric current between the two ends of the coil is direct correlated to the magnetic field strength that the wire is surrounded by. I have covered this a couple of times.

The formula is:

ems=N *dΦ*1/dt ems =”electro motorical voltage”

N = numbers of turn of wire

dΦ = the change of magnetic flux

1/dt = the frequency that the field changes with

I’m very sorry if I just translate the terms I have learn in university here in Sweden. I don’t really know the correct terms in English.

So how is that related to our pickup? The primary part was covered by Mike. The magnetized sting moves above the coil, inducing current into the windings. And I agree, it is probably only the top winds that are affected. But a magnetized string (acting as a magnet itself) moving into a magnetic field (caused but the permanent magnets) will affect all of the magnetic field. Test this by using metal shavings (or whatever it is called) on a piece of paper and magnets under the paper. Move one magnet and the field of the other is affected. The moving magnetized string will actually affect the magnetic field in the lower part of the coil too (dΦ in the equation). This gives us that the structure of the magnetic field in the lower part of the coils also plays a role in the sound/output of the pickup. So, if the lower part of the coil is surrounded by a strong or weak magnetic field will for sure affect the amount of voltage produced by those particular windings. The total output is actually the sum of the output of all windings.

But lets skip the theories and get a bit more practical. Wind two identical coils in the above mentioned P90 respectively R90 design. The only thing that differs is the magnetic field structure (shape) and the field strength. A P90 is typical around 24-27 gauss and a trad SC around 28-37 (actual values from all pickups I had around). That difference might account for some of the difference in sound between a P90 and a R90 (and the difference must be heard to be understood). But that difference in magnetic flux alone isn’t enough. It is not only a matter of higher output or stronger treble. I can’t describe it in words but the difference is significant. They are completely different animals. So my meaning is that the structure (shape, strength) of the magnetic field in the bottom of the coil do really matter.. You can also try a HB with screw poles only vs a slug poles only (all other things equal) and you will find as big difference in sound. Most of that comes from the long screws diverting the magnetic field away from the bottom of the coils.

Have a look here for FEMM simulations of magnetic field structures for different popular pickups:

http://www.ampge.com/SKGS/sk/Images/pickup...f/Magnetics.htm

[erikbojerik]

This gives us that the structure of the magnetic field in the lower part of the coils also plays a role in the sound/output of the pickup.

That's why different metals used to make humbucker baseplate influence the tone of a humbucker.

[Mike Sulzer]

OK, I think that it is possible that there is some confuson about which magnetic field is under discussion. There are two:

1. the steady magnetic field caused by the permanent magnet and guided to the string by the pole pieces;

2. the time varying field caused by the vibrating string once it has been magnetized by the steady field from the pole pieces.

The field that matters in the equation for the ems is the varying field; that is why "change in magnetic flux" appears in the equation. The steady magnetic field does not enter into the equation, and so it has no effect. There is a changing magnetic field through all the turns of the coil, so they all contribute. But this field falls off with distance, so the top windings contribute more. The pole pieces help guide this field and prevent it from falling off too much.

The total magnetic field present anywhere in the pickup is the sum of the steady part and the varying part, as Peter said. But only the varying part contributes to the ems (signal from the pickup). But where the steady field matters is at the strings. The value of this steady field at other places is not importnat.

[Geo]

Thanks for sharing all this information!

"To my knowledge no base plate is used in a traditional P90 pickup."

I must have misinterpreted the diagram I was looking at. I've never seen a P90 out of a guitar, so I'm clueless. If there's no baseplate, how does the bobbin stay attached to the cover? I'm thinking of the dogear type that can "hang" in a hollowbody. If you have pictures or links, please share.

I'll probably make "normal" P90's rather than Jazzmaster-style pickups. I hadn't found anywhere to get bobbins, so thanks for the pointer to Allparts.

For bar magents... do you use "humbucker" magnets such as Allparts and Stewmac sell, or something else? I know the poles on a humb. magnet are along the thin edges rather than the flat "top and bottom" like the bar magnet on a cheap Strat style pickup. I think humbucker magnets would work. I would point two like poles (repelling poles) towards the screw polepieces.

[psw]

The "shape" of a pickups magnetic field influences how much of the string that is vibrating and it's combination of various vibrating nodes (canceling and reinforcing harmonic content) is sensed (and to what degree)...so an HB with a wide aperture to the strings has a darker sound than a single coil...or so it is commonly believed.

Perhaps the confusion is in a little of the theory.

The pickup coil senses disturbances in the magnetic field which passes through the core and in which the strings vibrate. A wider aperture to the strings will result in the effect described above. Other factors such as the core material, it permeability, saturation and mass also have an influence. A stronger magnet can produce more output, however too strong and the magnetic field will suppress the vibration of the string. No core, as you illustrate, provides a weak signal...but this is because of the ambient magnetism all around us I would imagine.

But where the steady field matters is at the strings. The value of this steady field at other places is not important.

So...I think you acknowledge that the magnetic field that dissects the string and the core is vital to the signal content of the vibrating string...yes?

The "shape" of the field is important in determining this...check out these FEMM diagrams of various pickup designs...

SK's FEMM page

BTW FEMM is a magnetic modeling program that is free and easy to use for basic functions like permanent magnetic fields...can be fun to play around with

Here is a P-90...

Note the two magnets below the coil with like polarities towards the screw pole.

Now compare with a single coil...

The density of the fields above the pickups are important (see the graphs) as is the density over various parts of the string.

The lines of magnetism are continuous from one polarity to another (without crossing), the path they travel from one to the other, determined by the shape of the field, is important. What goes on below the magnet draws the strength of the field down and away from the strings, or out further to the sides.

Perhaps I am not explaining it too well, and a lot of my knowledge is based on intuition and experimentation in the Sustainer Thread. With the sustainer driver, we are looking in effect (though different in specs) to a pickup in reverse. Experimentation in this field is heavily influenced by these factors as, unlike a pickup that senses these things, the driver emits it, and that can cause all kinds of problems if not controlled.

It is also interesting to look at new stacked single coil pickups that seek to emulate a true single coil sound. These primarily use such strategies to isolate the lower noise canceling coil from the vibrations of the string and the flux in the devices upper coil/core. Kinman for instance uses slug poles in the lower coil and a metal shield...the Fender/Lawrence Noiseless use a central magnetic structure that attracts the field to this part of the device and significantly leaving the lower coil to noise canceling duties.

This is an interesting conversation and I think we all learn more by participating, thanks... pete

[Mike Sulzer]

"So...I think you acknowledge that the magnetic field that dissects the string and the core is vital to the signal content of the vibrating string...yes?"

Are you saying that the magnetic field affects the vibration of the string? If so, i would answer "no, ideally the magnetic field does affect the vibration of the string." When it does, you have stratitis, or string pull. The plots that you show from FEMM show why a strat pickup would have more string pull than a P-90. The strength of the field is shown by how close the lines are together and how dark the color is. Note that the field strength is stronger over the Fender type pickup than the P-90.

The plots do not give a complete picture of the operation of the pickup. In principle you could complete it by placing a small piece of steel over the pickup (in the FEMM program) to represent the string. You could get the field and move this piece a bit, geting the field again, and subtract the magnetic fields to get the change in field that Peter's equation needs. A more practical method would involve using linearity, the fact that the total field is the sum of the steady part and the small changing part.

[Geo]

This discussion is great.... just to bump my question back to the top.....

For bar magents... do you use "humbucker" magnets such as Allparts and Stewmac sell, or something else? I know the poles on a humb. magnet are along the thin edges rather than the flat "top and bottom" like the bar magnet on a cheap Strat style pickup. I think humbucker magnets would work. I would point two like poles (repelling poles) towards the screw polepieces.

[Setain]

"So...I think you acknowledge that the magnetic field that dissects the string and the core is vital to the signal content of the vibrating string...yes?"

Are you saying that the magnetic field affects the vibration of the string? If so, i would answer "no, ideally the magnetic field does affect the vibration of the string."

If I am not mistaken, he is saying the exact opposite: the ferrous vibrating string is causing the magnetic field to move with it, which is what generates most of the current.

[SwedishLuthier]

For bar magents... do you use "humbucker" magnets such as Allparts and Stewmac sell, or something else? I know the poles on a humb. magnet are along the thin edges rather than the flat "top and bottom" like the bar magnet on a cheap Strat style pickup. I think humbucker magnets would work. I would point two like poles (repelling poles) towards the screw polepieces.

GEO

Right on spot. For once Gibson did some smart design decisions when designing the Hummer. They used the same pole screws and the same magnets as in the previous P90 design. And you should point the same pole against the screws.

Regarding the "hold the cover in place" question.

The pickup bobbin rests directly onto the wood in the rout. The cover is screwd down, over the bobbin with two small, long screws between the polce screws. Those two screws hold both the cover in place and the pickup down. Whas that a good enough description ? I dunno...

Edited September 13, 2007 by SwedishLuthier

[SwedishLuthier]

Everybody:

Try this: Lay down two magnets or one magnet and a magnetic (not magnetized) object on your desk pretty close to each other. Put a piece of paper on top. Sprinkle carbon steel (or other magnetic, not magnetized material) file dust/shavings (or what ever it might be called). The metal dust will lie down, following the magnetic field lines, pretty much like Steven Kerting’s FEMM simulations. Watch the pattern close to magnet 1. Move magnet 2. What happens with the pattern close to magnet 1? The pattern close to magnet 2? The pattern changes around both magnets/magnetic objects.

Placing a coil in close proximity of magnet 2 will produce a voltage according to the equation above. But as we saw that the field lines moved close to magnet 1 it means that we have a change in magnetic flux or dΦ in the equation. This will also induce a voltage into a coil placed close to magnet 1! Now substitute magnet 1 for our magnet structure of a P90 and Magnet 2 for the magnetized string. Wouldn’t the picture stay the same? Wouldn’t that mean that the magnetic field strength (flux) at the bottom of the coil play a role in the sound/output of a pickup?

I don’t claim to have the answers. I’m thinking out loud here, trying to combine my theoretical knowledge and my practical experience from pickup winding, to be able to understand the difference I hear between the P90s and R90s I make.

If I am not mistaken, he is saying the exact opposite: the ferrous vibrating string is causing the magnetic field to move with it, which is what generates most of the current.

Setain:

Not most but at least a contributing part

[psw]

"So...I think you acknowledge that the magnetic field that dissects the string and the core is vital to the signal content of the vibrating string...yes?"

Are you saying that the magnetic field affects the vibration of the string? If so, i would answer "no, ideally the magnetic field does affect the vibration of the string."

If I am not mistaken, he is saying the exact opposite: the ferrous vibrating string is causing the magnetic field to move with it, which is what generates most of the current.

Yes and No.

I was not saying the magnet effects the vibration of the string..."the magnetic field that dissects the string and the core is vital to the signal content of the vibrating string"...I am saying the shape of the field effects the part of the strings vibrations that are being sensed and to what extent, and so the various nodes and vibration modes in that area (determined by the magnetic shape) determine the range of harmonic content, cancellation and reinforcement etc. Not that it effects the string, but that the shape determines what and how much is sensed...does that make sense, it's kind of late.

the ferrous vibrating string is causing the magnetic field to move with it, which is what generates most of the current.

Well there are a lot of factors that effect the current and how much power comes out, but the shape of the magnetic field does determine what the pickup has to play with...

Anyway, hope you have some success making something!

I originally came here to make pickups but got distracted with the sustainer project that has taken over a little. I hope to get back to this in the future and hope people show as much interest as they have here. A lot of the Sustainer Project directly relates to pickup designs and it would be interesting to put some of this back into something a little different. BTW, some interesting new development in the works that will interest pickup makers who would like to add something a little different to what they can offer...watch out!

pete

Oh...almost forgot...

Everybody:

Try this: Lay down two magnets or one magnet and a magnetic (not magnetized) object on your desk pretty close to each other. Put a piece of paper on top. Sprinkle carbon steel (or other magnetic, not magnetized material) file dust/shavings (or what ever it might be called). The metal dust will lie down, following the magnetic field lines, pretty much like Steven Kerting’s FEMM simulations. Watch the pattern close to magnet 1. Move magnet 2. What happens with the pattern close to magnet 1? The pattern close to magnet 2? The pattern changes around both magnets/magnetic objects.

This is really fun, I always keep magnets close at hand to play with. To stop making a mess, put the filins in a plastic sleeve and you'll always have something to play with! p

Edited September 13, 2007 by psw

[Mike Sulzer]

"Wouldn’t that mean that the magnetic field strength (flux) at the bottom of the coil play a role in the sound/output of a pickup?"

But let us look at where the flux is changing the most. The string gets magnetized over the pole piece. The field from the "string magnet" is strongest at the string and decreases as you get farther away. The pole piece modifies this field, slowing down the rate of decrease somewhat. The magnet below the coil has some effect, too, due to its magnetic permeability (that is, this field applied to the magnet causes small changes in its internal magnetic alignment). When the string vibrates, the changes in the field follow this same pattern, stronger near the string, weaker farther away. But the field from the permanent magnet is not part of this change. It did its job in magnetizing the string.

So in the equation you have the term d(phi)/dt. This says "rate of change of the magnetic flux". The magnetic flux is magnetic field through the coil times the area of the coil with allowances for the spatial variation of the field. So the ems (voltage) across the terminals of the coil depends on the rate of change of the flux. It is the sum of the voltages induced in each turn of the coil (series voltages add). The voltage from each turn depends on the change in flux through that turn. The flux changes most near the string. The part of the core closest to the string has the most effect modifying or amplifying the changing flux, and the magnet below has less effect.

[Geo]

The pickup bobbin rests directly onto the wood in the rout. The cover is screwd down, over the bobbin with two small, long screws between the polce screws. Those two screws hold both the cover in place and the pickup down. Whas that a good enough description ? I dunno...

I get it now... thanks!

So essentially, the bobbin hangs from the cover. The cover is screwed to the bobbin with screws between the polepieces. Now, that sounds like the "soapbar" style. But I'm hoping to use the dogear style, so that my pickups can hang in bottomless pickup routes (this will be a semihollow). I don't see the between-polepiece screws on a dogear pickup.

I can definitely figure it out, and I don't have to do it "the Gibson way". Just curious.

[SwedishLuthier]

Now, that sounds like the "soapbar" style. But I'm hoping to use the dogear style, so that my pickups can hang in bottomless pickup routes (this will be a semihollow). I don't see the between-polepiece screws on a dogear pickup.

I can definitely figure it out, and I don't have to do it "the Gibson way". Just curious.

Yes I was describing the soapbar mounting style. Sorry, didn’t really realize you were after the dogear style. I haven’t used dogears so I can’t help you with that one. They might actually come with some type of base plate, I dunno…

But let us look at where the flux is changing the most. The string gets magnetized over the pole piece. The field from the "string magnet" is strongest at the string and decreases as you get farther away. The pole piece modifies this field, slowing down the rate of decrease somewhat. The magnet below the coil has some effect, too, due to its magnetic permeability (that is, this field applied to the magnet causes small changes in its internal magnetic alignment). When the string vibrates, the changes in the field follow this same pattern, stronger near the string, weaker farther away. But the field from the permanent magnet is not part of this change. It did its job in magnetizing the string.

The flux changes most near the string. The part of the core closest to the string has the most effect modifying or amplifying the changing flux, and the magnet below has less effect.

Mike, have you measured where the flux changes the most? I’m asking out of curiosity, not to pick a fight. I’m trying to learn here. I have not measured, but I’m not totally convinced about all this. I would love to be able to measure the change in flux within the coil. That would really tell us something about what happens in a pickup.

So in the equation you have the term d(phi)/dt.

I think that it can also be interpreted as dΦ*df as f is the frequenzy (f=1/t). This would mean that the output is linear to the change in frequency and linear to the change in flux. Meaning we get a lesser and lesser output when the frequency goes down?

[Mike Sulzer]

"Mike, have you measured where the flux changes the most?"

No I have not, but one certainly expects magnetic fields to decrease with distance from the source. Maxwell's equations (which describe all of E&M) are really well proved. Understanding them was one of the things leading up to special relativity, and so on. In any case, one could make such a measurement approximately by partioning the coil into two or more sub coils along the core.

"Meaning we get a lesser and lesser output when the frequency goes down?"

Yes, that is right. I would look at it this way:

The voltage is proportioinal to d(phi)/dt. (derivative of phi with with respect to time). The equation for a sine wave of frequency f is sin(2(pi)ft). The derivative of this with respect to time is (2(pi)f)cos(2(pi)ft). This is proportinal to frequency, and so you get less at lower frequencies, and more at higher frequencies. The frequency response of the pickup is also modified by the properties of the circuit it is in, as I described above.

[Mike Sulzer]

Here is an illustration of how the flux decreases further from the string. Remember that funny kind of humbucker (stacked), that was never too popular? Where you had two coils wound on the core, one above the other? Those coils are connected out of phase to cancel the hum. But you still get signal, some signal, but not as much as you would like. If the flux did not decrease, the signal would cancel completely. The more modern stacked humbuckers mentioned above use a shield between the two coils, so you get less signal cancelation, and so more signal.

[psw]

Hey fellas, there must be something in the air at the moment....

In the sustainer thread, and at this particular time, there is quite a bit of discussion about these kinds of theories. Much of the theory about driver styles are directly related to pickup design. My unique design for drivers involve a "thin coil" and this was derived from experimentation. It is a design that through extensive experimentation, I found to have many advantages...but we have yet to be able to explain them through theory. Member Col is presently doing a lot of work in this area and a lot of this has been discussed lately in relation to "ideal coils" and such...

discussion like this....

Remember its not about 'how many layers' there are radiating out from the core.... it is about the flux generated by each individual winding - the optimal situation is that the flux from each individual winding surrounds all the other windings... this is more likely to happen as the bundle becomes more square - as soon as you start stretching it horizontally or vertically, you risk losing efficiency due to a drop in flux linkage.

may well be of interest or you may have ideas and information/knowledge that can extend our knowledge of such things further...

Take a look here...LINK

The idea that the top part of a coil will have more effect than the lower coils, would provide a lot of support for my "thin coil theories" which have all the driving coil as close as possible to the strings in a very shallow flat configuration. But I am not so sure it is in fact "true" (though, because it works and a lot of experimentation suggests it is superior for this application, something seems to be going on!)....

But let us look at where the flux is changing the most. The string gets magnetized over the pole piece. The field from the "string magnet" is strongest at the string and decreases as you get farther away. The pole piece modifies this field, slowing down the rate of decrease somewhat. The magnet below the coil has some effect, too, due to its magnetic permeability (that is, this field applied to the magnet causes small changes in its internal magnetic alignment). When the string vibrates, the changes in the field follow this same pattern, stronger near the string, weaker farther away. But the field from the permanent magnet is not part of this change. It did its job in magnetizing the string.

I can't really speak to the formula or describe where depth of coil comes into play. Col has suggested that the shape of the coil effects the degree of "flux linkage" between the windings...perhaps his recent efforts in coming to terms with this stuff could help here.

As to the "shape" of the magnetic field I think that I can speak. There does seem to be some misunderstanding here. A pickup's coil detects disruptions to it's permanent magnetic field. SL's suggestion of taking two magnets and metal filings will readily illustrate that the effect of one magnet on the field of another disrupts all of the fields, not just those closer to the disrupting magnet.

What I am propositioning is that the shape of the magnetic field, does influence the content of a signal, not because of the magnet's part in the electromagnetic circuit... "It did its job in magnetizing the string"....quite right...but the amount of the string that disrupts the magnetic field and the extent that it is disrupted is very much influenced by the "shape" of the field.

Anyway....it would be interesting to see if more could be elaborated on the idea of the upper part of the coil having more effect. It bring it slightly back towards topic...does the wide flat coil of a P-90 have more effect than the wide flat magnetic field it exhibits? Would the proposition of Fender like poles but a wide coil make a more powerful pickup, or would the fact that the outer layers of the coil are further from the core negate their closeness to the strings. Col has shown that a "square" shaped cross-section of windings is more effective...

Got to leave it htere for now, but will be looking on and invite you all to discuss with others at the sustainer thread if you have a mind too... pete

[Mike Sulzer]

"There does seem to be some misunderstanding here. A pickup's coil detects disruptions to it's permanent magnetic field"

I would say that the pickup's coil detects fluctuations (in time) of the magnetic field (through the coil). These fluctuations come from the vibrating magnetized string. If you change the permanent magnetic field inside the coil somewhere without changing the permanent field at the string, you have not changed the fluctuations at all, and so the pickup output is the same. The permanent field inside the coil and the fluctuating part do not interact*; the total field is just the sum of the two. When you take the derivative in Peter's equation you get the same thing if you consider the total field or just the fluctuating part because the derivative of a constant (the permanent field) is zero. That is:

d(phif)/dt and d(phif + phip)/dt are the same, where phif is the fluctuating flux and phip is the permanent or unchanging flux.

*Now this is very slightly approximate. You can alter the internal state of a magnet with a strong magnetic field. This happens with large currents as in a speaker with alnico magnets. This might be what you are thinking of. But the fluctuating field from the vibrating string is weak. That is why it takes 5000 turns of wire to do a good job of picking it up, and then you still have to amplify. So you can ignore the effect of the vibrating string affecting the strength of the magnet at the string frequency. The permanent field of the magnet is just huge compared to the fluctuating part.