Bill Lawrence Microcoils, Analysis & Review

[antigua]

wildepickups.com/Wilde_Bill_s_MicroCoils.html

Bill Lawrence Microcoils

Bridge MC-A SL
- DC Resistance: 7.406K ohms
- Measured L: 1.462H
- Calculated C: 69pF (79 - 10)
- Gauss: 600G (AlNiCo)

Middle MC-A SM
- DC Resistance: 7.073K ohms
- Measured L: 1.430H
- Calculated C: 71pF (81 - 10)
- Gauss: 600G (AlNiCo)

Neck MC-A SN
- DC Resistance: 6.894K ohms
- Measured L: 1.398H
- Calculated C: 73pF (83 - 10)
- Gauss: 600G (AlNiCo)

Bridge unloaded: dV: 9.3dB f: 14.8 kHz (black)
Bridge loaded (200k & 470pF): dV: 6.5dB f: 5.36kHz (blue)
Middle unloaded: dV: 8.5dB f: 14.8 kHz (red)
Middle loaded (200k & 470pF): dV: 6.5dB f: 5.36kHz (green)
Neck unloaded: dV: 8.5dB f: 14.8 kHz (pink)
Neck loaded (200k & 470pF): dV: 6.5dB f: 5.36kHz (gray)

Coil height incuding bobbin: 0.2185", without bobbin: 0.1375"





I've been wanting to look at Bill Lawrence Microcoils for a long time, because arguably they're a superior single coil design, although the way the product was implemented might not make then a desirable to some.

The superior aspect of the design is that most of the coil is placed near the string. The bobbin is very short and flat, only 0.12" tall, where as a typical Strat pickup coil is closer to 0.44", and a PAF bobbin about 0.22". Conforming to Faraday's Law, each turn of wire is responsible for generating a voltage as the magnetic field from the strings passes though them, which when combined in series as a coil of many turns, creates a sum voltage. If those turns of wire are farther away from the strings, the magnetic field from the moving guitar strings is weaker, and so the voltage for those turns is smaller. A typical Stratocaster or Telecaster pickup has a rather tall coil, so tall that the turns of wire further from the strings don't contribute much to the voltage. The turns of wire at the very bottom of the coil are essentially dead weight, increasing the inductance without increasing the output. The short, flat coil is therefore more efficient, more output for less inductance (and capacitance). Lace Sensor pickups are essentially Microcoils from this standpoint. In fact, the reason a PAF style humbucker is so much louder than single coil is not just because the pickup is wider, but because the two coil layout has the effect of ultimately placing more loops of wire closer to the strings.

But what some guitarists might not like is that Bill Lawrence made his Microcoils very bright pickups by not putting very many turns of wire on the small coil, possibly due to the space restrictions. The result is a very low inductance of only 1.4 henries, where as ~2.4 henries is more common for a Strat pickup. I also get the sense, based on the more conventional "Keystones", that Bill Lawrence liked brighter pickups in general.

One reason this design might not have been pursued more by other pickup makers is that it's not as simple to fabricate. Rather than having the coil former and pickup base all in one piece, as is typical, the coil former has to be a distinct section from the base, so as to be nested up inside the pickup cover. You can see from the pictures below that the Microcoil has a shorter fiberglass bobbin that is suspended above the base plate by a combination of the AlNiCo pole pieces and a black plastic retainer piece. The lead wires are soldered directly to the fiberglass bobbin, and there is very little space to work with since the coil comes right up to the edge of the bobbin. Were this geometry easier to construct, the design might have been more readily copied.

The Microcoil is offered with screws or AlNiCo pole pieces. I bought the AlNiCo set. They don't say what grade of AlNiCo is used, but they appear to be as tall as typical Strat AlNiCo pole pieces, and fully charged they measure similar to AlNiCo 2. They have no stagger and are perfectly flush with the pickup cover. The covers are similar to the Keystones, with a very rounded edge, similar to the vintage Bakelite pickup covers. I suspect these pickups are not wax potted due to how clean the are. I'm interested to see how microphonic they are or are not, as a result. The impedance plot shows that all three coils are all remarkably alike. The middle pickups is RW/RP, but the neck and bridge pickup are interchangeable.

On the sides, there is a rivet that is flattened on the bottom, but not the top. A screw holder the base to the plastic spacer piece inside, and it that screw is remove, the base plate can be carefully pried away from the two rivets on the sides.

In the pics you can see a manufacturing defect, one strange of wire looped around one of the AlNiCo pole pieces instead of the bobbin.


~*~*~


This plot shows a comparison of the Microcoil neck and a Fender Pure Vintage '56, with the exciter coil place in the same spot above both pickup, and is shows that the output is effectively identical, which is the real hat trick of the Microcoil. The 1dB difference could be attributed to difference in bobbin thickness, which causes the exciter coil to be a tiny fraction of an inch nearer or further from the surface of the coil itself.







I'm planning to put these pickups into a 12 string Strat. The 12 strings seems to work better with really bright pickups, and it looks like here I have a pickup that is very bright, with an output that is on par with any other Strat pickup. It's definitely a unique pickup. I wish the company would consider making a Microcoils with a more standard inductance target, such as 2.4 henries.













Comparing the Fender and the Microcoil output levels, with Ken Willmott's integrator device pictured kenwillmott.com/blog/

[roadtonever]

I used to own a set of microcoils in the steel pole version. I really miss them and I'm thinking about buying another set. Especially the neck pickup sounded amazing, very lively and responsive to how you play in a gratifying way. I think it's down to the combination steel pole configuration plus low wind. They weren't significantly less output than standard singlecoils and seemed to take gain better. No doubt Bill did his homework. At the same time I think the alnico microcoils and keystones were made to appease vintage enthusiast, not necessarily his best work.

[roadtonever]

BTW if you did wonder what I meant with "they take gain well":
soundcloud.com/amund-blix/microcoils_dry

[gckelloch]

Hey, nice review Antigua. I think the poles are some type of AlNiCo II. I didn't know they could be opened up without being destroyed. AFAIK, Wilde pots all coils. They aren't necessarily brighter than Fender pickups, though. Maximum brightness is really in the 3-3.5kHz range. As you see, the resonance peak is easily above that with a typical load, and the strong note fundamentals from the very thin 44~45AWG wire gives them more warmth than typical Fenders. It might be interesting to try placing (or taping in) a long nail along each side of the poles under the coil of the bridge MC to see if it significantly increases inductance. Maybe place several nails in there and measure it after adding each one?

Bill had discussed using Permalloy back when he was designing the Microcoils. I think the core inserts and pole screws in the Nd-powered MC's are probably Permalloy, so there isn't much high-end roll-off. I find the pole screws invaluable for adjusting individual string timbre per position.

[roadtonever]

I'm trying to understand how the thin wire would increase fundamentals. Do the thin bobbins close to the strings affect the magnetic field or is that a constant? On a different note EMG claims a low ratio of resistance to inductance increases the low end of their pickups but I'm not sure which parts of the design influences that.

[gckelloch]

My understanding is it's like how microphones with larger diaphragms have a stronger proximity effect. The total coil density close to the strongest magnetized portion of the string increases the stronger string vibration voltage more than the weaker ones. Those are the note fundamentals and first few harmonics. Thinner wire also creates a smoother/wider Q due to more consistent impedance. A Permalloy core would normally increase the coil inductance a lot more than AlNiCo, but Bill had told me Nd can actually counter that. DI recordings of my Nd Microcoils sound warmer and less bright than the 42AWG SC's DI recordings I made in the same guitar to the point that they sound very well-balanced without going through a guitar amp sim, and would make very nice uncolored clean DI tracks. Dirty tones would at least need some high-end filtering to sound "good".

The EMG claim probably has to do with the core alloy. Bill once wrote essentially that a "soft" (Fe) core increases the lows (the statement was lost when the Wilde-gate boards crashed some years ago). I assume that's because while the coil inductance increases, strong eddy currents roll off the highs. I'm not sure if that's the same as increasing the lower note harmonics (stronger string vibrations) or the bass vs treble range. I think Permalloy increases the whole frequency spectrum much more evenly due to very high permeability but low coercivity, but don't quote me on that. All this from a guy with a "...toxic frame of mind that prevents you (me) from receiving social value that's otherwise readily on tap." Aha.

[aquin43]

Apr 29, 2021 13:58:03 GMT -5 gckelloch said:

My understanding is it's like how microphones with larger diaphragms have a stronger proximity effect. The total coil density close to the strongest magnetized portion of the string increases the stronger string vibration voltage more than the weaker ones. Those are the note fundamentals and first few harmonics.

The analogy with the microphone doesn't hold at all - the physics are completely different. In the case of the pickup, you are describing a non-linear process, more sensitive to large movements than to small. How would reducing wire diameter bring this about?

Read the pickup sections of the Gitec Book and ignore the commercial pickup gurus.

[gckelloch]

More thinner wire can simply be fit into the same space as thicker wire, just like more finer sand can fit in the same space as coarse sand. So there's essentially 2x the amount of 45AWG wire within the same space as 42AWG wire. The gaps are more filled in. I think what happens is the increased density emphasizes the stronger vibrations more than the weaker ones at the same distance from the strings as if the coil is actually closer to the strings.

Yes, I generally ignore pickup gurus. Say, that's a lot of info to weed through in that book. Which part pertains to this topic?

[aquin43]

Apr 30, 2021 16:55:44 GMT -5 gckelloch said:

More thinner wire can simply be fit into the same space as thicker wire, just like more finer sand can fit in the same space as coarse sand. So there's essentially 2x the amount of 45AWG wire within the same space as 42AWG wire. The gaps are more filled in. I think what happens is the increased density emphasizes the stronger vibrations more than the weaker ones at the same distance from the strings as if the coil is actually closer to the strings.

Yes, I generally ignore pickup gurus. Say, that's a lot of info to weed through in that book. Which part pertains to this topic?

I think that your intuition is leading you astray.  Section 5 of the book will give you enough background. Section 5.10 deals with the signal transfer from string to coil.

Generally speaking, the interaction between pickup and string is localised over a short length of the string. The different harmonics are represented on the string by wavelengths that get shorter as the harmonic number increases. The very highest harmonics are lost because they fit so completely into the pickup sensing window that they cancel themselves out.

The wider the window, the lower the harmonic where this process starts. Except for the pole piece, which more or less controls the window width, one might expect that going closer to the string would sense from a narrower window - so more higher harmonics.

[gckelloch]

No, man. It's a proximity-based thing. The lower to upper harmonic strength increases when any pickup is raised closer to the strings because the stronger vibrations become more emphasized compared to the weaker ones, same as with a microphone. It is indeed the same basic function.

Microcoils have the same aperture as Fender SC's. The magnetic aperture does spread a pickup is lowered, but it also weakens exponentially around the edges as the flux lines become more horizontal, so it's really just the coil width that determines the aperture window, unless there are also vertically aligned magnets outside the coil or something that increase power in the edges of the coil.

Aperture induced harmonic cancelations start at a specific range for each string and follow corresponding octaves i.e if it starts in the 4kHz range on one string with a given aperture, it would start in the 1kHz range at 2x the aperture. There is some increase in lower to upper harmonic strength for wider apertures, but it's much less significant than the cancelations.

I'll read back over that section and get back on this.

[ms]

May 1, 2021 10:47:03 GMT -5 gckelloch said:

No, man. It's a proximity-based thing. The lower to upper harmonic strength increases when any pickup is raised closer to the strings because the stronger vibrations become more emphasized compared to the weaker ones, same as with a microphone. It is indeed the same basic function.

Microcoils have the same aperture as Fender SC's. The magnetic aperture does spread a pickup is lowered, but it also weakens exponentially around the edges as the flux lines become more horizontal, so it's really just the coil width that determines the aperture window, unless there are also vertically aligned magnets outside the coil or something that increase power in the edges of the coil.

Aperture induced harmonic cancelations start at a specific range for each string and follow corresponding octaves i.e if it starts in the 4kHz range on one string with a given aperture, it would start in the 1kHz range at 2x the aperture. There is some increase in lower to upper harmonic strength for wider apertures, but it's much less significant than the cancelations.

I'll read back over that section and get back on this.

The aperture is not determined by the width of the coil.  I do not see why you are thinking this, but it cannot be true.

[aquin43]

May 1, 2021 10:47:03 GMT -5 gckelloch said:

No, man. It's a proximity-based thing. The lower to upper harmonic strength increases when any pickup is raised closer to the strings because the stronger vibrations become more emphasized compared to the weaker ones, same as with a microphone. It is indeed the same basic function.

Microcoils have the same aperture as Fender SC's. The magnetic aperture does spread a pickup is lowered, but it also weakens exponentially around the edges as the flux lines become more horizontal, so it's really just the coil width that determines the aperture window, unless there are also vertically aligned magnets outside the coil or something that increase power in the edges of the coil.

Aperture induced harmonic cancelations start at a specific range for each string and follow corresponding octaves i.e if it starts in the 4kHz range on one string with a given aperture, it would start in the 1kHz range at 2x the aperture. There is some increase in lower to upper harmonic strength for wider apertures, but it's much less significant than the cancelations.

I'll read back over that section and get back on this.

Your intuition is indeed leading you astray. I presume that you are referring to the proximity effect in pressure gradient mics. This is a function of the changes in the sound amplitude pressure gradient with distance from the source. In the far field, the amplitude pressure gradient is small. In the near field, where the wavefront is curved, the amplitude pressure gradient becomes large. It is a function of the frequency (wavelength) and distance so the effect is more pronounced at low frequencies resulting in a bass boost for close mics. Note that it is a frequency dependent effect. The mic does not differentiate between small and large amplitudes. If it did, it would distort the sound.

There is no corresponding effect for pickups. The transmission of the magnetic field from point to point happens at the speed of light. There are no frequency dependent gradients at audio frequencies.

The pickup aperture is determined largely by the poles, even for quite low permeability poles such as the Fender magnets.

[gckelloch]

Ah, so the proximity effect in a mic is really wave dispersion dependent, and the freq at which it starts to occur does appear to increase with larger diaphragms. For a pickup, the difference in the voltage swing is greater for larger than smaller string vibrations when the string is closer to the coil, although some higher harmonic level fluctuation occurs as they change in distance from the coil while oscillating on top of the lower ones.

I'm not sure how to fully explain it and I can't find any pertinent test of this in the book chapters you suggested, but I think the increase in Microcoil fundamental note strength is due to how more winds within the same space up closer to the string capture more of the exponentially stronger magnetic string vibrations compared to the exponentially weaker vibrations further from the string. I guess it is the combination of both factors that produces the result, but it is still a proximity-based function. Either way, the proof is in the pudding. Microcoils will produce stronger lower to higher harmonics than 42AWG pickups with the same magnets. It's the wire gauge, coil dimension, and proximity to the strings. Again, that is my understanding, and I don't have more to add on it.

I'm sure you understand that a wider coil will have a wider sensing aperture than a thinner coil, assuming the magnetic aperture is also wider? BTW, cancelations within a given aperture would actually increase with higher harmonics, rather than just per octave, as more phase-opposed string vibrations fit within it. I assume that's why wider apertures have more high harmonic roll-off.

Loss of highs when certain pickups are moved away from the strings is likely due to the design i.e. magnetic circuit within a coil size dimension. That stuff wasn't fully understood until Willi L Stitch (RIP) hit the scene.

[gckelloch]

After reading more about mic proximity boost, I can see how it's not the best analogy. Incidentally, we determined over at the Wilde-gate forum that the Nd Microcoils must have wire ~1 gauge thinner than the AlNiCo versions, so they'd have even stronger fundamentals. Not sure exactly why the discrepancy, but the Nd version coils were developed after the AlNiCo version coils, even though the Nd's were released first.

[aquin43]

Antigua, is it possible to repeat one of the measurements with the pickup upside down to get a feel for the ratio of string flux at the top and the bottom of a normal coil. I have done some simulations in 2D space which would give the short coil roughly 42% of the flux in the whole coil. The 3D percentage may well be higher, in fact, the measured resistance implies that the number of turns is not that much greater than normal implying a much higher percentage.

[gckelloch]

Antigua hasn't been active for almost a week now, so I hope he's OK. I'm curious to learn how you do those simulations, aquin43. What's the software app? 42% of the flux from the top sounds about right considering the inverse-square law and the potential contribution from within the poles.

Not sure I understand correctly, but these coils have nearly half the winds of a ~6k Ohm 42AWG Srat coil -- the DCR measures of course being higher because of the 44~45AWG wire. The pickups have the same wind count but measure differently only because the bobbins are progressively wider from the N to L pos to match the string spacing.

There's a type of "Magnetic Viewing Film" available that reveals the flux lines of magnets. One could video a pickup through the film being driven by a string or whatever and then slow the video down to see what's actually happening compared to a simulation.

[roadtonever]

May 1, 2021 5:41:39 GMT -5 aquin43 said:

The wider the window, the lower the harmonic where this process starts. Except for the pole piece, which more or less controls the window width, one might expect that going closer to the string would sense from a narrower window - so more higher harmonics.

Top notch info. It's fascinating how the shape, strength and directionality of the magnetic field can affect the transfer of the oscillating strings. Because in such a system those variable have to affect the distribution of harmonics of the notes that will the reach the amp. Take away the magnet and there is no sound. With a highly directional field upper harmonics are cancelled out, with a small window lower harmonics are not fully captured.

It's as interesting as changing the tone with varying external loads but far more difficult to figure out and I'm still learning.

[gckelloch]

This app should clear up how the magnetic and/or coil aperture width, as well as the pos along the string, etc affects harmonics, but it doesn't address the affects of proximity and coil density: www.till.com/articles/PickupResponseDemo/index.html

Here's what makes sense to me about string proximity and aperture. The flux lines come out the top of the pole in a funnel shape. The flux lines around the edges of the field hit the string more straight on when that pole is closer to the strings. Those same lines would then hit the string at more of an angle when the pole is further from the string, therby contributing less to the total pickup output. The total magnetic aperture power might then acually become slightly thinner, but I doubt it makes much differnce in magnetic aperture either way. Raising a pole screw within a magnetic insert may have some audible affect on aperture with regard to the total length of the pole, but I think the effect on note timbre is less sigificant than changing the coil height itself has. I only wish BL was here to clear this up, but I know someone who would have opinion on this over at Wilde-gate.

[aquin43]

May 4, 2021 22:04:12 GMT -5 roadtonever said:

May 1, 2021 5:41:39 GMT -5 aquin43 said:

The wider the window, the lower the harmonic where this process starts. Except for the pole piece, which more or less controls the window width, one might expect that going closer to the string would sense from a narrower window - so more higher harmonics.

Top notch info. It's fascinating how the shape, strength and directionality of the magnetic field can affect the transfer of the oscillating strings. Because in such a system those variable have to affect the distribution of harmonics of the notes that will the reach the amp. Take away the magnet and there is no sound. With a highly directional field upper harmonics are cancelled out, with a small window lower harmonics are not fully captured.

It's as interesting as changing the tone with varying external loads but far more difficult to figure out and I'm still learning.

I wrote that, but I wish I hadn't. It was meant as an illustration of where intuition can lead. One might expect all sorts of things but there is actually no evidence that the pole aperture varies with distance to any significant degree. Certainly not enough to affect the tone. The pickup is very non-linear and generates its own harmonics which increase as the distance to the string is reduced. This distortion is not distinguishable as such because the individual strings hardly interact at all so their tones don't intermodulate and intermodulation is the sure sign that tells the ear that there is distortion present.

[ms]

May 4, 2021 22:27:40 GMT -5 gckelloch said:

This app should clear up how the magnetic and/or coil aperture width, as well as the pos along the string, etc affects harmonics, but it doesn't address the affects of proximity and coil density: www.till.com/articles/PickupResponseDemo/index.html

Here's what makes sense to me about string proximity and aperture. The flux lines come out the top of the pole in a funnel shape. The flux lines around the edges of the field hit the string more straight on when that pole is closer to the strings. Those same lines would then hit the string at more of an angle when the pole is further from the string, therby contributing less to the total pickup output. The total magnetic aperture power might then acually become slightly thinner, but I doubt it makes much differnce in magnetic aperture either way. Raising a pole screw within a magnetic insert may have some audible affect on aperture with regard to the total length of the pole, but I think the effect on note timbre is less sigificant than changing the coil height itself has. I only wish BL was here to clear this up, but I know someone who would have opinion on this over at Wilde-gate.

Tillman assumes the aperture is the pickup width.  He has hedged on that a bit in the last few years.  Assuming something does not clear up anything.

The string is a high permeability very elongated object, and so the string magnetization is along its length.  The direction must switch over the pole.  This means that the necessary field from the string magnetization pointing along the axis of the coil is almost entirely over or very near the pole.  You cannot get much signal from anywhere else on the string.  aquin43 showed that the magnetization  pattern of the string has a high degree of symmetry in the direction around the string.  He showed that the magnet can be removed from below the string and moved 90 degrees so that the field comes in from the side without changing the output of the pickup significantly.

[roadtonever]

May 5, 2021 6:02:42 GMT -5 aquin43 said:

The pickup is very non-linear and generates its own harmonics which increase as the distance to the string is reduced.

Ignoring the filter shape caused by the RLC interactions, is the non-linearity not caused by:
1. The requirement of string movement to generate voltage
2. The magnetic field cant be 100% uniform

May 5, 2021 6:02:42 GMT -5 aquin43 said:

This distortion is not distinguishable as such because the individual strings hardly interact at all so their tones don't intermodulate and intermodulation is the sure sign that tells the ear that there is distortion present.

Is distortion perhaps a unfortunate term? It might lead you to think of amp distortion which has a different cause and audible quality. Unless someone happened to bodge a pickup design...

[aquin43]

May 5, 2021 12:18:17 GMT -5 roadtonever said:

May 5, 2021 6:02:42 GMT -5 aquin43 said:

The pickup is very non-linear and generates its own harmonics which increase as the distance to the string is reduced.

Ignoring the filter shape caused by the RLC interactions, is the non-linearity not caused by:
1. The requirement of string movement to generate voltage
2. The magnetic field cant be 100% uniform

May 5, 2021 6:02:42 GMT -5 aquin43 said:

This distortion is not distinguishable as such because the individual strings hardly interact at all so their tones don't intermodulate and intermodulation is the sure sign that tells the ear that there is distortion present.

Is distortion perhaps a unfortunate term? It might lead you to think of amp distortion which has a different cause and audible quality. Unless someone happened to bodge a pickup design...

This is all pretty basic stuff that has been much discussed here. The waveform induced in the coil is not the same as the velocity waveform of the string. It is distorted because the pickup response is non-linear as you would expect because the response falls off with distance and the movement of the string obviously involves changing distance. The distortion adds to the harmonic structure of the waveform but is not distinguishable as distortion to the ear because 1 - it is the only sound that has been heard and is accepted as OK, 2 - there is no intermodulation with the other strings to give the usual clues.

There is intermodulation between the generated harmonics and the slightly detuned "harmonics" of the string which adds to the richness of the sound.

[roadtonever]

Thanks for clarifying.

May 5, 2021 12:44:23 GMT -5 aquin43 said:

There is intermodulation between the generated harmonics and the slightly detuned "harmonics" of the string which adds to the richness of the sound.

I suspect this is part of what makes up growl in bass pickups. Or twang in Teles, and kerrang in Rickenbackers.

[gckelloch]

May 5, 2021 12:44:23 GMT -5 aquin43 said:

May 5, 2021 12:18:17 GMT -5 roadtonever said:

Ignoring the filter shape caused by the RLC interactions, is the non-linearity not caused by:
1. The requirement of string movement to generate voltage
2. The magnetic field cant be 100% uniform

Is distortion perhaps a unfortunate term? It might lead you to think of amp distortion which has a different cause and audible quality. Unless someone happened to bodge a pickup design...

This is all pretty basic stuff that has been much discussed here. The waveform induced in the coil is not the same as the velocity waveform of the string. It is distorted because the pickup response is non-linear as you would expect because the response falls off with distance and the movement of the string obviously involves changing distance. The distortion adds to the harmonic structure of the waveform but is not distinguishable as distortion to the ear because 1 - it is the only sound that has been heard and is accepted as OK, 2 - there is no intermodulation with the other strings to give the usual clues.

There is intermodulation between the generated harmonics and the slightly detuned "harmonics" of the string which adds to the richness of the sound.

Let me first say that I definitely do not understand everything about guitar pickups. AFAIK, flux lines traveling along a string perpendicular to the coil should contribute virtually no voltage in the coil, so it follows that they will contribute exponentially less to the signal the closer they are to perpendicular. At some point, some portion of the flux lines will circle back around to the opposite side of the poles, which can create some level of cancelation if they go back through a portion of the coil or an adjacent pickup of the same phase. It’s not the same as flux lines coming in from the side of the string. The voltage generation may then stem solely from the curving flux lines or even the return path lines, but I will scrutinize the relevant experiment. Yes, intuition in no way dictates reality.

Either way, given the way flux lines travel in a string (simulations may or may not be correct), I don’t see how the total string sensing aperture could be much wider than the coil. Coil width is definitely part of the total aperture equation.

Different string alloys can have different hysteresis factors, so wave asymmetry as a string oscillates closer and farther from the coil would be somewhat dependent on that. It may be more pronounced when the coil is closer to the string, along with the note fundamental and transient strength. I don’t fully understand the effect of wave asymmetry, but I’ve read that the 2nd harmonic then becomes more dominant. That makes sense to me, and should even counter some of the effect of the proximity induced increase in note fundamental and transient strength. I don’t know how the coil in a passive pickup could generate harmonics, and I would need to see some real evidence of it.

[ms]

May 5, 2021 20:16:43 GMT -5 gckelloch said:

"It’s not the same as flux lines coming in from the side of the string."

What matters is the magnetization excited in the string; the string is what moves and causes changing flux through the coil.  Of course the result of the flux lines from the magnet producing magnetization in the string when located on the side is not exactly the same as underneath, but it apparently is very close.  The magnetization excited in one location of the string affects that in neighboring locations.  The result is a "self-consistent" solution in which the geometry of the high permeability material plays a huge role.

For example, wind some closely spaced turns around a high permeability toroid, covering only a small part of the toroid.  The flux is almost totally confined to the toroid and  uniform around it.  This looks nothing like the field produced by the coil with no toroid present.

[aquin43]

May 5, 2021 20:16:43 GMT -5 gckelloch said:

I don’t know how the coil in a passive pickup could generate harmonics, and I would need to see some real evidence of it.

The coil doesn't generate harmonics. It is the non-linear relationship between the position of the string and the amount of flux that it puts through the coil that generates the harmonics. From common experience, the sensitivity of the pickup falls off rapidly as the distance of the string from the pole increases. But this happens over distances that are comparable with the distance the string moves through as it vibrates. There you have the non-linearity. The gain changes during the string movement. Put in a sinusoidal string movement and out comes a voltage which includes harmonics.

[gckelloch]

I'm saying that I understand how the fundamental is reduced in the asymmetrical waveform so that the 2nd harmonic becomes more prominent, but not how artificial harmonics would be generated from that. Where do you get that from? A coil has no gain limiting function until heat becomes a factor, and heat compression doesn't happen in a guitar pickup. It sounds like you are conflating the non-linear function that creates wave asymmetry with a non-linear system that limits the output compared to the input. There is no core saturation function in a guitar pickup as can occur in a transformer.

[gckelloch]

May 6, 2021 7:14:01 GMT -5 ms said:

May 5, 2021 20:16:43 GMT -5 gckelloch said:

"It’s not the same as flux lines coming in from the side of the string."

What matters is the magnetization excited in the string; the string is what moves and causes changing flux through the coil.  Of course the result of the flux lines from the magnet producing magnetization in the string when located on the side is not exactly the same as underneath, but it apparently is very close.  The magnetization excited in one location of the string affects that in neighboring locations.  The result is a "self-consistent" solution in which the geometry of the high permeability material plays a huge role.

For example, wind some closely spaced turns around a high permeability toroid, covering only a small part of the toroid.  The flux is almost totally confined to the toroid and  uniform around it.  This looks nothing like the field produced by the coil with no toroid present.

That's interesting, but how does it relate to the aperture window of a pickup? Magnetic power decreases by the inverse square law, so whatever magnetism in a string has that much less influence farther away from the coil, and I already explained that flux lines traveling along the string contribute virtually nothing to the output. I may be misunderstanding something, but it appears you are conflating two unrelated functions.

[ms]

May 6, 2021 16:27:37 GMT -5 gckelloch said:

May 6, 2021 8:23:07 GMT -5 aquin43 said:

The coil doesn't generate harmonics. It is the non-linear relationship between the position of the string and the amount of flux that it puts through the coil that generates the harmonics. From common experience, the sensitivity of the pickup falls off rapidly as the distance of the string from the pole increases. But this happens over distances that are comparable with the distance the string moves through as it vibrates. There you have the non-linearity. The gain changes during the string movement. Put in a sinusoidal string movement and out comes a voltage which includes harmonics.

That's interesting, but how does it relate to the aperture window of a pickup? Magnetic power decreases by the inverse square law, so whatever magnetism in a string has that much less influence the farther away from the coil, and I already explained that flux lines traveling along the string contribute virtually nothing to the output. I may be misunderstanding something, but it appears you are conflating two unrelated functions.

A magnetic dipole has a one over distance cubed function, not squared.  (There are no magnetic monopoles.)  A collection of dipoles could fall off slowly nearby and then like a dipole far away.

[gckelloch]

May 6, 2021 17:36:49 GMT -5 ms said:

May 6, 2021 16:27:37 GMT -5 gckelloch said:

That's interesting, but how does it relate to the aperture window of a pickup? Magnetic power decreases by the inverse square law, so whatever magnetism in a string has that much less influence the farther away from the coil, and I already explained that flux lines traveling along the string contribute virtually nothing to the output. I may be misunderstanding something, but it appears you are conflating two unrelated functions.

A magnetic dipole has a one over distance cubed function, not squared.  (There are no magnetic monopoles.)  A collection of dipoles could fall off slowly nearby and then like a dipole far away.

Ok, but the power from one axis of the dipole decreases by inverse square, right? Not sure how it works from the side of the dipoles. I suppose it has to do with the point on the vertical axis the power is measured i.e. exponentially more horizontal power loss closer to the top of a pole piece than from a higher point. Either way, the total string sensing width would ultimately be limited by the coil width.

It appears there is some level of deductive reasoning being applied in this thread that may be based on physics functions not fully understood, as with my misunderstanding of the mic proximity effect. The question I was initially addressing was how Microcoils produce a stronger note fundamental & transient ratio at the same distance as other pickups. While this is all interesting stuff, I have said all I can on that point, and I am wary to participate in any further speculation on other functions. Nor do I encourage it. I also wouldn't assume that software simulations are accurate representations of real functions, especially if the relevant functions are misunderstood to begin with.