FEMM uniform field for simulating rejection

[aquin43]

Some lua routines for FEMM for setting up a quasi unbounded work region containing a uniform magnetic field which could be used for simulating humbucker rejection. Based on www.femm.info/wiki/UniformField

There are two functions: mk_planarABC(rad_work, airmesh, B_uni) which sets up the workspace and rot_uf(angle) which can set up the angle of the field to the horizontal.

rad_work is the workspace radius, airmesh the mesh size and B_uni the field strength. If B_uni is omitted it is automatically set to zero. After the workspace is set up, the angle of the field to the horizontal can be set with rot_uf()

function mk_planarABC(rad_work, airmesh, B_uni)
-- Define a circular work area with an ABC boundary and a
-- uniform horizontal field of B_uni Tesla
-- Define the problem type. Magnetostatic Planar, Units of mm
-- Precision of 10^(-8) for the linear solver, 10 for
-- the depth dimension and an angle constraint of 30 degrees

-- Create a new Magnetostatics document to work on.

B_uni = B_uni or 0 -- can be called without B_uni

_rw = rad_work

newdocument(0)
mi_probdef(0, 'millimeters', 'planar', 1.e-8, 10, 30)
mi_makeABC(10,_rw,0,0,0)
mi_addblocklabel(0,_rw - 1)
mi_getmaterial('Air')
mi_selectlabel(0, rad_work - 1)
mi_setblockprop('Air', 0, airmesh, '<None>', 0, 0, 0)
mi_clearselected()

if(B_uni ~= 0) then
local mu_0 = 1.256637e-6
local Hc = 2 * B_uni/mu_0
mi_modifymaterial('u1',3,Hc)
mi_modifymaterial('u2',3,Hc)
mi_modifymaterial('u3',3,Hc)
mi_modifymaterial('u4',3,Hc)
mi_modifymaterial('u5',3,Hc)
mi_modifymaterial('u6',3,Hc)
mi_modifymaterial('u7',3,Hc)
mi_modifymaterial('u8',3,Hc)
mi_modifymaterial('u9',3,Hc)
mi_modifymaterial('u10',3,Hc)
end
end

function rot_uf(angle)
-- rotate the inclination of the uniform field created in
-- mk_planarUF() to angle
mi_selectlabel(_rw * 1.00, _rw * 0.15)
mi_setblockprop('u1',0,0,'<None>',angle,0,1)
mi_clearselected()
mi_selectlabel(_rw * 0.96, _rw * 0.29)
mi_setblockprop('u2',0,0,'<None>',angle,0,1)
mi_clearselected()
mi_selectlabel(_rw * 0.93, _rw * 0.42)
mi_setblockprop('u3',0,0,'<None>',angle,0,1)
mi_clearselected()
mi_selectlabel(_rw * 0.87, _rw * 0.56)
mi_setblockprop('u4',0,0,'<None>',angle,0,1)
mi_clearselected()
mi_selectlabel(_rw * 0.78, _rw * 0.67)
mi_setblockprop('u5',0,0,'<None>',angle,0,1)
mi_clearselected()
mi_selectlabel(_rw * 0.69, _rw * 0.80)
mi_setblockprop('u6',0,0,'<None>',angle,0,1)
mi_clearselected()
mi_selectlabel(_rw * 0.58, _rw * 0.89)
mi_setblockprop('u7',0,0,'<None>',angle,0,1)
mi_clearselected()
mi_selectlabel(_rw * 0.44, _rw * 0.98)
mi_setblockprop('u8',0,0,'<None>',angle,0,1)
mi_clearselected()
mi_selectlabel(_rw * 0.31, _rw * 1.04)
mi_setblockprop('u9',0,0,'<None>',angle,0,1)
mi_clearselected()
mi_selectlabel(_rw * 0.15, _rw * 1.07)
mi_setblockprop('u10',0,0,'<None>',angle,0,1)
mi_clearselected()
end


A stacked humbucker showing the excellent symmetry of this configuration:

[antigua]

Is it safe to say that so long as the pickup is symmetrical, the outcome of the model will be symmetrical? 

[aquin43]

Feb 28, 2022 1:05:58 GMT -5 antigua said:

Is it safe to say that so long as the pickup is symmetrical, the outcome of the model will be symmetrical? 

Probably. The questions are: How many degrees of symmetry are required? What happens when the pickup is not perfectly symmetrical, like a standard humbucker? How much asymmetry is acceptable?

[ms]

What an interesting idea: adding current to the material that establishes the equivalent of no boundary.  I see that his write up says to set the direction as well as the magnitude of Hc.  I do not see where you do that, and so I assume that this has defaulted somehow (or I missed it)?

If you subtract the uniform field from the result of, for example, the case you show above, and then examine it near the "boundary", then it should tend towards a simple result, the 2D equivalent of "All magnetic fields are dipole if you get far enough away."  This would allow testing the method, at least down to the limit where the result turns into numerical noise.

[aquin43]

Feb 28, 2022 10:35:56 GMT -5 ms said:

What an interesting idea: adding current to the material that establishes the equivalent of no boundary.  I see that his write up says to set the direction as well as the magnitude of Hc.  I do not see where you do that, and so I assume that this has defaulted somehow (or I missed it)?

If you subtract the uniform field from the result of, for example, the case you show above, and then examine it near the "boundary", then it should tend towards a simple result, the 2D equivalent of "All magnetic fields are dipole if you get far enough away."  This would allow testing the method, at least down to the limit where the result turns into numerical noise.

In mk_planarABC() the lua function mi_makeABC is used to set up the boundary which it does with default zero magnetisation and zero magnetisation angle. Then the Hc value is allocated to the ten materials u1 ...u10 that it creates. The workspace radius is allocated to a variable _rw  which is global by default so that it will be accessible to the angle setter rot_uf().

It seems that mi_makeABC() places labels for the materials it creates in a set of standard positions at fixed angles. The function rot_uf() selects these labels using _rw and the measured sin and cos multipliers for the angles. and the block properties of the materials are altered to include the angle of magnetisation.

Once the problem is set up, rot_uf() can be used either from the program or from the lua console and repeated analyses made if desired.

[ms]

Thanks, I understand this better now.  This tool complements the hardware tool I have for measuring sensitivity to a spatially nearly constant field:  a sawed off 5 gallon paint bucket with two coils wrapped around it  I have not used it in quite a while since it is not very convenient.

[aquin43]

Rather than trying to make a Helmholtz coil, I was thinking of using a small distant solenoid source to create a field of known divergence. It could be driven at a few hundred Hz and a synchronised very narrow band filter of some sort could be used to make the measurement. If the source was small and at a distance of 3.5m or 10 ft then the flux ratio across the 25mm width of a humbucker would be about -33dB... ( (1+25e-3/3.5)^3) - 1

----------------------------

Zollner remarks that the standard humbucker seems to have rejection than the stacked type. The magnet breaks the symmetry.

Pole mu 100, magnet mu 3.5, flux angle 45deg.

[antigua]

Mar 1, 2022 10:07:26 GMT -5 aquin43 said:

Zollner remarks that the standard humbucker seems to have rejection than the stacked type. The magnet breaks the symmetry.

Pole mu 100, magnet mu 3.5, flux angle 45deg.

That's pretty interesting. That also mean a humbucker with a ceramic magnet would be quieter also. 

[ms]

I think that idea would work well.  The filter would use ffts, although I would probably use a cross spectral technique rather than a simple power spectrum.

Oh yeah, a great hum detector if you increase the permeability of the material connecting the two coils.  I tried that some years ago in hardware without thinking it through first!  

Seth Lover's patent, U.S. Patent 2,896,491 (patentimages.storage.googleapis.com/db/ac/09/ef18558290da83/US2896491.pdf), claim five, seems to imply that the magnet helps complete the flux path and makes the pickup work better.  If it really did that to any significant degree, the pickup would hum badly!  Maybe I am misreading that claim.

[aquin43]

I think Seth Lover's "metallic magnetic return circuit" in claim No 5 is referring to the pole piece transferring flux from the magnet pole to the quite distant string.

The best Gibson humbucker would have been just two underwound Strat pickups side by side with staggered magnets to volume match the strings of the day. I wonder why they didn't just do that. It may have been that the overall cost of the 12 cylindrical magnets would have been greater than the one bar magnet. The adjustable poles were an afterthought from the marketing department apparently.

Yes, a ferrite magnet will restore the symmetry and will also reduce the unwanted coupling between the coils that serves only to increase the inductance.

[ms]

There is much more in that patent than I remembered.  I think claim 5 actually refers to the sidewinder pickup described in figures 11-13, which has end plates that tend to complete the circuit, except that part of the circuit is low permeability permanent magnets, and so I think this actually does not work as well as he describes it.  But again, maybe I misunderstand.

This is after he describes the pickup where each coil is for three of the strings, that is, like the split precision bass pickup from 1957 and on.  Since this patent was filed in 1955,  I wonder if Lover should be considered the inventor of the precision bass split pickup?  Did Leo Fender know about this patent application?

[aquin43]

Having discovered the init.lua file in the FEMM installation which reveals how the boundary is set up, I have condensed the code into a much more succinct form:

function mk_planarABC(rad_work, airmesh, B_uni)
-- Define a circular work area with a 10 layer ABC boundary and a
-- uniform field of B_uni Tesla. B_uni may be omitted and will
-- default to zero. Define the problem type as Magnetostatic Planar,
-- Units of mm Precision of 10^(-8) for the linear solver, 10 for
-- the depth dimension and an angle constraint of 30 degrees

-- Create a new Magnetostatics document to work on.

B_uni = B_uni or 0
_rw = rad_work -- make work radius globally available
newdocument(0)
mi_probdef(0, 'millimeters', 'planar', 1.e-8, 10, 30)
mi_makeABC(10,_rw,0,0,0)
mi_addblocklabel(0,_rw - 1)
mi_getmaterial('Air')
mi_selectlabel(0, _rw - 1)
mi_setblockprop('Air', 0, airmesh, '<None>', 0, 0, 0)
mi_clearselected()

if(B_uni ~= 0) then
local n = 10
local Hc = 2 * B_uni/uo
for k = 1,n do
mi_modifymaterial('u' .. k,3,Hc)
end
end
end

-----------------------------------------------------------

function rot_uf(angle)
-- rotate the inclination of the uniform field created in
-- mk_planarUF() to angle
local R, r, n, z
n = 10
R = _rw
for k = 1,n do
r = R*(1 + (2*k - 1)/(20*n));
z = r*exp(I*(90/(n+1))*k*Pi/180);
mi_selectlabel(re(z),im(z));
mi_setblockprop("u" .. k, 1, 0, "<None>", angle, 0, 1);
mi_clearselected();
end
end