Mike Sulzer

You go between to and bottom many times before you get enough turns on, so you can always arrange to stop at the bottom, not that it matters so much when the coil form is pretty much full.

http://www.buxcomm.com/catalog/index.php?m...ex&cPath=22

Please remember that that article you referred to is an advertisement. Not everything in it is misleading. There is nothing wrong with putting the magnets around the edge. But they are just magnets. And the claim that they draw some of the flux from magnetic interference through them rather than letting it pass through the coil has some validity. But they are not telling you anything about the core of the coil. Is it air? I doubt it because the inductance is quite high. If they use cores of magnetic material, then those cores also concentrate the field from interfering sources and so the magnetic shielding ability is limited. And also those cores tend to make the the pickup more sensitive to the part of the string right over them, and so the claim that they sense over the the whole coil is exaggerated. That article is 80% flimflam and 20% engineering. In other words, it is a great ad!

No, the current needs to run through a coil, not a resistor.

A couple of posts above is a description of how a simple air core inductor works. Many of these ideas apply to inductors with ferromagnetic cores, and these ideas can be applied to solving a practical problem: reducing the magnetic hum from a single coil pickup without losing the "single coil" sound. Magnetic hum reduction requires a cancelation technique; this is a summary of the specifics of this system: 1. It uses a a dummy coil. 2. The coil is designed to be buffered with a very simple active preamp. 3. The active preamp feeds adjustment pots, one for each pickup, which in turn put a correction voltage in series with the pickup. 4. The active preamp is only for the dummy; the pickups can remain passive or you could continue to use most preamps or equalizers, making this practical for use with a bass with single coil pickups. 5. The preamp uses only four parts (in addition to the adjustment pots), a FET, a resistor, and two capacitors. 6. The preamp draws less than 100 micro amps and runs on three volts (Lithium battery for very long life, voltage can be higher if desired). It needs only to reproduce the mv level hum signal. Why use a preamp? As is well known, a dummy coil has an inductance and a capacitance similar to the pickup itself. The series combination of the two thus has about double the inductance and half the capacitance. So the resonant frequency of this system alone has not changed. But when connected to the cable capacitance, the resonant frequency drops due to the higher inductance, and the loss of high frequencies destroys the bright single coil sound. One solution that has been around a long time is to put a preamp (or it could be called a "buffer") on each pickup and the dummy. Then the outputs of all are added in a way that assures that hum cancelation occurs with each combination of pickups. This works well, but it is complicated and uses more power than I like. It also means that if you want to use some specific preamp or active equalization, you need to make the dummy part of this system. This might or might not be easy to do. So a simpler solution is to just use a preamp on the dummy and then feed adjustment in series with each pickup into the wire that normally would be connected to ground. The presentation of this idea is in this order: 1. First, the preamp circuit. 2. The interfering hum is described and the degree of cancelation is demonstrated. 3. The design of the dummy is described. It needs some fairly specific characteristics, and some understanding of its circuit properties is required. The preamp circuit is found here: http://www.naic.edu/~sulzer/bufferedDummy.png. It uses a JFET as a source follower. Followers have a gain slightly less than unity, and the gain is fairly stable, a requirement for a cancelation circuit. The dummy coil must have a higher sensitivity to the hum magnetic field than the pickups so that the adjustment can be made. The use of battery bypass capacitor is good practice; I built one without it and it works fine, but might not in all circumstances. I use a large Sony Triniton "humblaster" CRT TV as a hum source. I run it off a circuit that is switched in two places, and this apparently makes a big loop of current, great for making a magnetic field. The hum output of a guitar with single coil pickups is shown here: http://www.naic.edu/~sulzer/humTimeDomainPlot.png. This waveform looks nothing like a sine wave, and so it is full of harmonics. Thus the cancelation circuit must work over a large frequency range. The dummy coil looks pretty much like a pickup (that is just convenient, not necessary) and is mounted inside the guitar. It must be aligned in the same direction (or 180 degrees, that is down, instead of up). You can always switch the wires to get the polarity right. I shorted out the hum cancelation and pointed the guitar so as to maximize the hum, and measured the result. Then unclipped the cancelation, and measured again after adjusting the pot. The resulting spectral measurements are shown here: http://www.naic.edu/~sulzer/humSpectralPlot.png. The blue is with no cancelation, the red with. This is a best case. Over time you will not do so well on average. The coil uses a strat type bobbin from Guitar parts USA. I use ferrite beads from CWS Bytemark as pole pieces. Two beads, each .2" in diameter and .4 inches long are glued together. I use the material with the highest permeability (about 4700) so that I can make the most sensitive coil with the fewest turns. My pickups have 7000 turns; the dummy has 5100, but still has a higher sensitivity due to the higher permeability and the longer length of the pole pieces. The reasons for doing it this way are a bit subtle. (I suggest reading Lemme's article on pickups for a good description of the pickup circuit.) It is necessary to understand that a simple model for the pickup is a voltage source in series with a inductor. Then we must add a capacitor representing the inter-winding capacitance that also cuts out high frequencies. The cancelation should put another ideal voltage source in series with the pickup inductor; this is not perfect in this circuit, but the resistance of the voltage divider is small enough so that the sound of the pickup is not affected noticeably. But the problem is that the inductance and capacitance of the dummy filter its output, destroying the cancelation at the higher harmonics. The resonant frequency is almost high enough since the pickup capacitance is a lot smaller than the cable capacitance, but we need to move it up a bit. The solution is to use the properties of an inductor as described a couple of posts above. Suppose we take turns off the coil; the inductance depends on the square of the number of turns (roughly), so it goes down quickly. The sensitivity to external magnetic fields depends linearly on the number of turns (that is, is proportional to the number of turns). It falls more slowly than the inductance as turns are removed. If we use higher permeability pole pieces and make them longer, we increase both almost together. So if we bring the sensitivity back up, the inductance comes back up as well, but not to its original level. Also, we have lowered the pickup capacitance. In this way we get a higher resonant frequency, and can move the peak up high enough so that it is not a problem.

For the plain strings you want piano wire, sometimes called music wire. It is a high carbon steel. You can find some places selling it on the web, but it is not really all that common. I think you are out of luck on the wrapped strings. Also, for bulk pre-made strings, you can try juststrings.com in addtion to the others suggested.

Thank you David, I am glad you find this interesting. I agree that pickups are quite complicated and that we cannot do it all here. But I do think that some of the results are useful. For example, the field induced by the moving string falls off through the pole piece with increasing distance from the string. This suggests that the shallow wide flat coil of the P-90 is more efficient for high output than the narrow tall coil of the Fender tele and strat design. Then there is that old question about the spatial sampling of the string. The FEMM plots indicate that only the part pretty much right over the pole piece is sampled significantly. I will be presenting some more stuff using the circuit properties of the pickup soon.

Using two coils wound to have different resonant frequencies might be able to achieve this with some additional passive components. But why not just use active equalization like bass players do?

It has nothing to do with the component burning out. The idea is to limit the possible 60 Hz current in a fault situation to non-lethal values while normally providing a low impedance path for the higher harmonics that cause "buzz". I consider this a bad strategy because you cannot really be sure the current will be low enough to be safe, but if you think you are safe, you might not bother to test the grounds. You must make sure that everything is properly grounded.

It was mentioned above that we need to discuss the circuit aspects of the pickup. A pickup coil is an inductor, but it is a complicated inductor. Let's start by looking at a simple inductor with the goal of learning how inductors work and how they serve as a simple example of the law of induction and even provide an easy way to remember how this law works. Here is the equation (which you could justify by a series of measurements) for the inductance of a single layer coil: L = Fn^2r. This says that the inductance depends on some factor F, discussed below, the square of the number of turns, and the radius r of the coil. F is a geometrical factor. It is large for a short coil, and small for a long coil. We assume the following: 1. An inductor works by the law of induction. When the current through the inductor changes, a voltage is induced that opposes the change in current. 2.The magnetic field inside the coil depends on the current through the coil and inversely on the radius of the coil. Remember that if you are far from a magnet or system or currents, the magnetic field falls off with the cube of the distance, but if you are close or inside it, it is complicated, and someone has to compute it. Referring to the equation above, how can it be that the magnetic field falls off with r but the inductance increases with r? This tells us something about the law of induction. We have something like this: r is proportional to x/r, where x is unknown. This works if x = r^2. The area of a circle is (pi)r^2, so this suggests that the law of induction results in a voltage that depends on the area of the coil. It certainly does not prove the general case, but it suggests that this should be checked for other cases. And if you did, you would find that this is how the law of induction works. Now, what about the n^2 in the above equation? Lets start with one turn. When the current through the loop changes, the magnetic field in the loop changes and by the law of induction, a voltage is induced around the loop. If we add a second turn, the same thing happens in it due to the current through it. (And the current through the two turns is the same since they are in series.) So this would suggest us that the inductance depends on n, not n^2. But something more happens. If the turns are really close together, the same field from turn one that passes through itself also passes through turn two. So we have "mutual coupling". We add up all the voltages: in 1 from 1; in 1 from 2; in 2 from 1; in 2 from 2; For three turns we have in 1 from 1; in 1 from 2; in 1 from 3; in 2 from 1; in 2 from 2; in 2 from 3; in 3 from 1; in 3 from 2; in 3 from 3; For 2 turns we have 4 voltages; for 3 turns we have 9 voltages. And so on. This n^2. Two or more turns cannot occupy the same space, and so the field through turn 2 from turn 1 is not really the same as "in 1 from 1". This is where the factor F comes in. We have n^2 voltages, but the amount of coupling goes down with how far away turn 1 is from turn 2. So in summary, we have three important things: 1. The fact that the inductance increases with the radius of the coil suggests the correct form of the law of induction: that the induced voltage depends on the area of the coil. 2. the n^2 dependence comes from the mutual coupling of each coil with all the others. 3. The factor F comes from the fact that turns further away from each other couple less.

I think I have not been very clear about the variation of the magnetic field in the horizontal direction. With circular pole pieces a small movement of the string in the horizontal direction does not cause a significant loss of signal. A small motion in the vertical direction does. This tells us that even with circular pole pieces, we have an asymmetry that favors sensitivity to vertical vibration. (The FEMM results are in agreement.) Therefore, using a pole piece with even higher asymmetry is not a big effect; we already have the asymmetry with the circular poles. For pickups I have measured, the interwinding capacitance is less than the cable capacitance. No matter how much you reduce the former, the latter is still there unless you use a preamp. Now lets look at some of your quotes from the patents. Bartolini: "Since both the inductance and capacitance of a sensing coil vary linearly with its mean radius, replacing one coil by multiple small coils can reduce the impedance the pickup system by a factor equal to the number of coils and raise the self-resonant frequency by a factor to the square root of the number of coils." The inductance of multi-layer coils with ferromagnetic cores is not simple; let us leave that for another time. But looking at high frequencies where the impedance is capacitive, the statement about impedance and resonant frequency frequency is not correct if there is a significant cable capacitance in the system. Kozinsky: The same type of comment applies to the first part of that paragraph. Second part: "Second, because one coil structure is wound around a plurality of pole pieces, rather than around each individual pole piece, the magnetic lines of force produced by the pole, pieces will only cut two sides of the coil structure rather results m low attenuation of all high order frequencies than all four sides. This results in a decreased induced current and therefor adversely affects the sound reproduced by the instrument. This loss is compounded by the fact that the magnetic field is reduced by the square of the distance, between a pole piece and the coil structure." The law of induction states that it is the changing flux across the whole area of the turn that counts. His argument about "two sides" and "higher order frequencies" does not make sense. The last sentence is really strange. How the field falls off does not matter in any simple since the pole piece is still included in the area of the loop. And if it did matter, it would be "falls off with the cube", not square.

David, I agree that the Bartolini design has a very small variataion of the magnetic field intensity in the horizontal direction. But this solves a non-existent problem. The field from a pickup changes quickly in the vertical direction. You know this because the output gets weaker as you increase the height of the string. If the field of a round pole pickup changed as quickly in the horizontal direction, string alignment over the pole piece would be critical, and even very small bends would cause a big loss in signal. Neither happens with the standard round pole pickups. I do not know why individual coils give a clearer sound. I have made such pickups, but not noticed the effect.

"So... if Femm models magnetic fields, we also have things like the geometry of the coil to account for (plus the aspects of the coil itself.. wire gauge, number of turns, etc.)" That is true, Dvid, we have not discussed here the circuit aspects of the pickup, and coil geometry is important for determining the inductance of the coil. The work presented here is pretty much in conflict with what Bartolini says. Consider this part of the patent write-up you quoted: "For example, pickup systems with circular pole pieces provide a magnetic field having the form of a symmetrical sinusoidal shell and a string vibrating within such a magnetic field will generate approximately equal magnitude electrical signals for string vibrations both parallel and perpendicular to the string plane." Horizontal motion has not been considered in the work above because an examination of the fields produced by FEMM indicated that vertical motion is the dominant effect for the circular pole pieces assumed. I cannot put a numerical value on the v/h ratio; that would require more work, but it certainly appears that the horizontal is significantly smaller than the vertical. It looks like what Bartolini is saying is incorrect. Also, the circuit discussion in the last paragraph cannot be applied generally. For example, in a passive system, it is the cable capacitance that dominates (with the volume up), not the inter-winding capacitance.

Now it is time to put all this together and predict the response of a pickup to a sinusoidal string motion. This figure: http://www.naic.edu/~sulzer/nlmMagAndFluxVsDis.png reviews the previous results, and presents one new one. The blue curve is the field produced by the magnetization of the "string" as a function of the distance from the pole piece. (This curve is a bit different from the one presented before. It has been smoothed to reduce noise which was only visible if you blow it up.) The red curve is proportional to the magnetic flux through the pole piece, as a function of the distance from the pole piece, for a constant level of magnetization. We multiply the two curves together to get the curve we need; this is the green curve. If the pickup were linear, this curve would be a straight line. Over the approximate maximum motion of a string (.07 to .13 inches), there is significant curvature. So the question is this: if a string moves in a sinusoidal way, how non-sinusoidal is the response of the pickup. (We know the string motion is not a simple sinusoid, having various harmonics, but let's start simple.) To answer this question, we think of the string moving such that the time history of the distance from the pole piece traces out a sine wave. This corresponds to "motion" along the green line; we pick out the point we need at each time. Since we have the function at certain evenly spaced points only, we use a spline interpolation routine to generate the time sequence that we want. The results are show here: http://www.naic.edu/~sulzer/nlmFluxAndDervVsT.png . The blue line is proportional to the magnetic flux through the pole piece as a function of time. It is clear that it is not sinusoidal, but looks sort of like the output of a triode preamp stage at a very high level but before saturation. We know that this wave form has second harmonic and probably others as well. However, the blue curve is not what the pickup would produce. It is the change in flux with time that counts. We generate this from the blue curve, and this is the red curve. It looks even less like a sine wave; this is expected since the differentiation emphasizes the harmonics. Those familiar with calculus will see why it looks as it does: parts of the blue curve look a lot like a parabola, and the derivative of a parabola is a straight line. Fourier analysis of the red curve gives about 30% second harmonic, 4% third harmonic, and less than 1% of higher harmonics.

Even at full volume, the pot is a resistor placed acros the pickup. A 10K pot would cause a substantial loss of volume, especially with an overwound humbucker. Piezos should be fed directly into a very high impedance pickup for best frequency response. But whatever you like is what is best for you. Tone pots: Too small a value eliminates the brightest tones.

Go look at the material available on AX84.com to get a good idea of beginner, intermediate, and more advanced ampbuilding projects (tube only, of course)

This subject of this post is what happens to the magnetic flux through the pole piece when the magnetized "string" moves up and down. Errors (noise) in the FEMM simulations prevent us from looking directly at the magnetic field perturbations in the pole piece due to the B field produced when the string is magnetized by the permanent field. Therefore, we use the field at the string as a measure of the magnetization that is produced, remove the permanent magnet, and replace the string with a permanent magnet that generates the same field. This figure shows how this works: http://www.naic.edu/~sulzer/nlmAsmVsIndMag.png. The red line is like one of the curves from the set at the bottom of the plot described in the previous post. It is shown here on a larger scale, and the simulation noise is clearly visible. The simulation tries to compute the additional field from the string as induced by the permanent magnet at the bottom of the pole piece. It has limited accuracy. The blue line shows the field from a permanent magnet replacing the string, with the permanent magnet at the bottom of the pole piece removed. This field is in good, but not perfect, agreement with the induced field and it has no visible noise right through the pole piece. This figure, http://www.naic.edu/~sulzer/FieldThroughPP.png, shows how the field through the pole piece varies for five different positions of the string magnet. The plot uses a log scale so that the entire range can be seen. The peaks look wider because of the log scale. It shows the field through a single contour in the pole piece. It would be good to know the field along all possible contours to determine the flux through the pole piece, but the relative changes in flux are not much affected by just looking at one. So as a proxy for the total flux, we just add up the field along the contour for each string position. These five numbers then represent the flux. They are shown on the plot from the previous post, http://www.naic.edu/~sulzer/nlmPickupResp.png, in the middle set along with two lines. The light blue curve is a scaled version of the green line below (or the dark blue above). The fact that the points do not fit the light blue line shows that a different function describes the variation of flux with distance (with the magnetization constant). A good fit (purple line) is easily obtained by steepening the slope a bit. So the purple curve determines the relative variation of flux with distance if the string magnetization remains constant. But we know that it does not. So it is necessary to multiply the two variations together to get the total response. That will be the subject of the next post.

The purpose of this post is to start the process of showing that a magnetic pickup is non-linear. This means that if one were to move a string in a perfect sinusoid, the output of the pickup would consist of the fundamental and some harmonics. Since real string motion already has harmonics, the non-linearity modifies the harmonics, and thus alters the sound. In his article "The Secrets of Electric Guitar pickups", (http://buildyourguitar.com/resources/lemme/), Helmuth Lemme briefly discusses the non-linear distortion of a guitar pickup due to the hyperbolic relationship between the distance of the string from the pole piece the flux through it. The idea here is to show a simplified guitar waveform resulting from this non-linearity. In this post we look at how a small piece of steel (representing the string) at various distances over the pole piece is magnetized to produce a perturbation the the total field. A later post will look at how the field from the "string" produces magnetic flux through the pole piece. Then it is necessary to show how to put these two things together to get the simplified waveform from the pickup. Non-linear effects are amplitude sensitive; therefore it is important to measure how far the string moves from its equilibrium position. At mimf.com, Bill Machrome suggested making a mini strobe light from a white LED. Driving it very near the vibration frequency almost freezes the motion, and a rule can be used to determine the peak vibration amplitude. This turns out to be just under 1/16 inch (#1 E string, .011"), and so I have used +/-.03 inches as a maximum. The pickup modeled here is a single steel pole piece with a small neo magnet on the bottom. A small piece of steel (the "string"), is located .1 inches above this pole piece, and can move up and down. The "string": is actually a small ring, .010 inch thick and .1 inch in diameter. This is what I can model in FEMM using the mode with cylindrical symmetry. This figure (http://www.naic.edu/~sulzer/nlmPickupResp.png) shows the result discussed this post (and part of the next) . First consider the set of curves near the top of the plot. The five peaked plots show the magnetic field with the string located at five different heights above the pole piece. (We are looking at the field along a vertical contour extending up from the pole piece .05 inches from its center. This contour passes through the "string".) Also, one line (dark blue) shows the field with no "string". It is the baseline that the other fields approach as the distance from the string is increased. The lowest set of curves is like the upper set, but with the baseline subtracted. The green line running along the peaks of the curves is the the field with no string, scaled by 40% in order to show that the variation with distance of the intensity of the magnetization of the string is very nearly the same as the field that causes it. We would expect this to be true because the string has very little material compared to the pole piece. But we would not necessarily expect such a simple result if we put a much larger piece of steel over the pole piece. Magnetic problems can be quite complicated, and it is good to find a simple result! This simple result means that a single application of FEMM determines all we need to know about the magnetization of the string as the string varies in height. Remember, the magnetization of the string is essentially instantaneous: it varies with the field as the string moves up and down. This is similar to how an iron core audio inductor works: as the current in the audio wave form varies, the magnetization of the core varies along with the current. There is a middle set of two curves and five black points. They will be discussed later.

Peter, Here is some more info on the way I measure inductance: 1. Make a parallel resonant circuit with the pickup coil and a cap of say 1000pf. (Coill might have 100 or 200 additional C). 2. Feed with random noise from computer random noise generator through 1 Mohm. 3. Look across the coil with computer scope. 4. Use the FFT analyzer mode. Average for a long time to get good results. Here is an example. It is a guitar parts SC bobbin with high permeability ferrite pole peices; about 2000 turns on the coil. This the blue curve. From the peak frequency I get about 1 H. (L = 1/((2*pi*f)^2)*C). (Wikipedia, LC_circuit) That is the blue curve. The red is same coil, air core, about .3 H. I also show the effect of putting a steel bar against the coil. http://www.naic.edu/~sulzer/inductanceMeas.png

When I make pickups, I set the pole height to follow the curve defined by the string height, but lower the pole under the (unwound) G string a bit to allow for its increased sensitivity. The original Fender staggering is currently wrong (as Peter implied) because it was set up for a wound G string. But pole hieght staggering does matter if you want good string balance. This is especially important when playing clean, and maybe not of much concern to many. I would do a lefty pickup to follow this rule as well. When Jimi played a righty guitar lefty, there was no change required, right?

So it looks as though modeling a pickup with FEMM has to be a two step process: 1. Model a magnet/polepiece and have that illuminate a peice of steel representing the string. 2. Replace the steel "string" with a hard ferromagnet, that results in the same total field as in step one. 3. Remove the permanent magnetization from the pole piece, keeping the permeability the same. 4. Model the fluctuating field through the pole piece. This is pretty much a continuation of the same procedure, except the idea in step two is to get the field right, not just have approximately the right form. It is also necessary to see how much the magnetizatoin of the "string" changes as a function of the string position when the string vibrates. It appears that this is very little, since this effect should make the pickup non-linear (and pickups are quite linear). I will try to have some results soon on the linearity of pickups.

Peter, I misread your post and missed that you said that the steel plate remains far from the strings in both positions. So if I understand, in one case the coil is close the the plate, and in the other case it is not. Since the inductance of the coil could be affected by how close the plate is to the coil, it could be that the high frequency effects are due to the inductance changes. But that is only a possibility. Maybe we can devise an experiment to tell.

Very interesting Peter. Our test pickups are very different, so I do not think it is a big deal about the factor of 2 or 3. When you do the steel plate test, the steel plate is close to the strings in one of the test positions? I wonder what that does? Mike

The FEMM plots at the beginning of this discussion show the magnitude of B. What we really want to look at, for applying the law of induction, is the change in B when the string moves. This is harder to do; you have to subtract two cases with the string magnet at different heights. This requires writing out data from FEMM. It is possible to do this for B on a single contour, a line or curve on the image plot. You also have a choice as to what to write out; for example it can be the component of B along the contour. I have been saying that the magnitude of B is a good indicator how how big the change is. Of course the shape of the curve matters also. It is possible to show how accurate those magnitude plots are at showing the change by using the capabilities of FEMM described above . The plot linked to below has three curves. The blue one is the component of B parallel to the pole piece at a distance of .04 inches from the center (axis) of the pole piece. (This is inside the pole piece.) That is, this contour is .04 inches from the left side of the plot linked to in the first post of this discussion. (The scale is like the second plot where I knocked down the coercivity by a factor of 1000.) The red line is this component of B for a vertical contour just outside the pole piece. It is very small and negative (points in the other direction). The green line is the result of subtracting the blue from a similar one with the string magnet lowered by .005 inches. It decreases with increased distance from the string, as expected, but the shape is different from the blue line. Notice that the green line is "noisy". This is due to the finite accuracy of the computation in the simulation. It shows up on the difference because the magnitude has been reduced quite a bit by the subtraction (and scaled back up, notice the right hand scale). It is this noise that limits how much we can do. If you magnetize the pole piece from below and use a piece of steel for the string, you can see that it becomes magnetized. But if you move the "string" down, and look at the difference (analogous to the green line) it is too noisy. This is because the difference is very small, and the computation noise dominates. So it looks tough to do the full simulation that I want to do, but I will play some more. http://www.naic.edu/~sulzer/BalongContours.png

Does it do this with any amplifier? The reason I ask is this sounds as though there could be a small dc voltage on the amp input which is getting back into the guitar. Just a possibility, but you might want to try another amp if you have not.