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Post by aquin43 on Jan 23, 2022 11:00:39 GMT -5
A point of view: while accepting the magnetised string pickup model, it is just a model. A guitar pickup is a hybrid of variable reluctance and moving magnet but for the sake of convenience it is useful to consider only the variable part of the flux and model it as a moving magnet system. If the string were made of a soft magnetic material, then the only magnetisation would be that immediately caused by its immersion in the static magnetic field. In this case we would have a pure variable reluctance pickup in which the string causes a flux change in the coil by variably re-routing a small part of the magnetic flux from the static field set up by the magnets. It is extremely difficult to analyse this because of the geometric complexity, the non-linearity of the problem and the fact that the flux variation within the coil is such a small fraction of the static flux. Knowing that the large static part of the field in the pickup produces no output, we can construct a more tractable model and consider the string, magnetised by the static field, as a moving magnet. The flux from this moving magnet then passes through mostly air and also the magnet pole and some of it couples to the coil. The magnet pole influences the routing of this flux by virtue of its incremental permeability, determined by its material and the local static flux density. This allows us to ignore the underlying large magnetic field and consider only the part that varies. This model is valid for very small amplitude vibrations of the string but for larger amplitudes it is necessary to remember that the magnetisation of the string, both the degree and the details of the pattern, depend on the location of the string relative to the pickup. This dependency adjusts so rapidly that it can be considered instantaneous so a static analysis is sufficient to model it for any frequency. Such a dependency acts to increase the non-linearity of the pickup. We know from measurements and simple experiment that the magnetisation of the string is longitudinal and we have a good idea of the pattern of flux within the string. The real guitar string is more of a hard magnetic material so it is capable of taking on a degree of permanent magnetism, particularly if it is allowed to touch the pickup pole as it is being installed. In practice this does seem to be rather less than the total induced magnetism and fades with time and use but it must mean that the flux variations in the coil are a mixture of the true moving magnet and the variable reluctance but certainly with the variable reluctance dominant. One would expect any permanent magnetisation of the string to reduce the non-linearity somewhat. In sum, the slight re-distribution of the whole field by the moving string is mostly what really happens and the concept of the string as a moving magnet is a convenient incremental model that vastly simplifies the analysis. Note that the magnet doesn't have to be inside the coil for the flux to be diverted by the string. Above or to one side will do since the flux is diverted along the length of the string and it is the whole three dimensional field of the magnet that is in play.
This sort of modeling is very common, e.g. calculating the gain of a transistor stage from the emitter resistance and the load resistance when the transistor is, in fact, modulating a large standing collector current with an exponential current/voltage curve. The emitter resistance is the gradient of the current/voltage curve and is simply a factor in a model.
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Post by antigua on Jan 23, 2022 12:50:26 GMT -5
That's a good summary. I've been finding it's helpful to find analogs with other areas of research, such as comparing a guitar string and a transformer, or the modeling with transistors, because it goes to show that we who are talking about this are not discovering anything that somehow eluded Einstein, it's just a new application of well understood concepts, from sectors that are a lot more profitable and well researched than electric guitar pickups.
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Post by ms on Jan 23, 2022 14:03:32 GMT -5
Hi aquin43. Another point of view: We have physics, and we have methods for solving physics problems. The physics is that the string becomes magnetized. This can be by one or more means, and the magnetization can change with time. The concept of variable reluctance is part of a method for solving certain simple problems involving magnetic materials. As you point out, it is not simple to apply to a guitar pickup. Thus the concept of variable reluctance is useful only as an analogy, not a method of solution. I think it is a dangerous analogy that can hide the physics.
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Post by antigua on Jan 23, 2022 17:33:50 GMT -5
Hi aquin43. Another point of view: We have physics, and we have methods for solving physics problems. The physics is that the string becomes magnetized. This can be by one or more means, and the magnetization can change with time. The concept of variable reluctance is part of a method for solving certain simple problems involving magnetic materials. As you point out, it is not simple to apply to a guitar pickup. Thus the concept of variable reluctance is useful only as an analogy, not a method of solution. I think it is a dangerous analogy that can hide the physics. I think the reluctance model is useful when thinking about the relative voltage output of a single coil with steel poles versus AlNiCo, as was being talked about in the other ongoing thread. If you just imagine the guitar string as being magnetized, then it gives a false impression that AlNiCo poles will produce more output than steel poles, because a Gauss meter will tell you the flux density at the top of steel poles is 250 to 500 Gauss, but at the top of the AlNiCo pole it's 600 to 1100 Gauss, but it turns out the steel poled pickup will have a higher output because the reduction of reluctance is greater than the increase of static flux, or another way of putting it, the reduction of metaphorical resistance is greater than the increase of metaphorical source voltage. Most of the confusion seems understandable, in that they're not intuitive, such as how much magnetism is lost to reluctance in air gap versus steel versus AlNiCo. A lot of people seem to think the magnetic flux flows like water in a pipe, or current in wire, where the losses would be little or nothing, when in fact the flux density diminishes a lot in a short distance, and that seems to be where a lot of inaccurate descriptions come from. For example, people say the P-90 has a "wider" window because of the wide coil and or the wide magnet arrangement, but they're not considering that the flux change at that point along the magnetic reluctance path is a fraction of a fraction compared to the portion of the path that is in the immediate area of the guitar strings. I've also seen people speculate that the magnetism of the guitar string extends down the length of the string, and that's the same kind of mistake, and that mistake leads people two think that RW/RP sounds different than non RW/RP, using reasoning that presumes the two pickups magnetically interact via the length of guitar string in between the pickups. If you assume that magnetism dissipates much more rapidly with distance than you would have guessed, a lot of that misconception clears up. |
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Post by aquin43 on Jan 24, 2022 10:07:50 GMT -5
Hi aquin43. Another point of view: We have physics, and we have methods for solving physics problems. The physics is that the string becomes magnetized. This can be by one or more means, and the magnetization can change with time. The concept of variable reluctance is part of a method for solving certain simple problems involving magnetic materials. As you point out, it is not simple to apply to a guitar pickup. Thus the concept of variable reluctance is useful only as an analogy, not a method of solution. I think it is a dangerous analogy that can hide the physics. Hello, ms.
Looked at one way, the string provides a low reluctance channel that removes some of the flux that would otherwise have passed through the coil and the variation of this removal is the source of the signal.
Looked at another way, the same result arises because the string becomes magnetised in such a way that the leakage of flux from it subtracts from the standing flux. Ignore the standing flux and you can treat the string as a source.
I agree that the second point of view makes the problem much more intuitive.
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Post by ms on Jan 24, 2022 18:54:44 GMT -5
I think the reluctance model is useful when thinking about the relative voltage output of a single coil with steel poles versus AlNiCo, as was being talked about in the other ongoing thread.... The reluctance method depends on two things: 1. The same mathematical form applies to 1.) current density equals conductivity times E field and 2.) magnetic flux density (B) equals permeability times magnetic field (H). 2. The magnetic problem is equivalent to a network of resistors driven by a voltage. The first applies here, but the second does not. The plot below is of a tiny neo magnet (simulating the string, almost a simple dipole field) over a pole piece, showing two different permeabilities. It is in the cylindrical symmetry mode, and so the plots are of just the right half. When mu equals one, the pole piece does nothing. The flux falls off quickly as expected. Note that the flux is heavily clipped near the magnet; that is, we would need a lot more colors to show how strong it gets near the magnet. When mu = 500, it does not fall off so fast. So, do the plots look right for mentally replacing the small magnet with an electric dipole, replacing the spatial variation of permeability with conductivity, and getting current density instead of flux density? They do to me, and so this analogy helps me to decide that the Femm result is useful.  |
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Post by antigua on Jan 25, 2022 1:00:30 GMT -5
I think the reluctance model is useful when thinking about the relative voltage output of a single coil with steel poles versus AlNiCo, as was being talked about in the other ongoing thread.... The reluctance method depends on two things: 1. The same mathematical form applies to 1.) current density equals conductivity times E field and 2.) magnetic flux density (B) equals permeability times magnetic field (H). 2. The magnetic problem is equivalent to a network of resistors driven by a voltage. The first applies here, but the second does not. The plot below is of a tiny neo magnet (simulating the string, almost a simple dipole field) over a pole piece, showing two different permeabilities. It is in the cylindrical symmetry mode, and so the plots are of just the right half. When mu equals one, the pole piece does nothing. The flux falls off quickly as expected. Note that the flux is heavily clipped near the magnet; that is, we would need a lot more colors to show how strong it gets near the magnet. When mu = 500, it does not fall off so fast. So, do the plots look right for mentally replacing the small magnet with an electric dipole, replacing the spatial variation of permeability with conductivity, and getting current density instead of flux density? They do to me, and so this analogy helps me to decide that the Femm result is useful. The thing is that magnetic resistance happens just by having air gap, but with direct current and voltage the losses are minimal so long as the copper wires are all connected. When people think about direct current in wire, the air around the wire matters a whole lot less than air around a magnetic path. With a magnetic field, it extends though air, but when you snip a wire and create and air gap, the direct current stops flowing. There's capacitive coupling, but most people just think in terms of direct current and touching wires, imagining water in pipes. So then I suppose you have to talk about how the air in the magnetic field is like lots of resistors, and that gets more confusing than things have to be. I think that FEMM model is a good way to show someone how the string relates to the pole piece, for all the people who believe it's work is done once it magnetizes the guitar string. |
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Post by ms on Jan 25, 2022 7:05:12 GMT -5
The thing is that magnetic resistance happens just by having air gap, but with direct current and voltage the losses are minimal so long as the copper wires are all connected. When people think about direct current in wire, the air around the wire matters a whole lot less than air around a magnetic path. With a magnetic field, it extends though air, but when you snip a wire and create and air gap, the direct current stops flowing. There's capacitive coupling, but most people just think in terms of DC current and touching wires, imagining water in pipes. So then I suppose you have to talk about how the air in the magnetic field is like lots of resistors, and that gets more confusing than things have to be. I think that FEMM model is a good way to show someone how the string relates to the pole piece, for all the people who believe it's work is done once it magnetizes the guitar string. Yes, that is important. The ratio of high to low conductivity can be very high in typical problems, while the ratio of high to low permeability is not so high. This means that you must be very careful how you apply the analogy. It is easy to come to false conclusions. |
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Post by ms on Jan 25, 2022 7:34:19 GMT -5
A point of view: while accepting the magnetised string pickup model, it is just a model. A guitar pickup is a hybrid of variable reluctance and moving magnet but for the sake of convenience it is useful to consider only the variable part of the flux and model it as a moving magnet system. If the string were made of a soft magnetic material, then the only magnetisation would be that immediately caused by its immersion in the static magnetic field. In this case we would have a pure variable reluctance pickup in which the string causes a flux change in the coil by variably re-routing a small part of the magnetic flux from the static field set up by the magnets. I think that there is a very real difference between variable reluctance and moving magnet. I do not think it has to do with whether we have a permanent magnet or not, but a lot to do with how much the flux changes around the whole path of the magnetic circuit. I think a variable reluctance system must use a "closed versus nearly closed" magnetic path with high permeability material to get enough reluctance change so that the dominant flux change through the sensing coil is the result of the flux change around the whole path. The magnetic circuit associated with the guitar pickup is nearly all high reluctance (or maybe I should say " high reluctivity" in analogy to "high resistivity"). Moving the string results in extremely little change in the field far from the string, while in a true variable reluctance system, the flux changes significantly around the whole path. |
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Post by aquin43 on Jan 25, 2022 8:22:27 GMT -5
Consider one pole of a strat pickup with N facing upwards. The flux in the coil consists of the flux in the magnet going up and a smaller flux in the coil outside the magnet returning down. What happens if you introduce an unmagnetised string from infinity to the normal working position? The flux in the magnet increases and the returning flux decreases. There is a net gain in flux within the coil. The magnet flux increases because the space near to the magnet has a marginally lower reluctance than before so the mmf of the magnet can produce a larger flux. The return flux in the coil windings decreases because the return path including the string now has a slightly lower overall reluctance near the N pole. The lua program www.aquinaudio.co.uk/DD/plate.luawill run on any FEMM installation and illustrates this, albeit in 2D. Download and run from the bottom selection in the file menu of FEMM The results appear in the lua console which the program opens.
The plate mu is set at 10 so that it doesn't intercept too much flux. Perhaps 1.1 would better represent
the effect of a thin string. At 1.1 the increase in flux is still there but the change in the flux lines is no longer perceptible.
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Post by ms on Jan 27, 2022 10:20:32 GMT -5
Consider one pole of a strat pickup with N facing upwards. The flux in the coil consists of the flux in the magnet going up and a smaller flux in the coil outside the magnet returning down. What happens if you introduce an unmagnetised string from infinity to the normal working position? The flux in the magnet increases and the returning flux decreases. There is a net gain in flux within the coil. The magnet flux increases because the space near to the magnet has a marginally lower reluctance than before so the mmf of the magnet can produce a larger flux. The return flux in the coil windings decreases because the return path including the string now has a slightly lower overall reluctance near the N pole. The lua program www.aquinaudio.co.uk/DD/plate.luawill run on any FEMM installation and illustrates this, albeit in 2D. Download and run from the bottom selection in the file menu of FEMM The results appear in the lua console which the program opens.
The plate mu is set at 10 so that it doesn't intercept too much flux. Perhaps 1.1 would better represent
the effect of a thin string. At 1.1 the increase in flux is still there but the change in the flux lines is no longer perceptible.
Yes, it runs as it should. The 5+% change in flux through the coil with a plate permeability of 10 is a bit more than I would have expected, even with a plate replacing the string, but I am sure that it is right. If you increase the plate permeability to 500, then you get a 15% change, and the plate becomes a really good magnetic shield with very low field above it. You can reduce the permeability in the y (vertical) direction to unity and still get a big effect, as one would expect from the plate geometry. What is the physical explanation? For that we have to drop a level below material permeability, which is a convenience introduced into the macroscopic Maxwell equations too allow easier mathematical solutions to problems involving magnetic materials. High permeability in a ferromagnetic material means that the tiny magnetic domains can be moved towards alignment with a small applied field. That is, it is easy to magnetize the material. Thus the physical explanation is that the system composed of magnet and plate reaches its lowest energy state when the plate becomes magnetized in such a way that the B field above the plate is almost canceled. |
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Post by aquin43 on Jan 27, 2022 11:08:06 GMT -5
Consider one pole of a strat pickup with N facing upwards. The flux in the coil consists of the flux in the magnet going up and a smaller flux in the coil outside the magnet returning down. What happens if you introduce an unmagnetised string from infinity to the normal working position? The flux in the magnet increases and the returning flux decreases. There is a net gain in flux within the coil. The magnet flux increases because the space near to the magnet has a marginally lower reluctance than before so the mmf of the magnet can produce a larger flux. The return flux in the coil windings decreases because the return path including the string now has a slightly lower overall reluctance near the N pole. The lua program www.aquinaudio.co.uk/DD/plate.luawill run on any FEMM installation and illustrates this, albeit in 2D. Download and run from the bottom selection in the file menu of FEMM The results appear in the lua console which the program opens.
The plate mu is set at 10 so that it doesn't intercept too much flux. Perhaps 1.1 would better represent
the effect of a thin string. At 1.1 the increase in flux is still there but the change in the flux lines is no longer perceptible.
Yes, it runs as it should. The 5+% change in flux through the coil with a plate permeability of 10 is a bit more than I would have expected, even with a plate replacing the string, but I am sure that it is right. If you increase the plate permeability to 500, then you get a 15% change, and the plate becomes a really good magnetic shield with very low field above it. You can reduce the permeability in the y (vertical) direction to unity and still get a big effect, as one would expect from the plate geometry. What is the physical explanation? For that we have to drop a level below material permeability, which is a convenience introduced into the macroscopic Maxwell equations too allow easier mathematical solutions to problems involving magnetic materials. High permeability in a ferromagnetic material means that the tiny magnetic domains can be moved towards alignment with a small applied field. That is, it is easy to magnetize the material. Thus the physical explanation is that the system composed of magnet and plate reaches its lowest energy state when the plate becomes magnetized in such a way that the B field above the plate is almost canceled. The other intuitive explanation also works. In this linear system, the plate becoming magnetised produces a leakage B field that adds to the standing field due to the magnet. In the pickup region, the extra flux, being directed upwards, adds to the flux the magnet and subtracts from the flux in the coil. In other words, the moving magnet model.
I was thinking that another factor that adds legitimacy to the moving magnet model is the non-linear magnetisation characteristic and hysterisis of the string. This will cause the magnetisation of the string to vary much less than proportionally with the changing field from the pole piece that it encounters as it moves. This will add complexity to any variable reluctance model while removing complexity from the moving magnet model.
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Post by asher on Feb 12, 2023 11:33:36 GMT -5
This article seems quite good on the question of the magnetic component of guitar strings: www.gitec-forum-eng.de/wp-content/uploads/2020/08/poteg-3-string-magnetics.pdf. If I'm understanding the reluctance model, it is premised on the string reaching flux saturation such that it is no longer effectively permeable. The article suggests that due to tension-based construction requirements, very little variability is possible in steel grade and content. It also concludes that the saturation point for common strings is around 1.5T (15,000 Gauss). How could strings ever reach saturation if the strongest magnets in pickups are usually not even 1200 Gauss (.12T)? >> Edit I think the answer is that Flux-max = Flux-saturation * Effective-area. For High E that would mean .229mm diameter, which gives about 0.062µT (.0006 Gauss). So even with a high saturation point, the effective area is so tiny that it takes almost nothing to saturate.
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Post by ms on Feb 13, 2023 7:37:05 GMT -5
This article seems quite good on the question of the magnetic component of guitar strings: www.gitec-forum-eng.de/wp-content/uploads/2020/08/poteg-3-string-magnetics.pdf. If I'm understanding the reluctance model, it is premised on the string reaching flux saturation such that it is no longer effectively permeable. The article suggests that due to tension-based construction requirements, very little variability is possible in steel grade and content. It also concludes that the saturation point for common strings is around 1.5T (15,000 Gauss). How could strings ever reach saturation if the strongest magnets in pickups are usually not even 1200 Gauss (.12T)? >> Edit I think the answer is that Flux-max = Flux-saturation * Effective-area. For High E that would mean .229mm diameter, which gives about 0.062µT (.0006 Gauss). So even with a high saturation point, the effective area is so tiny that it takes almost nothing to saturate.
The string saturates because it is made from a ferromagnetic material, and therefore has a permeability significantly higher than one. That is, the string in effect "amplifies" the field so that a relatively small applied field increases to a large value inside the string. The reluctance model does not depend on string saturation. As the reluctance varies, so does the magnetization of the string. This could result in the string going in and out of saturation, but the model works for weak fields with no saturation. |
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Post by asher on Feb 13, 2023 16:42:08 GMT -5
What is the source of the reluctance in question, then?
It seems to me that the string remaining saturated is essential to the frequency creating a uniform signal, because once saturated dɸ depends only on string velocity (velocity of a constant flux). If ɸ is changing (not at saturation) then dɸ is flux-change-dependent velocity. In other words, if we can assume the string reaches saturation, we don't need to concern ourselves with the string's flux magnitude.
Is the reluctance model stated formally somewhere?
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Post by aquin43 on Feb 13, 2023 17:10:36 GMT -5
If your theory has to assume saturation of the string, then it is obviously wrong because a pickup will respond in some fashion to any amount of any kind of ferromagnetic material.
The variable reluctance idea assumes that the string will redirect flux that normally would have to pass through high reluctance empty space to complete the magnetic circuit. It is valid but seems to be beyond computation. The moving magnetised string model is much more approachable.
The output normally depends on both the string velocity and the string position and so is a non linear function of string velocity.
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Post by ms on Feb 13, 2023 17:39:45 GMT -5
What is the source of the reluctance in question, then? It seems to me that the string remaining saturated is essential to the frequency creating a uniform signal, because once saturated dɸ depends only on string velocity (velocity of a constant flux). If ɸ is changing (not at saturation) then dɸ is flux-change-dependent velocity. In other words, if we can assume the string reaches saturation, we don't need to concern ourselves with the string's flux magnitude. Is the reluctance model stated formally somewhere? In the variable reluctance description, the reluctance around some path composed of permeable material changes when the position of a permeable object changes. For example, if we cut a slot in the cross section of a permeable toroid and move magnetic material in and out of the slot, the flux around the toroid changes, assuming, for example, a coil with current drives the flux, or maybe a permanent magnet. The magnetization in the moving magnetic material varies. If this moving magnetic material is saturated, then there still might be some change in the flux around the path, but this would be very subtle and I do not see how you could attribute to variable reluctance. |
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Post by asher on Feb 13, 2023 22:39:38 GMT -5
So if the guitar string is always saturated, the reluctance model cannot explain things?
The math above seems to suggest that with any normal pickup magnet, the strings are always saturated (as claimed by multiple articles).
Also, if the permeable character of the string is changing, how could the change in flux consistently correspond to the velocity? As the string gets closer/further from the magnet, the rate of change of ɸ would increase/decrease, creating inconsistencies in the frequency produced from string velocity. That we demonstrably can achieve a consistent resolved frequency from a guitar string would seem to serve as evidence that this is not happening.
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Post by antigua on Feb 14, 2023 0:57:08 GMT -5
Variable reluctance includes the air gap between the string and the pickup, and the air gap changes as the string moves. The saturation of the string would just be one factor, and you'd have to account for hysteresis, the magnetization won't exactly rise and fall in accordance with movement. Either way, the velocity is the same, but variable flux in the non saturated guitar string would add a distortion, a harmonic.
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Post by ms on Feb 14, 2023 6:04:58 GMT -5
So if the guitar string is always saturated, the reluctance model cannot explain things? The math above seems to suggest that with any normal pickup magnet, the strings are always saturated (as claimed by multiple articles). Also, if the permeable character of the string is changing, how could the change in flux consistently correspond to the velocity? As the string gets closer/further from the magnet, the rate of change of ɸ would increase/decrease, creating inconsistencies in the frequency produced from string velocity. That we demonstrably can achieve a consistent resolved frequency from a guitar string would seem to serve as evidence that this is not happening. The guitar string is not saturated right over the center of the pole piece and for some distance near the center. The direction of longitudinal magnetization changes as its magnitude passes through zero. The details and how they change as a function string position are complicated. Who said the induced voltage is exactly proportional to string velocity? It is actually significantly non-linear, (product of more than one factor) as aquin43 explained above. "Proportional to velocity" is just a good approximation. Antigua: The air gap between the string and the pole piece is a small part of the total air gap around the path of varying flux. The gap is so large that the main purpose of the variable reluctance method, simple solution for certain simple problems, does not apply. One of the conditions for a simple solution is that the air gap in the nearly complete path of permeable material must be small enough so that the fringing field (lines curving outward at the edges of the gap) is small. In the case of a pickup, the fringing field dominates, and other methods of solution are better. |
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Post by asher on Feb 14, 2023 7:19:13 GMT -5
I said that dɸ with a saturated string becomes velocity, not that voltage is linearly related to velocity. Theoretical voltage is N*dɸ/dt, which is obviously not linear. In what situation would this be true? A pole piece pointing upward has either the N or S pole pointing toward the string. The center of a pole is generally the strongest point in the field, not the weakest. If you mean that the direction of the MMF vector changes, then I agree, but so what? The flux of the string either A. is strongest at the center and varies at distance B. is saturated and does not vary. The best explanation I have found for any role reluctance might play is the slimmest of explanations given in this patent By this explanation we are to believe that the pickup is effectively measuring spatial displacement? It's not clear to me whether aquin43's descriptions here are to be taken as serious descriptions of the hypothesis What would it mean to "remove" or "subtract" flux? I don't understand all this discussion of reluctance. The math on inductor behavior in differential flux fields seems fairly straightforward. It seems to me that the complexity is in how to understand what the math tells us. What am I missing? |
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Post by ms on Feb 14, 2023 7:40:13 GMT -5
The magnetization of a long thin piece of permeable material is almost completely along it. In pickup, the component of permanent field along the pole axis does very little. The string is magnetized by the horizontal component (field bends over), which maximizes away from the center.
The component of time varying field in the direction through the coil results from the change in direction of the longitudinal magnetization.
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Post by aquin43 on Feb 14, 2023 8:46:48 GMT -5
So if the guitar string is always saturated, the reluctance model cannot explain things? The math above seems to suggest that with any normal pickup magnet, the strings are always saturated (as claimed by multiple articles). Also, if the permeable character of the string is changing, how could the change in flux consistently correspond to the velocity? As the string gets closer/further from the magnet, the rate of change of ɸ would increase/decrease, creating inconsistencies in the frequency produced from string velocity. That we demonstrably can achieve a consistent resolved frequency from a guitar string would seem to serve as evidence that this is not happening. You aren't thinking it through. Yes, "as the string gets closer/further from the magnet, the rate of change of ɸ would increase/decrease, creating inconsistencies in the frequency produced from string velocity" BUT these "inconsistencies" obviously will vary synchronously with the string movement and so will represent harmonics of the string frequency. In other words distortion.
Pickups work perfectly well with the string at some distance so obviously saturation of the string is not necessary. The distribution of flux in the string has been discussed and modeled extensively on this forum.
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Post by asher on Feb 14, 2023 9:24:49 GMT -5
The strings require so little flux to become saturated (due to their tiny effective area) that they will be saturated at essentially any guitar-based distance with any existing pickup magnet. Check the math.
That's not correct. They would create a distinct shape on either side of the expected frequency curve that would stand out. This has not been exhibited.
Links please to any that you feel have made useful and accurate conclusions. From what I see, the math regarding saturation is plain as day.
For all parts of the material that are in the field of flux. From the measurements I've seen, that's about 3cm along the string.
Define what you understand this to mean.
Do you mean that it contributes very little to the generation of the voltage signal? This is true, insofar as you don't count its function in magnetizing the string or creating a flux field wherein flux differentials can exist.
You certainly couldn't remove the permanent field and still have things work as expected. I assume you will say that the strings can become permanently magnetized and then used without the pickup magnet. This is true, but only for a short time, and not with the same output.
Still not understanding any explanation of this.
What is your basis for this claim? This just seems wrong.
The string is magnetized by crossing flux lines. Where are you getting the difference between the vertical and horizontal component of the flux field? The horizontal component would be on the side of the pole. The string is not exactly on the side of the pole.
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Post by aquin43 on Feb 14, 2023 9:54:47 GMT -5
"a low reluctance channel that removes some of the flux that would otherwise have passed through the coil"
It is plain English. Flux used to flow one way and now it flows another. It is, therefore, removed from where it used to flow.
Another thing, how can an any kind of deterministic multiplier that is directly related to the string position not vary synchronously with the string vibration? That being so, any modulation of the pickup output that it produces must be harmonically related to the string vibration.
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Post by ms on Feb 14, 2023 10:09:27 GMT -5
==> I think the answer is that Flux-max = Flux-saturation * Effective-area.
This equation does not imply that a small cross section means easy saturation.
longitudinal magnetization:
I believe that aquin43 mentioned this above:
Remove the magnetization from the pole piece. Use a magnet* to magnetize from the side, that is, along the face of the pickup. The pickup works (good output) even though the permanent field does not point through the coil along the pole piece. Thus it works as we have described. If you do not want to remove a pickup magnet, you can reduce the output from one of the E strings by locating a magnet as described with the polarity selected to partially cancel the longitudinal magnetization caused by the pickup magnet.
* You need to use a magnet that could be used as a pole piece (such as an actual Fender type alnico pole piece magnet) in order to get the correct spatial field variation.
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Post by ms on Feb 14, 2023 10:18:48 GMT -5
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Post by antigua on Feb 14, 2023 12:53:01 GMT -5
Antigua: The air gap between the string and the pole piece is a small part of the total air gap around the path of varying flux. The gap is so large that the main purpose of the variable reluctance method, simple solution for certain simple problems, does not apply. One of the conditions for a simple solution is that the air gap in the nearly complete path of permeable material must be small enough so that the fringing field (lines curving outward at the edges of the gap) is small. In the case of a pickup, the fringing field dominates, and other methods of solution are better. I realize the air gap is small, but the voltage output is small, and you have to have ~7000 turns of wire to sum up a usable output voltage. My understanding is that reluctance and resistance are similar ideas, so let's say the string near the pickup is resistance reluctance A and the string far from the pickup is resistance reluctance B, then as the string moving gives a magnemotive force of A - B, and this difference is where the voltage comes from in the coil. I would think that even if you modeled the string as a permanent magnet that moves back and forth, that the delta of flux through the coil that produces the expected voltage would compute out the same as you had looked as it as reluctance model, but the thing that makes the reluctance model appealing is that it automatically accounts for the contribution of the permeable core in the pickup, since you're looking at all the permeable elements at once, and how the sum reluctance between them changes when the guitar string is moving. To the question of the string saturating, I think that if you put a neodymium magnet beside the string while it moves, it increases the output a bit more, wouldn't that indicated that the string was not at the peak of it's BH curve? |
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asher
Apprentice Shielder
Posts: 26
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Post by asher on Feb 14, 2023 13:27:58 GMT -5
How do you figure? It means exactly that.
What math do you take this to correspond to?
Magnetic flux is famously difficult to shield, which is what "removing some of the flux" would amount to. It can be done to some extent by creating barriers from super-permeable material (dissipating the flux into the material), but that is certainly not what is happening in a guitar.
Where do you think the flux is going?
Likely due to paramagnetism. It will continue increasing, but at a much slower rate.
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Post by ms on Feb 14, 2023 14:29:20 GMT -5
==> I think the answer is that Flux-max = Flux-saturation * Effective-area.
This equation does not imply that a small cross section means easy saturation.
==> How do you figure? It means exactly that.
On the left side we have flux; it must also be so on the right, and so Flux-saturation is a flux density, giving flux when multiplied by an area. So all this equation says is that the maximum flux through an area is found by multiplying the maximum flux density by the area.
==> Magnetic flux is famously difficult to shield, which is what "removing some of the flux" would amount to.
"Magnetic flux is famously difficult to shield" means that reducing the magnetic field to near zero is difficult. "Removing some of the flux" with high permeability material is easy.
Are there not more important things to discuss? For example, you are claiming that the model of consisting of longitudinal magnetization in the string which changes sign as it crosses the pole piece, producing a radial field, is wrong. Can you show some theoretical or experimental evidence for this?
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