Reducing mag. field hum with air and ferrite core coils

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In this discussion we will look at reducing hum in the pickup signal from magnetic fields using one or more coils that can have either air or ferrite cores, depending on circumstances discussed later.  First, we need a measurement system.  This is necessary to get meaningful numerical results, especially because hum from both electric and magnetic fields is present, and the methods for reducing them are very different.


I call the thing in the picture a field bucket.  Reminder: magnetic fields are caused by currents [charge in motion], and coils are useful for various purposes.

T


The two spaced coils are called a Helmholtz coil and are usually used in applications requiring a nearly constant field inside.  The guitar body with pickups and cancelation coils is too big, and so I turn it on its side and put the guitar body and measurement electronics about ten feet away.  The axes of the coils point towards the field bucket.  The neck is removed and replaced with a small piece of wood (such as used in finishing a body) and mounted in a heavy drill press vise.

This is the guitar used for the tests shown first:




The P-90 pickups are under-wound to give a sound similar to PAF humbuckers.

The field bucket is driven with a 170 Hz square wave at about 15 volts RMS; its resistance is about 200 ohms.  A square wave is used to give a distinctive pattern of harmonics.  First, look at the time domain response of the output of the neck pickup:



The pickup sees time rate of changes in the flux density, and so we get output at the transitions of the square wave.  The bandwidth of the pickup rounds what would otherwise be sharp spikes.  Disconnecting the current at the field bucket makes the distinctive waveform disappear, and so we know we are looking at the magnetic interference from a source we have created.

Now for the frequency domain:




We have pickup from our source, 60 Hz and harmonics, and also other unknown sources.  The 170 Hz from the square wave is the biggest signal, and it is marked with a horizontal blue line.  The first four harmonics are marked with vertical dashed lines to identify them; the higher harmonics are obvious.  A square wave should have only odd harmonics because of its symmetry, but a weak 2nd harmonic is visible, resulting from imperfections somewhere in the system.  The harmonics fall rapidly above 3 KHz because of the bandwidth of the pickup.  There is almost no 60 Hz, and the harmonics increase, reaching a maximum at 300 Hz, falling rapidly at higher frequencies.  For cancellation, we should not worry about anything above about a KHz.  The control cavity in the guitar is shielded; however, we expect the 60 Hz and harmonics to be the result of both electric and magnetic fields.

The next post looks at the effect of an air core cancellation coil.

[stratotarts]

What is the guitar configuration? Is this an RWRP pickup pair in the middle position? With no cancellation coils installed?

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Mar 7, 2024 11:37:45 GMT -5 stratotarts said:

What is the guitar configuration? Is this an RWRP pickup pair in the middle position? With no cancellation coils installed?

NO, no RWRP.

[stratotarts]

Aha, so it's a reference point for the forthcoming posts. Got it.

[ms]

Yes, so the noise cancellation coil looks like this:




Underneath the cover (on the right) is a bobbin with 500 turns of # 41 wire.  That is wrapped in copper shielding tape that is grounded.  More details on the coil later, but for now here is the spectrum with the cancellation in the circuit:



The line at 170 Hz is 30 db lower; the line at 510 is only about 22 db weaker, but it seems that the hum cancellation is successful.  The hum harmonic at 180 is down by less than 10db. Why? The first possibility is that the residual is the result of an electric field, which would not have been canceled by this method. It could also be caused by a hum source that is very close, and so the pickup and canceling coil do not see the same strength field.  I suspect that the first is more likely.  The line at 60 Hz has increased; maybe there was a change, such as a motor turning on.  I do not think it is a result of the cancellation coil; we will see later that this did not happen in the equivalent measurement for the bridge pickup.  So we see why we need to make our own hum source to get accurate measurements.

[stratotarts]

It's possible your generator is radiating RF.

[ms]

So next we look at the spectrum of the bridge pickup without the cancellation coil.  However, it is a bit more complicated than that.  The bridge pickup has more turns that the neck pickup, but we want to use the same air core coil since these things are a pain to make and occupy significant space.  So we make a core using a small ferrite rod as a core.  It is put in series just with the bridge pickup so that it provides the additional necessary opposite hum pickup.  That is, we use an additional coil to make the level match what the air coil coil provides. So if we look at this series combination the 170 Hz line should have the same strength as that of the neck pickup alone.




So it does within about .1 db, a bit lucky to get that close.

Here is the plot with the cancellation in place:



At 170 Hz this is not as good as expected.  I do not know why, but cancellation requires both amplitude and phase matching.  This will require some more work to understand.

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Mar 7, 2024 16:14:10 GMT -5 stratotarts said:

It's possible your generator is radiating RF.

Is this in reference to the increase in 60 Hz?

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Here is a reference to a paper that provides complete information about designing coils for sensing magnet fields, both coils using air as a core and also those using a magnetic material:
www.tumanski.x.pl/coil.pdf

[stratotarts]

Mar 7, 2024 16:46:09 GMT -5 ms said:

Mar 7, 2024 16:14:10 GMT -5 stratotarts said:

It's possible your generator is radiating RF.

Is this in reference to the increase in 60 Hz?

<abbr>No, the 510 Hz. You said it was unexpectedly strong. If you don't think so, I'll go along with that.

[ms]

Mar 7, 2024 17:42:30 GMT -5 stratotarts said:

Mar 7, 2024 16:46:09 GMT -5 ms said:

Is this in reference to the increase in 60 Hz?

<abbr>No, the 510 Hz. You said it was unexpectedly strong. If you don't think so, I'll go along with that.

Well, I am not getting as good cancellation at 510 Hz as 170 Hz.  I suspect that this is a phase issue rather than amplitude.  When you are trying to cancel signals that are the outputs of second order low pass filters, the phase matching can be a problem at lower frequencies than the amplitude.  Not sure that this is the case here, and the fact that the pickup coil has effective L and R that vary with frequency make this a bit difficult.  I think this will take a couple of days to figure out.

[antigua]

Could the Ilitch sized dummy coil be made a lot smaller with a high permeability ferrite core? The air core dummy with a lot impedance has to have a lot of area, but I'm thinking with a ferrite core, maybe if could be really small and still have low impedance. 

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Mar 9, 2024 4:01:18 GMT -5 antigua said:

Could the Ilitch sized dummy coil be made a lot smaller with a high permeability ferrite core? The air core dummy with a lot impedance has to have a lot of area, but I'm thinking with a ferrite core, maybe if could be really small and still have low impedance. 

That is the question that I wanted to answer, and I will go into details later. But here is a summary:  Ferrite sensing coils require a long thin piece of the material (such as a rod) to be very sensitive.  Look at the ferrite antenna in an old AM radio if you have one lying around, or read that paper I referred to above.  Here the length of the rod is restricted by the thickness of the guitar body.  First consider a strat pickup, not very sensitive.  You can wind enough wire on a rod short enough to fit in the guitar to cancel the hum but the inductance is too high.  You can use multiple coils: if you cut the number of turns down by a factor of N (for example 2), then the inductance goes down by N^2 (for example  4) and if you put N (for example 2) of these in series, you have kept the sensitivity the same, but cut the inductance by a factor of N (for example 2).  For a strat you need 4 or 5 coils.  This works; I got a cheap "almost strat" body and mounted the coils in holes drilled under the pick guard.  There is enough room since the control route is not nearly as big as the area of the pick guard.  I also implemented the ferrite technique on a Warmoth soloist body by mounting four cols in the extra large control cavity, drilling the coil locations just a little bit deeper.  (There are details I will cover later.)  A P-90 pickup with the standard 10,000 turns is about 9 db more sensitive than a strat pickup.  This would be too many coils, although if you really wanted to do it this way, I suppose you could.  As difficult as the large flat air core coils are to work with, it is still the better way to go for a P-90.  For example, it has lower inductance than so many of the small ferrite core coils in series.

So the really brief answer is that Ilitch is right if you want a single technique that can be adapted to any pickup.

[stratotarts]

Side note: Impedance is moot if you have an active preamplifier and a mixer for both the pickup and balance coil. Because then, there's no need to put them in series or parallel combination that would introduce the need for an undesired pickup impedance or some unwieldy passive compensation. Also the set input gain to the mixer, would dramatically loosen constraints on the balance coil.

I do fully understand the desire to avoid active electronics in a guitar.

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Mar 9, 2024 13:48:43 GMT -5 stratotarts said:

Side note: Impedance is moot if you have an active preamplifier and a mixer for both the pickup and balance coil. Because then, there's no need to put them in series or parallel combination that would introduce the need for an undesired pickup impedance or some unwieldy passive compensation. Also the set input gain to the mixer, would dramatically loosen constraints on the balance coil.

I do fully understand the desire to avoid active electronics in a guitar.

I devised a "half active technique" quite a while ago, where the cancellation coil goes to the input of a source follower, and the pickups are removed from ground and connected to the output of the source follower.  The cancellation coil is just another pickup, but you should make it very slightly more sensitive.  I suppose that you could argue that once you have introduced active electronics into the guitar,  you might as well go all the way put a preamp on the pickups as well.  But you could also argue that the source follower can be low current for long battery life, and when the battery goes dead, the guitar still works, and all you lose is hum cancellation.

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So now it is time to understand how a cancellation coil in series with a pickup works.  I do not yet understand all the details, but enough to do a good job.  The top part of the figure below illustrates a simplifying principle:  if you only have impedances in series with the noise voltage sources, then achieving cancellation does not depend on what those impedances are or their relative values, nor on the load impedance.  Of course, we want the impedances in series with the cancellation coil to be low value compared the in the pickup since we do not want to influence the sound.

So what do you do if you have a coil capacitance that goes across the pickup, as shown in the bottom part of the figure?  This is a situation where you can find the Thevenin equivalent, where for analysis, you replace the network you have with another that consists of a voltage source, Vth, that depends on the elements in the circuit, in series with an impedance, Zth, that also depends on the elements in the circuit.  So then you have to find circuit element for the cancellation circuit such that when they are put in the circuit, its Thevenin equivalent voltage is the same as that of the pickup, that is, same magnitude versus frequency, but opposite phase.  It is not assured that this is possible in all cases, but you certainly can do a good approximate job if you only need good results over a limited frequency range.  In fact, you do not have to do any actual analysis.  You can examine the circuit, do some arithmetic, and try things until you get something that works well enough.

Later, we look at the result of this process.

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So here is the circuit from the previous post with the adjustment network in place.


The first common sense thing to do is to get rid high frequencies from the cancellation coil that you do not need. Maybe they can cause trouble.  Ch dos this; the value was chosen while recognizing that it might have some effect at frequencies we care about, but also recognizing that the other vales we choose will take the into account.  The next thing to do is to get the low frequency cancellation working as well as possible with the resistor Ra.  In this case the unadjusted correction voltage is a bit high, and so we a reduce it with one resistor.  If it were a bit low, a slightly more complicated network would be necessary.  The variable resistor for Ra is left in the circuit since a small readjustment might be necessary after the next step.  It is surprising that even as low as 170 Hz there is a phase error.  We know it is phase because we can measure the magnitudes of the pickup and cancellation coil voltages, noting that their difference is less than the measured residual.  I suspect that this caused by eddy currents excited in the pole screws excited by the test B field.  In any case Cp shifts the phase and improves the cancellation at 170 Hz.  It also hurts the cancellation at higher frequencies, but this can be improved by Rs.

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Before proceeding, let's look at the test results from a humbucker, measured the same way as the pickup/cancellation coil.  i went looking around for a humbucker, and the first one I found is a Seymour Duncan Jazz neck (SN2n).  The first plot is the measurement from one coil.  The second is for the two coils in series, that is, hum-canceled.  The actual signal output is about 6 db more than that of one coil, and so six db must be added to the db differences on the two plots to get the degree of cancellation.

The pickup parameters are 3.722 H, 7.21 K at 100 Hz.  The individual coils are 1.6226 H at 3.54 K and 1.6208 H at 3.67 K.  This is remarkably well matched in inductance, although this is achievable with careful turns counting.  The resistance measurements are not so close since it is not possible to wind two coils in exactly the same way, even if the turns counts are the same.  Also achieving such close inductances requires careful matching of the slugs and screws; that is materials and lengths must be carefully selected.  So, given such good matching, how good is the cancellation?











It looks like we have a bit less than 50 db of hum reduction at 170 Hz, and significant reduction over the whole useful signal bandwidth (about 5 KHz).

A very well engineered and manufactured pickup!