Coil area x turns calculations

[Marco Pancaldi]

Hello,
I need to improve my knowledge about the subject:

- how to compute the coil area? I need to subtract the core/poles/magnets or not? (I guess yes not but not sure)
- I need to compute coil height?
- how is the relation between area x turns and output level (not changing magnetic circuit of course).

Thanks
m.p.

[copperheadroads]

Are you fimiliar with the coil estimator ?

[Helmholtz]

how is the relation between area x turns and output level (not changing magnetic circuit of course).

Because of the non-uniform spatial distribution of the magnetic flux, there is no simple relation between output level and coil area/turns.

PU output is the sum of the induced signal voltages in each turn. The signal voltages per turn vary strongly depending on distance to string and loop width.
Prof. Zollner found that the voltage per turn drops at least by a factor 6 from top to bottom in a Strat PU. A wider outer turn may produce 30% more voltage than an inner turn. So the upper, outer turns contribute most.
Generally turns voltage is not proportional to loop area.

[Mike Sulzer]

Because of the non-uniform spatial distribution of the magnetic flux, there is no simple relation between output level and coil area/turns.

A wider outer turn may produce 30% more voltage than an inner turn.

With a steel pole piece,the difference can be negligible since the higher permeability material carries nearly all the flux within it, and the flux that does escape is almost perpendicular to the coil axis and so contributes little.

This even more so for a high permeability ferrite core. For example, here is a FEMM simulation with an assumed material permeability of 500:

polepiecestringcontours.pdf

This is axisymmetric mode, right half of cylindrical pole piece is shown.

[Helmholtz]

Thanks, makes sense. If the primary AC flux is confined to the core, increasing loop area won't increase EMF. Generally very wide wire loops will produce less EMF/turn caused by the opposite phase returning flux portion.

(IIRC, Helmuth Lemme has been offering his high µ ferrite core PUs since decades.)

[David King]

I think OP's question is referring to hum cancelling of external junk signals, not the string signal so Number of Turns times the area of the average turn will need to include all area inside the coil unless different cores will have some effect on the background signal strength of external noise. The height of the coil is also presumably irrelevant to the calculations at hand. I would have thought that the turns closest to the core (inside-most turns) and closest to the top of the coil (nearest the strings) would have the largest signals. This would seem to be at odds with the Prof. Zollner data presented above. I suppose this will explain why thinner, wider coils like P-bass are so efficient compared to Jazz bass coils but clearly that effect is more from all the turns being closer to the strings rather than the wider turns area which leades to a much smaller effect overall.

[Mike Sulzer]

I think OP's question is referring to hum cancelling of external junk signals, not the string signal so Number of Turns times the area of the average turn will need to include all area inside the coil unless different cores will have some effect on the background signal strength of external noise. The height of the coil is also presumably irrelevant to the calculations at hand. I would have thought that the turns closest to the core (inside-most turns) and closest to the top of the coil (nearest the strings) would have the largest signals. This would seem to be at odds with the Prof. Zollner data presented above. I suppose this will explain why thinner, wider coils like P-bass are so efficient compared to Jazz bass coils but clearly that effect is more from all the turns being closer to the strings rather than the wider turns area which leades to a much smaller effect overall.

To simulate a hum source, move that little magnet further away and make it bigger. Both changes make the field lines spread out less, but the attached FEMM result shows that the pole piece still concentrates the flux within itself and creates a hole around it. With a high perm. pole piece, most of the hum flux is within it and so the same conclusions as for the string apply.
polepiecehum.pdf

[Joe Gwinn]

- how to compute the coil area? I need to subtract the core/poles/magnets or not? (I guess yes not but not sure)
- I need to compute coil height?
- how is the relation between area x turns and output level (not changing magnetic circuit of course).

Is this is for humbucking using a larger coil? I'll answer that question.

Single-coil pickup with iron core: The full form is to compute the area bounded by each and every turn (treat the turn as a closed curve), add all these per-turn areas, and multiply by the effective permeability of the core. The effective permeability is best determined experimentally, but will be two or three. With such a low permability, the effective permability will be larger close to the core than near the air.

Using a computer, one can do all 10,000 turns, but it's simpler to divide the actual coil into a finite number of layers, compute each layer by multiplying a representative turn by the number of turns in that laye, and sum the layes as before.

Larger air-core cancellation winding: Compute each and every turn as fro the pickup coil, and add the turn areas.

For hum cancellation, the two area-turns products must be equal. One uses computations to get into the ballpark, and then experiments away.

There were a number of threads on this when a patent was issued on this some years ago.