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Post by antigua on May 6, 2021 22:30:06 GMT -5
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. I know this has been discussed before, but I'm still not sure why this would be. The harmonics are suppressed when you have a receptive field that is so wide that it experiences both positive and negative flux change in tandem, and the two cancel out. The objective then is to have an inductive field that is narrow enough to capture a positive movement would also seeing a corresponding negative movement. How would the wider loops of a wider coil not result in the capture of both positive and negative flux changes of higher harmonics, more so than smaller loops? |
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Post by antigua on May 6, 2021 23:09:23 GMT -5
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.
Here is a Microcoil measure top side and bottom side, the difference is ~11.7dB. I'm not sure what this tells you exactly, but I measured from the top, and the underside is the same as if they exciter coil was 10mm above the pickup instead of directly against it. In the original OP though I had compared it to a Fender style single coil and the Microcoil was only about 1dB louder, and I just test it again with another Strat pickup I have on hand, and the result was the same. Some of that difference might be due to the thickness of the cover and coil formers, it's practically within a margin of error. When a coil core has steel pole pieces instead of AlNiCo, that alone seems to make a much bigger difference in the output voltage.  I had said this coil layout was technically superior, but given that the difference is less than 1dB, superior is probably much too strong an adjective; but lot of people like Bill Lawrence so maybe I was being too charitable. This coil geometry barely makes a difference, and there's probably no audible difference at all. The whole design seems kind pointless in fact. It's more complicated to produce than an ordinary Strat pickup, and provides virtually no benefit. The original Microcoils had steel pole pieces, and in that case the end result probably isn't much different from a split humbucker whose inductance is similar. |
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Post by gckelloch on May 6, 2021 23:33:52 GMT -5
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. Here is a Microcoil measure top side and bottom side, the difference is ~11.7dB. I'm not sure what this tells you exactly, but I measured from the top, and the underside is the same as if they exciter coil was 10mm above the pickup instead of directly against it. In the original OP though I had compared it to a Fender style single coil and the Microcoil was only about 1dB louder, and I just test it again with another Strat pickup I have on hand, and the result was the same. Some of that difference might be due to the thickness of the cover and coil formers, it's practically within a margin of error. When a coil core has steel pole pieces instead of AlNiCo, that alone seems to make a much bigger difference in the output voltage. I had said this coil layout was technically superior, but given that the difference is less than 1dB, superior is probably much too strong an adjective; but lot of people like Bill Lawrence so maybe I was being too charitable. This coil geometry barely makes a difference, and there's probably no audible difference at all. The whole design seems kind pointless in fact. It's more complicated to produce than an ordinary Strat pickup, and provides virtually no benefit. The original Microcoils had steel pole pieces, and in that case the end result probably isn't much different from a split humbucker whose inductance is similar. All else being equal, I think the 1dB higher output of the MC's is just the efficiency of more than 2x the winds in the same space all up closer to the strings (overcompensating for the potential voltage loss of the thinner wire), but that doesn't tell you about the stronger note fundamental & transient ratio compared to pickups with thicker wire. You would have to measure the output with the exciter device set to the same voltage at say 4mm & 8mm from the top of the coil cover, and then do the same on another pickup (over a pole piece that sticks out roughly the same distance), and then compare the output difference between the two measured distances for each pickup. I'm assuming the MC would have more of an output discrepancy between the two distances. Otherwise, I wouldn't know how it could have stronger fundamentals & transients at the same string distance, even though it clearly does. I'm pretty sure the original Nd-powered MC's (that I have) have Permalloy inserts & pole screws in the core, as well as a Permalloy "moderator bar" to possibly spread the field more evenly into the inserts. Permalloy increases coil inductance a lot (like Steel) but doesn't significantly reduce the high end, so it essentially sounds like an AlNiCo pole pickup of equal inductance with 42AWG wire, but with stronger fundamentals & transients and a much better signal to hum improvement I'd estimate at ~10dB or better. I imagine the thin copper shielding under the coil also reduces the hum harmonics in the critical hearing range and above. I actually just lowered the pole screw heights on my MC's to compensate for the thinner gauge "V-Strings" I now use (which produce weaker fundamentals and more high harmonics) and I got the note timbre just right for each string and pickup position. I did have to put slivers of electrical tape in each screw hole so the screws stay where I set them, but it was worth the work to get the note timbre and overall output balance just right in a way that can not be achieved with any other pickup I know of. |
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Post by aquin43 on May 7, 2021 4:20:38 GMT -5
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. I am sorry, you are adding complications where none are needed. I described how the mere fact that the sensitivity of the pickup changes with distance from the pole is sufficient to explain the generation of harmonics.
Consider a sine wave. It is the only shape of wave that has no harmonics. Pass it through a system where the gain changes according to the level at any instant. It comes out a different shape. The different shape represents the addition of harmonics. A 10% change in gain over the range of movement, for example, will give roughly 10% distortion.
That's all there is. There is no more.
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Post by aquin43 on May 7, 2021 4:27:29 GMT -5
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.
Here is a Microcoil measure top side and bottom side, the difference is ~11.7dB. I'm not sure what this tells you exactly, but I measured from the top, and the underside is the same as if they exciter coil was 10mm above the pickup instead of directly against it. Thanks. I was trying to get a figure for the difference in signal flux at the top and bottom of an ordinary coil. It gives an indication of how much is being lost by using a short coil and would also be a consideration in a stacked humbucker.
Another point - I have a suspicion that the Microcoils may be a bit more non-linear than the standard pickups.
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Post by gckelloch on May 7, 2021 5:57:48 GMT -5
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. I am sorry, you are adding complications where none are needed. I described how the mere fact that the sensitivity of the pickup changes with distance from the pole is sufficient to explain the generation of harmonics. Consider a sine wave. It is the only shape of wave that has no harmonics. Pass it through a system where the gain changes according to the level at any instant. It comes out a different shape. The different shape represents the addition of harmonics. A 10% change in gain over the range of movement, for example, will give roughly 10% distortion.
That's all there is. There is no more.
OK, I follow that. Assuming the wave asymmetry stems from the string becoming more magnetized when it moves closer to the pole piece during a wave cycle, and the opposite occurs when it moves away, wouldn't the shorter rounder wave formed in the 2nd half of the cycle effectively cancel any artificial harmonics generated from the taller sharper wave formed in the 1st half of the cycle? If the string becomes magnetically saturated at some point during the "up cycle", that would further complicate matters. |
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Post by ms on May 7, 2021 7:25:08 GMT -5
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. I know this has been discussed before, but I'm still not sure why this would be. The harmonics are suppressed when you have a receptive field that is so wide that it experiences both positive and negative flux change in tandem, and the two cancel out. The objective then is to have an inductive field that is narrow enough to capture a positive movement would also seeing a corresponding negative movement. How would the wider loops of a wider coil not result in the capture of both positive and negative flux changes of higher harmonics, more so than smaller loops? The short answer is because the aperture is determined by the poles, and they are narrower than the coil. So when the poles magnetize the string, the part of the string over the poles contributes the most vibrating field pointed down through the coil. This falls off quickly as you move along the string away from the poles. Also, because the pole has permeability, it amplifies the field from the part of the string right above it. Flux passing through the coil, but away from the poles, does not get so amplified. |
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Post by aquin43 on May 7, 2021 9:27:39 GMT -5
I am sorry, you are adding complications where none are needed. I described how the mere fact that the sensitivity of the pickup changes with distance from the pole is sufficient to explain the generation of harmonics. Consider a sine wave. It is the only shape of wave that has no harmonics. Pass it through a system where the gain changes according to the level at any instant. It comes out a different shape. The different shape represents the addition of harmonics. A 10% change in gain over the range of movement, for example, will give roughly 10% distortion.
That's all there is. There is no more.
OK, I follow that. Assuming the wave asymmetry stems from the string becoming more magnetized when it moves closer to the pole piece during a wave cycle, and the opposite occurs when it moves away, wouldn't the shorter rounder wave formed in the 2nd half of the cycle effectively cancel any artificial harmonics generated from the taller sharper wave formed in the 1st half of the cycle? If the string becomes magnetically saturated at some point during the "up cycle", that would further complicate matters. The gain variation comes both from the changing magnetisation of the string and the variation in interaction between the string and coil, which are in step with each other.
Harmonics of half of a wave cancelling those of the other half is a common misconception, but harmonics only exist for continuous waves. Anyway, the gain curvature is always in the same direction so why would one expect subtraction?
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Post by antigua on May 7, 2021 13:38:44 GMT -5
I know this has been discussed before, but I'm still not sure why this would be. The harmonics are suppressed when you have a receptive field that is so wide that it experiences both positive and negative flux change in tandem, and the two cancel out. The objective then is to have an inductive field that is narrow enough to capture a positive movement would also seeing a corresponding negative movement. How would the wider loops of a wider coil not result in the capture of both positive and negative flux changes of higher harmonics, more so than smaller loops? The short answer is because the aperture is determined by the poles, and they are narrower than the coil. So when the poles magnetize the string, the part of the string over the poles contributes the most vibrating field pointed down through the coil. This falls off quickly as you move along the string away from the poles. Also, because the pole has permeability, it amplifies the field from the part of the string right above it. Flux passing through the coil, but away from the poles, does not get so amplified. I understand how the pole piece can be a dominant effect over the area of the loops alone, but what if you had a standard pole piece, but the coil was six inches in diameter. Wouldn't the sum area of flux change be so wide that is wouldn't see non-cancelling flux change of string segments that are much less than six inches? If the pole piece is still dominant even with a very wide loop, then maybe suppose the pole piece is a ceramic magnet and contributes now permeability. Supposing this is the case, the extra width of a P-90 or a Microcoil would be trivial, but it's the principle of the thing. |
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Post by ms on May 7, 2021 14:14:05 GMT -5
The short answer is because the aperture is determined by the poles, and they are narrower than the coil. So when the poles magnetize the string, the part of the string over the poles contributes the most vibrating field pointed down through the coil. This falls off quickly as you move along the string away from the poles. Also, because the pole has permeability, it amplifies the field from the part of the string right above it. Flux passing through the coil, but away from the poles, does not get so amplified. I understand how the pole piece can be a dominant effect over the area of the loops alone, but what if you had a standard pole piece, but the coil was six inches in diameter. Wouldn't the sum area of flux change be so wide that is wouldn't see non-cancelling flux change of string segments that are much less than six inches? If the pole piece is still dominant even with a very wide loop, then maybe suppose the pole piece is a ceramic magnet and contributes now permeability. Supposing this is the case, the extra width of a P-90 or a Microcoil would be trivial, but it's the principle of the thing. Yes, if you make the coil too wide you get cancellation, but I think the aperture is still bounded by the pole. You could figure out which part of the aperture gets canceled first as the coil width increases, but is this really of much practical importance? |
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Post by antigua on May 7, 2021 14:22:03 GMT -5
I understand how the pole piece can be a dominant effect over the area of the loops alone, but what if you had a standard pole piece, but the coil was six inches in diameter. Wouldn't the sum area of flux change be so wide that is wouldn't see non-cancelling flux change of string segments that are much less than six inches? If the pole piece is still dominant even with a very wide loop, then maybe suppose the pole piece is a ceramic magnet and contributes now permeability. Supposing this is the case, the extra width of a P-90 or a Microcoil would be trivial, but it's the principle of the thing. Yes, if you make the coil too wide you get cancellation, but I think the aperture is still bounded by the pole. You could figure out which part of the aperture gets canceled first as the coil width increases, but is this really of much practical importance? It's not practically important, but neither are the quarter inch pole pieces, I just want to be able to say something could theoretically matter, but this is why it doesn't, instead of saying it can't matter at all. In the case of a Jazzmaster pickup, the pole pieces are less permeable AlNiCo 5 and the coil is especially wide, so that might push the limits of the concept for a production pickup, but even still, those pickups sound very bright and there's no audible indication that the limits of the aperture are below the limits impose by other aspects of the system. |
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Post by gckelloch on May 7, 2021 18:58:47 GMT -5
OK, I follow that. Assuming the wave asymmetry stems from the string becoming more magnetized when it moves closer to the pole piece during a wave cycle, and the opposite occurs when it moves away, wouldn't the shorter rounder wave formed in the 2nd half of the cycle effectively cancel any artificial harmonics generated from the taller sharper wave formed in the 1st half of the cycle? If the string becomes magnetically saturated at some point during the "up cycle", that would further complicate matters. The gain variation comes both from the changing magnetisation of the string and the variation in interaction between the string and coil, which are in step with each other. Harmonics of half of a wave cancelling those of the other half is a common misconception, but harmonics only exist for continuous waves. Anyway, the gain curvature is always in the same direction so why would one expect subtraction?
I was mistakenly thinking the wave half would be shorter and rounder as the string moves away from the pole because of the progressive decrease in magnetic power, but now I see why both halves should actually just be sharper than a sine wave. Again, the extent to which might depend on the hysteresis factor of the string alloy? I may be misunderstanding how hysteresis applies as well. |
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Post by gckelloch on May 7, 2021 19:14:47 GMT -5
Yes, if you make the coil too wide you get cancellation, but I think the aperture is still bounded by the pole. You could figure out which part of the aperture gets canceled first as the coil width increases, but is this really of much practical importance? It's not practically important, but neither are the quarter inch pole pieces, I just want to be able to say something could theoretically matter, but this is why it doesn't, instead of saying it can't matter at all. In the case of a Jazzmaster pickup, the pole pieces are less permeable AlNiCo 5 and the coil is especially wide, so that might push the limits of the concept for a production pickup, but even still, those pickups sound very bright and there's no audible indication that the limits of the aperture are below the limits impose by other aspects of the system. The field from the short AlNiCo V pole pieces would spread out closer to the pole ends more than a longer pole piece, so there might be some partial cancellations as the outer flux lines go back through edges of the wide coil. I've read that JM Pickups are in the 3.5H range, so that could be why they would sound brighter than lower L pickups with the same C & R load, as the peak could easily be down in the 3-3.5kHz range. JM guitars also have higher pot values than Strats. BTW, Microcoils are standard Fender width. |
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Post by gckelloch on May 8, 2021 1:37:07 GMT -5
I know this has been discussed before, but I'm still not sure why this would be. The harmonics are suppressed when you have a receptive field that is so wide that it experiences both positive and negative flux change in tandem, and the two cancel out. The objective then is to have an inductive field that is narrow enough to capture a positive movement would also seeing a corresponding negative movement. How would the wider loops of a wider coil not result in the capture of both positive and negative flux changes of higher harmonics, more so than smaller loops? The short answer is because the aperture is determined by the poles, and they are narrower than the coil. So when the poles magnetize the string, the part of the string over the poles contributes the most vibrating field pointed down through the coil. This falls off quickly as you move along the string away from the poles. Also, because the pole has permeability, it amplifies the field from the part of the string right above it. Flux passing through the coil, but away from the poles, does not get so amplified. I really appreciate your patience with those of us (me) who are ignorant on such matters. One caveat about your last statement. It sounds like you are describing a perpetual motion machine. How would the field in the strings amplify the field in the poles if the field is emanating from the poles? Wouldn't that create a runaway feedback loop that would eventually engulf the know universe?  |
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Post by aquin43 on May 8, 2021 4:46:11 GMT -5
The gain variation comes both from the changing magnetisation of the string and the variation in interaction between the string and coil, which are in step with each other. Harmonics of half of a wave cancelling those of the other half is a common misconception, but harmonics only exist for continuous waves. Anyway, the gain curvature is always in the same direction so why would one expect subtraction?
I was mistakenly thinking the wave half would be shorter and rounder as the string moves away from the pole because of the progressive decrease in magnetic power, but now I see why both halves should actually just be sharper than a sine wave. Again, the extent to which might depend on the hysteresis factor of the string alloy? I may be misunderstanding how hysteresis applies as well. You were correct in assuming that the two halves of the waveform would have different shapes with one half stretched and the other compressed. It is this asymmetry that indicates the presence of predominantly even harmonics. For example we have here a sinusoidal wave and its second harmonic and then the waveform shape when they are added. The waveform shape produced also depends on the phase (time) relationship between the fundamental and the harmonics.
Hysteresis is unlikely to be very important. The strings are made of materials that tend to keep their magnetisation and the total flux entering the string does not vary too much.
It is interesting that one of the earliest pickup designs had no magnets and relied on the strings being pre magnetised.
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Post by gckelloch on May 8, 2021 6:05:13 GMT -5
I was mistakenly thinking the wave half would be shorter and rounder as the string moves away from the pole because of the progressive decrease in magnetic power, but now I see why both halves should actually just be sharper than a sine wave. Again, the extent to which might depend on the hysteresis factor of the string alloy? I may be misunderstanding how hysteresis applies as well. You were correct in assuming that the two halves of the waveform would have different shapes with one half stretched and the other compressed. It is this asymmetry that indicates the presence of predominantly even harmonics. For example we have here a sinusoidal wave and its second harmonic and then the waveform shape when they are added. The waveform shape produced also depends on the phase (time) relationship between the fundamental and the harmonics.
Hysteresis is unlikely to be very important. The strings are made of materials that tend to keep their magnetisation and the total flux entering the string does not vary too much. It is interesting that one of the earliest pickup designs had no magnets and relied on the strings being pre magnetised. Oh, guess I shouda' trusted my first instinct. It's hard to imagine this stuff correctly. That will be helpful in future, thanks. So, how would there be wave asymmetry in the output if the strings don't become more magnetized when approaching the poles? Something about how the flux moves through the coil? Does it relate to why you think the MC's might produce more wave asymmetry? Either way, there are worse sounds than having an extra 2nd harmonic. |
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Post by aquin43 on May 8, 2021 6:51:48 GMT -5
Oh, guess I shouda' trusted my first instinct. It's hard to imagine this stuff correctly. That will be helpful in future, thanks. So, how would there be wave asymmetry in the output if the strings don't become more magnetized when approaching the poles? Something about how the flux moves through the coil? Does it relate to why you think the MC's might produce more wave asymmetry? Either way, there are worse sounds than having an extra 2nd harmonic. There are two factors changing the flux in the coil with distance, the change in string magnetisation and the change in the coupling of the string to the coil. Since the normal Fender and the Microcoils are built on the same magnet structure it is safe to compare just the string to coil coupling. A 2D simulation shows that the flux change in the Microcoil is more non-linear. In 3D space where everything varies faster with distance the difference is likely to be greater.
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Post by ms on May 8, 2021 7:27:16 GMT -5
The short answer is because the aperture is determined by the poles, and they are narrower than the coil. So when the poles magnetize the string, the part of the string over the poles contributes the most vibrating field pointed down through the coil. This falls off quickly as you move along the string away from the poles. Also, because the pole has permeability, it amplifies the field from the part of the string right above it. Flux passing through the coil, but away from the poles, does not get so amplified. I really appreciate your patience with those of us (me) who are ignorant on such matters. One caveat about your last statement. It sounds like you are describing a perpetual motion machine. How would the field in the strings amplify the field in the poles if the field is emanating from the poles? Wouldn't that create a runaway feedback loop that would eventually engulf the know universe? It is the pole piece that increases the field from the strings. Kind of like the core of an inductor: current in one loop of wire creates a magnetic field that passes through the other loops, inducing a voltage around each. When a high permeability core is present, the induced voltage increases, increasing the inductance. With a pickup, a field generated external to the coil (from the vibrating string) produces a field through the coil, and the permeability of the core increases the voltage induced around each loop of wire. |
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Post by aquin43 on May 8, 2021 9:33:03 GMT -5
I would say that the pickup is actually a "variable reluctance" device in which part of a fixed* amount of flux supplied by the magnet is diverted away from the rest of the pickup by the string. As the string moves, the amount and distribution of the diverted flux changes so that the amount of flux passing through the coil changes, thereby producing the signal.
The problem with variable reluctance as a model is that it gives no information about the distribution of the diverted flux or, if it does, it is only in terms of a minuscule change in the overall flux, virtually impossible to calculate or visualise.
Therefore, an alternative model is almost universally adopted in which the string with its induced magnetism is treated as a source. This is legitimate because it is only changes in the magnetic flux that are of importance, allowing the large static background field to be ignored. Magnetic fields can pass through one another without interference.
A caveat is that the magnetic properties of the magnet and poles used in the model must be those evaluated at the prevailing large static flux densities.
The pickup poles concentrate flux going to the string from the magnets and also, in the model, gather in flux from the magnetised string - to a large extent with steel poles and to a lesser extent with magnets as poles since magnets have quite low permeability to changes in flux when they are magnetised.
*The flux available from the magnet is not absolutely fixed in the case of Alnico magnets but the effect of the string on the operating point of the magnet is so small that it may be considered so for all practical purposes.
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Post by ms on May 8, 2021 10:26:13 GMT -5
I would say that the pickup is actually a "variable reluctance" device in which part of a fixed* amount of flux supplied by the magnet is diverted away from the rest of the pickup by the string. As the string moves, the amount and distribution of the diverted flux changes so that the amount of flux passing through the coil changes, thereby producing the signal. The problem with variable reluctance as a model is that it gives no information about the distribution of the diverted flux or, if it does, it is only in terms of a minuscule change in the overall flux, virtually impossible to calculate or visualise. Therefore, an alternative model is almost universally adopted in which the string with its induced magnetism is treated as a source. This is legitimate because it is only changes in the magnetic flux that are of importance, allowing the large static background field to be ignored. Magnetic fields can pass through one another without interference. A caveat is that the magnetic properties of the magnet and poles used in the model must be those evaluated at the prevailing large static flux densities. The pickup poles concentrate flux going to the string from the magnets and also, in the model, gather in flux from the magnetised string - to a large extent with steel poles and to a lesser extent with magnets as poles since magnets have quite low permeability to changes in flux when they are magnetised. *The flux available from the magnet is not absolutely fixed in the case of Alnico magnets but the effect of the string on the operating point of the magnet is so small that it may be considered so for all practical purposes. I think the reluctance concept is appealing because of its similarity to the electrical circuit case, but Faraday's law of magnetic induction is the fundamental way of describing how a pickup works because it is derived directly from Maxwell's equations. Simple magnetic circuits involving a nearly closed path of high permeability material with small gaps obey an analog of ohm's law in which reluctance is like resistance. This is a circuit concept in which the three dimensions of space are replaced with two terminal devices, sort of. The "devices" in the pickup magnetic circuit cannot be easily defined, just as the behavior of a 3D medium filled with material with spatially variable resistivity, illuminated by an E field derived from a couple of metal plates attached to a battery, cannot be solved easily with ohm's law. It is necessary to solve a complicated 3D partial differential equation. For the magnetic case it would be necessary to work with an analog of resistivity, maybe call it "reluctivity". But that is more complicated and less intuitive than working with MLoMI, which so easily and naturally applies to the geometry of a pickup magnetic circuit. |
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Post by aquin43 on May 8, 2021 10:56:46 GMT -5
I would say that the pickup is actually a "variable reluctance" device in which part of a fixed* amount of flux supplied by the magnet is diverted away from the rest of the pickup by the string. As the string moves, the amount and distribution of the diverted flux changes so that the amount of flux passing through the coil changes, thereby producing the signal. The problem with variable reluctance as a model is that it gives no information about the distribution of the diverted flux or, if it does, it is only in terms of a minuscule change in the overall flux, virtually impossible to calculate or visualise. Therefore, an alternative model is almost universally adopted in which the string with its induced magnetism is treated as a source. This is legitimate because it is only changes in the magnetic flux that are of importance, allowing the large static background field to be ignored. Magnetic fields can pass through one another without interference. A caveat is that the magnetic properties of the magnet and poles used in the model must be those evaluated at the prevailing large static flux densities. The pickup poles concentrate flux going to the string from the magnets and also, in the model, gather in flux from the magnetised string - to a large extent with steel poles and to a lesser extent with magnets as poles since magnets have quite low permeability to changes in flux when they are magnetised. *The flux available from the magnet is not absolutely fixed in the case of Alnico magnets but the effect of the string on the operating point of the magnet is so small that it may be considered so for all practical purposes. I think the reluctance concept is appealing because of its similarity to the electrical circuit case, but Faraday's law of magnetic induction is the fundamental way of describing how a pickup works because it is derived directly from Maxwell's equations. Simple magnetic circuits involving a nearly closed path of high permeability material with small gaps obey an analog of ohm's law in which reluctance is like resistance. This is a circuit concept in which the three dimensions of space are replaced with two terminal devices, sort of. The "devices" in the pickup magnetic circuit cannot be easily defined, just as the behavior of a 3D medium filled with material with spatially variable resistivity, illuminated by an E field derived from a couple of metal plates attached to a battery, cannot be solved easily with ohm's law. It is necessary to solve a complicated 3D partial differential equation. For the magnetic case it would be necessary to work with an analog of resistivity, maybe call it "reluctivity". But that is more complicated and less intuitive than working with MLoMI, which so easily and naturally applies to the geometry of a pickup magnetic circuit. In fact, thinking a bit further about the variable reluctance concept, the assumption that the magnet is the only source of flux is not literally true once we have a string with "hard" magnetic properties. Not only does it act as a conduit to divert the magnet's flux but it also acquires its own permanent magnetism, further justifying the adoption of the magnetised string model.
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Post by antigua on May 8, 2021 13:58:29 GMT -5
Regardless of whether you think about it as a string as a magnet, or as a reluctance between a string and a pole piece, the more complicated factor with respect to the Microcoil, is how non-linear the magnetic change will be depending on where the loops are located, and since a Microcoil is closer to a "cross section", where as a taller coil is close to an average across an area of space, it makes sense to me that the Microcoil's thin coil would produce more non linearity than a typical Strat coil. Where as a tall coil is picking up flux near and far, the Microcoil has more of a hard cut off, only picking up change that is near.
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Post by gckelloch on May 8, 2021 22:45:30 GMT -5
Regardless of whether you think about it as a string as a magnet, or as a reluctance between a string and a pole piece, the more complicated factor with respect to the Microcoil, is how non-linear the magnetic change will be depending on where the loops are located, and since a Microcoil is closer to a "cross section", where as a taller coil is close to an average across an area of space, it makes sense to me that the Microcoil's thin coil would produce more non linearity than a typical Strat coil. Where as a tall coil is picking up flux near and far, the Microcoil has more of a hard cut off, only picking up change that is near. I don't really understand how there would be significant wave asymmetry if there isn't significant flux change in the string, but that's on me. As for how a shorter denser coil would affect it, there are already stronger flux lines through more of the coil at a given distance, so why would there be more asymmetry rather than just more emphasized stronger string vibrations as I had originally thought? I fall in the: only the magnetized string matters camp, so I defer to the research of Dr. Scott Lawing. I'd be curious what he'd say about asymmetry: lawingmusicalproducts.com/dr-lawings-blog/how-does-a-pickup-really-work |
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Post by antigua on May 9, 2021 5:05:51 GMT -5
Regardless of whether you think about it as a string as a magnet, or as a reluctance between a string and a pole piece, the more complicated factor with respect to the Microcoil, is how non-linear the magnetic change will be depending on where the loops are located, and since a Microcoil is closer to a "cross section", where as a taller coil is close to an average across an area of space, it makes sense to me that the Microcoil's thin coil would produce more non linearity than a typical Strat coil. Where as a tall coil is picking up flux near and far, the Microcoil has more of a hard cut off, only picking up change that is near. I don't really understand how there would be significant wave asymmetry if there isn't significant flux change in the string, but that's on me. As for how a shorter denser coil would affect it, there are already stronger flux lines through more of the coil at a given distance, so why would there be more asymmetry rather than just more emphasized stronger string vibrations as I had originally thought? I fall in the: only the magnetized string matters camp, so I defer to the research of Dr. Scott Lawing. I'd be curious what he'd say about asymmetry: lawingmusicalproducts.com/dr-lawings-blog/how-does-a-pickup-really-workDo you wonder why the wave form's positive and negative sides of the cycle aren't the same? I think that's a case where the reluctance model makes it clear, in that when the string is moving closer, the reluctance (air gap) is decreasing, and when it's moving away, the reluctance is increasing. When the string is nearest to the coil, more lines of flux are involved with the coil, versus when it's further away. The peaks and troughs of the output waveform are of when the string velocity is at it's highest, which which is when it's physically passing the center point, and when the wave form is crossing the 0 and 180 degrees, that's when the string is physically either at the nearest point, or farthest point, from the the pickup. So the two sides of the wave form are, the string rushing away from the pickup, reluctance climbing, and then the string rushing towards the pickup, reluctance dropping. |
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Post by aquin43 on May 9, 2021 5:09:53 GMT -5
I have modelled the two styles of pickup in 2D space using FEMM. The string is modelled using an array of magnets to give a flux distribution within it similar to that measured in a real string. The flux through the coils at 15 different distances from the centre is weighted by one minus the count from the centre to take account of the number of turns enclosing it. The total effective flux (to an arbitrary scale) is plotted from 1mm above the pole to 10mm. The magnet is assumed to be alnico 2 with a mu of 3.5 The brown curve is the full coil, the red is the microcoil and the orange is the microcoil scaled to the full level for comparison. The only source of magnetic variation is the distance of the string from the pole.
The scaled mirocoil is obviously less linear over the range but it has a steeper gradient at close distances which will help to compensate for the reduced total magnetisation.
I would expect curvatures in 3D space to be greater but the pattern should be similar.
Zollner's empirical formula of the form 1/(constant + distance + x) is similar in shape to these curves. What the microcoild do is reduce the constant, thereby moving the working range deeper into the non-linear region.
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Post by gckelloch on May 9, 2021 6:13:32 GMT -5
Great stuff, guys. I'm just a simple caveman, so I don't fully understand the maths involved -- nor am I seeking a lesson. I only just got through "College Algebra" in the early '90s. It looks like there isn't much difference in the non-linearity, anyway. I may inquire with Dr. Lawing on this to see if he's done any comparitive measurements in his research. Thanks, again. All I can say supporting the increased fundamental strength is that the DI recordings of my 2.8H MCL & 1.8H MCM&N pickups with the screws poles set to the string raduis is vastly warmer and more balanced than those of the stock AlNiCO V ~6k DCR/~2.5H pickups they replaced in my Agile ST-625EB which sounded quite brittle and bright at virtually the same coil hieghts. The same is reportedly true for the AlNiCO MC's, so I can only assume it's the denser coil that makes the difference. Even my 43AWG wound GFS Bridge VEH has audibley stronger fundamentals & punch than my other 42AWG wound GFS PAF type with nearly the same wind count. It also seems to have a more prominent midrange, yet smoother upper-mid character. I haven't compared them in the same guitar, but thinner wire supposeldy has more consistent impedance. If I get another set of noiseless SC's, it will probably be some Z-Series Zexcoils. As much as I like my Wilde NF series sets, I think Scott's design is superior in a few ways, and the demos sound great. I think I'll leave off here. It's been interesting, and I appreciate all the thoughtful responses, but this is getting more into the weeds than is good for my OCD, and I should really turn my attention on some more pressing matters at this time. Takes care and thanks again to all concerned.  |
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Post by ms on May 9, 2021 10:35:51 GMT -5
I don't really understand how there would be significant wave asymmetry if there isn't significant flux change in the string, but that's on me. As for how a shorter denser coil would affect it, there are already stronger flux lines through more of the coil at a given distance, so why would there be more asymmetry rather than just more emphasized stronger string vibrations as I had originally thought? I fall in the: only the magnetized string matters camp, so I defer to the research of Dr. Scott Lawing. I'd be curious what he'd say about asymmetry: lawingmusicalproducts.com/dr-lawings-blog/how-does-a-pickup-really-workDo you wonder why the wave form's positive and negative sides of the cycle aren't the same? I think that's a case where the reluctance model makes it clear, in that when the string is moving closer, the reluctance (air gap) is decreasing, and when it's moving away, the reluctance is increasing. When the string is nearest to the coil, more lines of flux are involved with the coil, versus when it's further away. The peaks and troughs of the output waveform are of when the string velocity is at it's highest, which which is when it's physically passing the center point, and when the wave form is crossing the 0 and 180 degrees, that's when the string is physically either at the nearest point, or farthest point, from the the pickup. So the two sides of the wave form are, the string rushing away from the pickup, reluctance climbing, and then the string rushing towards the pickup, reluctance dropping. I think that the law of magnetic induction does a better job since you can count the number of flux lines passing through a loop of wire as a function of where the string is when given the form of the magnetic field. It appears to me that your discussion in the second paragraph shows that the distortion is not very big. The positive and negative peak voltages both occur in the same place in the magnetic field, but with oppositely directed motion. So the peak voltages have the same magnitudes. When the string is at either extremum the velocity magnitude is zero, and so the output voltages are zero, tending to hide the effects of different field strengths. That is, the zero crossings occur in the same placrs. I expect only a slight difference in the shape of the positive and negative half cycles from a sine wave motion. Maybe the asymmetrical appearance of the guitar waveform is mostly due to the even harmonics that are present in the string vibration. Possibly, when harmonics are present, the effect of the changers in the magnetic field strength are more important. |
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Post by aquin43 on May 9, 2021 11:23:27 GMT -5
If you accept Zollner's empirical formula for the effective signal flux in the coil as a function of distance from the pole in the strat pickup, which is effectively
flux ~ 1/(4.3 + d + x(t))
where d is the static string clearance and x the movement in mm, the distortion is as high as 16% for a 1mm peak string movement at Fender's preferred setting of 2mm for d.
It is the lack of intermodulation with the other strings that makes that sound OK. It probably adds to the fullness of the sound.
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Post by ms on May 9, 2021 12:51:10 GMT -5
If you accept Zollner's empirical formula for the effective signal flux in the coil as a function of distance from the pole in the strat pickup, which is effectively
flux ~ 1/(4.3 + d + x(t))
where d is the static string clearance and x the movement in mm, the distortion is as high as 16% for a 1mm peak string movement at Fender's preferred setting of 2mm for d.
It is the lack of intermodulation with the other strings that makes that sound OK. It probably adds to the fullness of the sound.
It changes the ratio of harmonics as a function time. Given that the ratio of harmonics is a function of time with no distortion, all it does is change the sound of the string a bit as a function of time. (Until you include the effect of the beating of natural and generated harmonics, probably a small effect, but nonetheless, something new.) I will have to check his derivation. |
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Post by antigua on May 9, 2021 17:09:16 GMT -5
I have modelled the two styles of pickup in 2D space using FEMM. The string is modelled using an array of magnets to give a flux distribution within it similar to that measured in a real string. The flux through the coils at 15 different distances from the centre is weighted by one minus the count from the centre to take account of the number of turns enclosing it. The total effective flux (to an arbitrary scale) is plotted from 1mm above the pole to 10mm. The magnet is assumed to be alnico 2 with a mu of 3.5 The brown curve is the full coil, the red is the microcoil and the orange is the microcoil scaled to the full level for comparison. The only source of magnetic variation is the distance of the string from the pole.
The scaled mirocoil is obviously less linear over the range but it has a steeper gradient at close distances which will help to compensate for the reduced total magnetisation.
I would expect curvatures in 3D space to be greater but the pattern should be similar.
Zollner's empirical formula of the form 1/(constant + distance + x) is similar in shape to these curves. What the microcoild do is reduce the constant, thereby moving the working range deeper into the non-linear region.
Could you do something like a single loop coil, and an effectively infinitely tall coil in order to define the boundaries? |
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