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Post by ms on Jan 26, 2017 7:14:48 GMT -5
One of the goals of the ongoing effort here (especially JohnH) is to turn a knowledge of the components that make up the impedance of a pickup into a good estimate of its frequency response, allowing the effects of external components to be accounted for as well. There is another approach that seems worth a try, at least along the way. That involves using the impedance measurements themselves, and using component values derived from them only as necessary. It is possible to identify a coil resistance, inductance, and capacitance, but do you need them all in order to compute the frequency response, even with external components? Furthermore, it does not appear to be so easy to model the part of impedance due to eddy currents into the smallest possible number of components. Perhaps taking this other approach will provide some insight. The changing magnetic field from the vibrating string induces a voltage around each turn of the the coil, and since they are all in series, we can model this as one voltage source in series with the inductance. The coil resistance also is in series with the inductance. It is well known that the capacitances between the many bits of wire can be represented as a single capacitor across the coil. So the first three are the series impedance of a voltage divider while the capacitance is the shunt element because the output is also taken across the coil. But what about the impedance due to eddy currents? I tend to think sometimes (incorrectly) that it also goes across the coil like the capacitor since it is like the secondary of a transformer, but this is not right. The effect of eddy currents appears around each turn of the coil just like the signal from the string, and this voltage opposes the build up of current: Lenz's law; there ain't no free lunch.) Thus, this is also goes in the series. So a model based on these ideas looks like this: So start with the measured impedance; it includes all four of the elements in the above representation. Suppose we find the C value somehow. (It seems practical to do this at the resonance by fitting to a model that incorporates the eddy current effects over a narrow frequency range so that Rse can be assumed constant over that range.) This C can be "unparalleled" leaving an impedance, call it Zu. The real and imaginary parts of this impedance are shown in the impedance plots shown earlier (green and yellowish lines), and the accuracy of the C measurement is shown by the removal of the shape of he peak from Zu. Now Zu and C can be used to make a voltage divider. That is, Zu replaces the three series elements in the above pickup model. Then the frequency response can be directly computed from the impedances of Zu and C. This is the idea I am trying, but it is necessary to measure the frequency response directly in order to check the results. I can do that with the same system used to measure the impedance, modified a bit.
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Post by ms on Jan 25, 2017 7:36:34 GMT -5
Here is the plot for the tele bridge pickup. Differences from the humbucker coil: 1. The eddy current factor (at the loaded resonance) is under one: more energy is dissipated in the coil resistance than in the eddy currents in the magnets. 2. You can barely see any effect on the inductance. 3. The curve of the real part is just pulling away significantly from the coil resistance. 4. Rse (not on the plot unfortunately) is about 1 Meg. 5. This is the expected results based on the plot of T in the previous post. The eddy current factor is computed in this way (real part at resonance - Rcoil)/Rcoil. The real part of the impedance as a function of frequency is the green line. The dot dash line is the resistance of the coil draw across the whole frequency range for convenience. Thus you can get an approximate value for the eddy current factor from the lines on the plot (and the zero tick mark).
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Post by ms on Jan 23, 2017 15:03:49 GMT -5
I can't say I agree. I think that those ridiculously over-wound pickups such as the SDS-1, Super D, JB and SSL-5 et el were an 80's thing. Now you see people going for Seth Lovers on the PAF side, or Lollar Blackfaces on the boutique side. Kids of the past might have been planning to cover Metallica, but I think guitars are appealing to a different demographic these days. Besides that, amps offer too much gain anymore, you don't have top push no front ends. Yes, people want "sweet highs", but even more, they don't want muddy chords. The boutique market owes Fender and Gibson a debt of gratitude for putting trashy pickups in their import lines. The verbiage they use, note separation, articulation, clarity, chime, jangle, are all qualities that track with a lower wound pickup, they've used this sales pitch to sell $300 pickup sets to teenagers for years, decades even. All I say for sure is that these hot stock pickups, the Fender Mexico and and Epiphone, have had a bad reputation in the community, while the Probucker's on Gibson's side, and the Tonerider AlNiCo OEMs in the Fender Vintage Vibe have received praise. Certainly there is an increased reverence for the past, but then you have to get rid of the high frequencies in order to get the sound you need. There is a reason why the boutique winders introduced the hot pickups way back when when Fender and Gibson still thought that people wanted good high frequencies for playing clean. (Look at some of those old Fender ads with short haired clean cut guys in tuxes smiling happily as they play their strats.) I still sometimes read of how that guy on the Eastern shore of Maryland who makes those really good expensive guitars cannot make a decent pickup. No, he just knows what his clientele needs.
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Post by ms on Jan 23, 2017 14:44:01 GMT -5
The first attachment here has the equation describing the effect of eddy currents (from the note I have posted previously) placed on a plot. This plot shows the factor T, which controls the onset of eddy current effects as a function of frequency, for two different values of Rse. Rse is the effective resistance of the material in which the eddy currents flow, but transformed up by the ratio of the coil inductance to the inductance of "secondary", the circuit supporting the eddy currents, such as humbucker slugs. Thus Rse is the value of resistance loading the pickup coil (Lc). k is the coupling constant between the pickup coil and the "secondary". k would be very close to one in a good transformer, but might be .5 in a pickup in a pickup with short open cores and lots of escaping flux. (In the real world Rse increases with frequency because of the skin effect, but the equation describes what happens if it stays constant.) T controls the process by which the low frequency parameters (Lc and Rc) are transformed into new values as a function of increasing frequency. The effective inductance decreases with frequency, while the losses increase. When Rse = 100,000 ohms, the effect of eddy currents remain very low for a few hundred Hertz, then increases quickly, leveling off at the higher frequencies. When Rse = 1 Meg, the effects have not gotten very large at the top of the audio range, and are small in the effective range that stops at 5KHz for a guitar speaker. These two values are meant to be typical of the range present in real pickups. But how well does the model represent what actually happens? Well, it cannot be perfect, because Rse rises with frequency from the skin effect, and that is very hard to model. We can allow for that to some extent. Rse should continue to increase some instead of leveling out, and the imaginary part of the impedance would not straighten out perfectly. The next attachments show impedance plots for the slug coil from an Japanese PAF clone. (Using just one coil eliminate the coupling between the two coils as a confusing factor.) The first plot shows the lower and most important frequencies. I have used an external capacitor so that the total is realistic for playing with a cable, and the computer code computes an eddy current factor at the resonant frequency, assuming that the most important frequency at which to evaluate the losses is the resonance. A factor on one would indicate that the losses from the resistance of the coil and eddy currents are equivalent. The green and yellowish lines follow the gray lines very closely for the first few hundred Hz and then deviate as expected. Rse measured at the resonance is about 68K, while K**2 is about .34 The final plot shows the full frequency range with no external C. The green line never levels out and the yellowish line never straightens out as expected with Rse increasing from the skin effect. A later post will show the effects from a single coil alnico pickup.
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Post by ms on Jan 23, 2017 13:19:41 GMT -5
I'll bet they will, too. There's always been attempts to lower the resonant peaks of Fender type single coils, to make the distortion sound "better" or less "weedy." Bill Lawrence stated some years back that his first hand knowledge was that the "secret" to the "pickup" part of Jimi Hendrix's unique Strat tone (e.g. "Purple Haze") was an extra long, extra crappy (high capacitance) cable which would shift the pickup resonant peaks down closer to 2K or so. Jimi would also reportedly switch to a shorter, "better" cable for cleaner sounds in the studio. That's amazing though, that Fender would put a 4 Henry single coil pickup in a Strat. That's in the territory where you could put in a parallel inductance a la Lawrence Q-Filter, and still have enough output in "clean sound" mode. But why you wouldn't use a humbucking pickup when you are in that inductance range, for noise reasons, is beyond me. All true. The Mexican Fender singles achieve 4H in part due to their steel cores, but the DC resistance of 7k shows that they deliberately applied a lot of wire. Another example of forcing hot pickups on consumers are Epiphone versus Gibson Les Pauls. In the low cost Epiphone Les Paul they used to install "AlNiCo Classics" where you have a hot bridge measuring, it's is said, up to 13k, and 8.5k for the neck, while on an actual Gibson Les Paul they install "57 Classics" which come in around 8k for the neck and bridge alike. Apparently they got the clue that people did not want hot pickups installed stock, and more recent Epiphones comes with "Probuckers", which are lower wound than the "AlNiCo Classics". I think people mostly do want hot pickups (that is, high level with increased overdrive capability, reduced high frequencies, and lower levels of resulting high order intermod distortion) because distortion is mostly what rock guitar playing is about, but it cannot be too harsh. Let's see, is this the exact 50th anniversary of the recording of Purple Haze? Not quite, but close. Where did those high frequencies from the strat go? How about a low impedance input fuzz face using a low beta germanium transistor? (In that case the cable would make little difference.) But wherever they went they were really gone and replaced by harmonics and intermods from the first few guitar harmonics. What happens when you give a couple of powder blue strats to some guys used to playing with much less lively guitars? You get Nowhere Man.
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Post by ms on Jan 19, 2017 16:30:01 GMT -5
Here's something to think about... One take away from the fact that splitting a coil into two chunks halves the capacitance, is that it shows how much the sum capacitance relies of the overall continuous geometry of the coil to arrive at a sum capacitance. In other words, the relationship between coil size and parasitic capacitance must be exponential, and not linear, because the whole thing is self-reinforcing. I always assumed the capacitive coupling was due to the side-by-side wire interaction, and the premise of scatter winding relies on this premise, but the fact that the whole coil is interacting with the entirety of itself, really undermines the premise of scatter winding as a means of reducing capacitance, because forget about the fact that the wire is not laid nicely, you still have roughly the same size and shape of coil, which appears to be the dominant determinant in the overall capacitance - not neatness of winding. I have observed lower capacitance in "hand wound" coils, and higher in machine wound. I believe, the above shows that it's not the scatter that causes the lower capacitance, but merely the fact that the coil is physically larger, for a given amount of conductive surface area. It also means that a benefit of a humbucker is that you are able to achieve a higher inductance for a given resonant peak, because the the fact that the productive coils are in two small chucks instead of one, inherently reduces the overall capacitance dramatically. Taking this thinking further, you should be able to get optimal loudness from a pickup by doing the same thing again, and having four coils, like this: Now you have achieve whatever inductance you might want, and the capacitance will be further broken up into smaller tanks. And unless I'm missing something, 43 or 44 AWG should automatically show a lower capacitance, again due to less physical size. The inductance of a coil is determined by the effect of the flux from each turn through every turn. Therefore, if you break up a coil into two smaller coils, you are losing many of these interactions. Putting two coils each with half the number of turns of the original in series should result in lower inductance than the original coil. If you take half the turns off a coil, its capacitance goes down. If you make another identical one and put them in series, the total capacitance is halved. You have lowered the capacitance by two different means. So I think this is more complicated than you are saying.
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Post by ms on Jan 19, 2017 7:34:07 GMT -5
The capacitance of a humbucker (assuming no high cap braided cable) should be lower than a strat pickup because the two coils in a humbucker are in series, and so the capacitance should be half that of one of the coils, possibly plus some amount determined by interaction between the coils. I've been messing with LTSpice trying to wrap my brain about how simply separating a coil into two halves can case the overall parasitic capacitance drop become half what it was, but if the modeling is to be believed, that's how it plays out. So I measure 110pF for the Antiquity neck. If I subtract 70pF for the cable, that leaves 40pF remaining. Two 80pF coils in series theoretically give you 40pF total. 80pF per each 3.8k 42 AWG coil is not unrealistic for a machine wound coil with a higher tension and uniform layering, so that at least gives me confidence that the numbers are not astronomically wrong, but I agree with your point that the inductance is going to be lower at the resonance than what is measures at 120Hz, though that would mean the capacitance would therefore have to be revised upwards even further to offset the lower inductance. One way to look at the series capacitance thing is to first say that series impedances always add. This is true for Rs, Ls and Cs. Then, since the impedance of a capacitor varies with the inverse of the capacitance, while the impedances add, the value of the total capacitance must go down.
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Post by ms on Jan 19, 2017 7:31:18 GMT -5
The capacitance needs to be based on an effective inductance at the resonant frequency. This effective inductance is lower than the 120 Hz inductance because of eddy currents. The eddy currents affect both the real and imaginary parts of the impedance. You can see this on the impedance plots that I have shown here. For example, consider this one: The yellowish line is the imaginary part of the impedance with the effects of the capacitance removed. For this humbucker it is significantly below the dashed line, which is what the imaginary part of the impedance would be if the 120 Hz inductance determined it completely. The resonant frequency is determined by the effective inductance. The capacitance of a humbucker (assuming no high cap braided cable) should be lower than a strat pickup because the two coils in a humbucker are in series, and so the capacitance should be half that of one of the coils, possibly plus some amount determined by interaction between the coils. In any case, measuring the capacitance is not easy. I think the values I show are good because the effect of the resonant peak appears well removed from the yellowish and green lines. But I do urge caution on capacitance values. It is not so easy. That makes sense. Can you think of any "rule of thumb" that might help us ball park the actual inductance at resonance, or the actual capacitance, for pragmatic purposes? Would most humbuckers tend to follow your plot, or should we expect that they will vary widely? I'll be honest, some of the conjecture I'm doing with numbers to approximate resonances from inductance are borderline sloppy, but I don't feel too bad about it because the pickup companies could, but won't, provide basic specification for their products, and part of me hopes that the potential for misrepresentation of their product might encourage them to be more forthcoming. Eddy current effects vary enough so that I think it is a good idea to account for them in the measuring process, that is, account of the effects on the effective inductance. Many do behave very similarly, of course, but how do yo know if you cannot measure it?
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Post by ms on Jan 18, 2017 18:17:53 GMT -5
I've updated the table www.echoesofmars.com/pickup_data/viewer/ , it now has PAF's and a few other pickups, wire gauge where it can be determined, and expanded filtering options. Here is the latest CSV file www.echoesofmars.com/pickup_data/viewer/pickups.csv . With this data, it's also possible to see how closely inductance and DC resistance relate for given classes of pickup, if anyone is interested in taking up that cause. I have a mystery to solve also; the capacitances look really low, but the are calculated based on peak resonance and inductance measured at 120Hz. For example, the Seymour Duncan Antiquity, only maths out to 110pF capacitance - and that's with braided hookup wire, which adds about 70pF capacitance all by itself. The resonant peaks of 6.5kHz to 7kHz are rather high for an inductance of 5.1H and 4.2H, that pushes the calculated capacitance numbers down a lot. By contrast, a Bare Knuckle Irish tour middle pickup also has a peak of 6.5kHZ, but only an inductance of 2.6H, and a wopping 210pF capacitance. This makes me suspect that the 120Hz inductance values are too high. If we assume the humbucker has at least as much capacitance as a typical Strat pickup, 150pF, then add the 70pF for the braided hookup cable, that should land well above 200pF. Could the fact that the two coils are in two halves account for the lower capacitance, since series capacitance decreases the overall capacitance? The capacitance needs to be based on an effective inductance at the resonant frequency. This effective inductance is lower than the 120 Hz inductance because of eddy currents. The eddy currents affect both the real and imaginary parts of the impedance. You can see this on the impedance plots that I have shown here. For example, consider this one: The yellowish line is the imaginary part of the impedance with the effects of the capacitance removed. For this humbucker it is significantly below the dashed line, which is what the imaginary part of the impedance would be if the 120 Hz inductance determined it completely. The resonant frequency is determined by the effective inductance. The capacitance of a humbucker (assuming no high cap braided cable) should be lower than a strat pickup because the two coils in a humbucker are in series, and so the capacitance should be half that of one of the coils, possibly plus some amount determined by interaction between the coils. In any case, measuring the capacitance is not easy. I think the values I show are good because the effect of the resonant peak appears well removed from the yellowish and green lines. But I do urge caution on capacitance values. It is not so easy.
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Post by ms on Jan 17, 2017 20:57:05 GMT -5
The purpose of this post is to describe how the impedance is computed from the raw measurements. A pickup with a resistor in series, connected as in diagram B above, is a linear filter. So what we need to do is compute the relationship between the output and the input, as a function of frequency, and then combine the various results of that process to get the impedance. One way to think of what a linear filter does is this: at each frequency of interest it scales the amplitude of the input signal and shifts the phase. (Of course you can think of this in terms of real and imaginary parts also.) One way to measure this is to use cross spectral analysis. To implement this, we divide the samples from the two inputs into convenient size sections and compute the fft of each. We add up the magnitudes squared (versus frequency) of all the sections from channel 1 and channel 2, but also we take the cross product. That is, we multiply channel 1 times the complex conjugate of channel 2 for each section and sum up the results. This latter result is an estimate of the cross spectrum; it is a complex quantity, which means that it has an amplitude and a phase. By taking the complex conjugate before multiplying, we are subtracting the phases, and so the phase of the cross spectrum is the phase shift introduced by the filter, averaged to reduce the effect of noise. In addition to the signal we want, the measurements have additive random noise. The relationship between the signals at the input and output can be thought of as coherent: there is a definite relationship between both the magnitude and phase. The noise, on the other hand, is thought of as incoherent since the noise at each frequency is not so related to the signal. There is a quantity called the coherence (or actually the squared coherency spectrum) which measures this relationship; it is near one at frequencies where noise is small and much smaller where noise dominates. This quantity is found by dividing the magnitude squared of the cross spectrum by the product of the two individual spectra. Here is a typical coherence measurement from this instrument: It is minimum at the frequency where the pickup self-resonates. This is because the pickup has a maximum in its impedance at this frequency, and so the voltage across the resistor is smallest, and so the effect of noise the greatest. However the coherence is still quite high, and we expect the measurement to be useful across the band. However, the ripples in the coherence are interesting; they imply small periodic changes in the SNR as a function of frequency. To see where this is coming from we look at the spectrum of the signal applied to the pickup: The response of the complementary codes is flat, and so we look at the rest of the system to see what this ripple is. I think it must be the antialiasing filter on the line output; I missed this at first, having misread the specs. It appeared that they were stating how flat the response of the system is across the band. Actually, they state the response at 20KHz. Sure enough, the figure shows that the response at 20KHz is just about between the extremes of the ripple. Of course, the +/- 1 db is not an issue since we take a ratio, and the coherence shows that the effect on the SNR of the measurement is small. The measured cross spectrum is the average of the product of the two voltages; we want the ratio of the voltage applied to the current through the resistor. We have the voltage squared, the self spectrum of the voltage across the resistor, and so we divide by that. Then we just have to multiply by the resistor to get the impedance of the pickup plus the resistance. So we subtract the resistance to complete the process.
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Post by ms on Jan 17, 2017 19:04:29 GMT -5
So I measured the impedance with A5 and A3. The results are here: There is not a lot of difference. The differences in magnitude are 100Hz: .05db, 1000Hz: .15 db, 5000Hz: .12 db, at peak: .06 db I do not think that factors relating to the impedance (conductivity, permeability) from the two magnets are audible. That leaves differences from field strength.
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Post by ms on Jan 16, 2017 18:36:21 GMT -5
It's true that humbuckers can have their magnets swapped with ease, but that would also impact the inductance and damping values a bit, which just taints the test results, but now that you mention steel poles pickups, it occurs to me that I could use neodymium buttons to alter the flux density of a ceramic/steel pickup without altering the reactance at all. I'll move this higher up in my long to do list. Sounds like a good plan. Yes, the magnet in a hum bucker affects things. Here are impedance plots of an SD SH1N with and without the magnet. The other thing that can happen is that a stronger field alters how the string vibrates due to the magnetic force. Not sure this is really what people mean when they say that different kinds of magnets sound different. Attachments:
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Post by ms on Jan 16, 2017 16:17:31 GMT -5
I think the magnetization of the string is not strong enough to move to a different slope on the curve. Maybe this is not a real effect, but results from not adjusting the volume back to the same level with the weaker magnets. Are you suggesting then that the magnetization of the steel string has an effectively linear relationship with the magnetic moment that intersects it? In other words, that the steel string is a linear reflection of the magnetization imposed upon it? That just doesn't seem right to me for some reason. Do you happen to know how much H it would take to max out the B of the steel? AlNiCo 5 is somewhat strong in close proximity. Is it safe to assume that it's too weak to saturate the steel string? I think it's a question worth asking, though I don't think the answer would necessarily validate the observations in this case. --- There are some Seymour Duncan pickups that are virtually the same, aside from one set using AlNiCo 2, and another using AlNiCo 5. The AlNiCo 2 produces a higher inductance, but I think the observed difference goes beyond overall amplitude. This can be tested, but it will have to wait until someone can fashion two pickups with either magnet and ensure that the inductance and resonance are equivalent. I did find that a couple of my pickup sets had similar inductance and resonance, but different magnets, A5 vs A3, and they were both in separated guitars. I compared how they sounded. I went back and forth between them, and I observed the usual differences you see people say about them, the AlNiCo 5 having a seemingly more prominent treble and bass. I don't like to trade in vague perceptions, but it motivates me to find an whole explanation for the difference. Saturating steel usually requires a closed magnetic circuit, that is, one in which the flux completes a loop with high permeability material. It is easy to change magnets in hum buckers. If you do not want the effect of the steel for this test, then use ferrite for the pole pieces.
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Post by ms on Jan 16, 2017 6:35:49 GMT -5
Is it possible instead that a weaker pole piece magnetically charges the steel guitar string more evenly over a greater width, due to the BH curve of the steel string ?
I think the magnetization of the string is not strong enough to move to a different slope on the curve. Maybe this is not a real effect, but results from not adjusting the volume back to the same level with the weaker magnets.
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Post by ms on Jan 15, 2017 17:40:56 GMT -5
"The same thing should happen when using magnets of lower flux density, such as AlNiCo 2 or 3, because like a magnet that is further away from the strings, having less flux for a given geometry of magnet will result in a more evenly distributed magnetic field. This is in contrast to having a smaller magnet with the same flux density, like if you were to make a tiny AlNiCo 5 magnet, for example." --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- I don't think so. Think of the magnet as made up of a huge number of very small identical magnets. Their distribution determines the geometry of the field. To make the magnet weaker, make each of the tiny magnets weaker by the same amount. The geometry of the field stays the same; all that changes is the strength.
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Post by ms on Jan 8, 2017 14:04:45 GMT -5
Yes, it is. It might be interesting to 'unparallel' the C and see how the eddy current effects show up. Easily done, here it is, with the same colours as your tests: The plots with C removed look to have the similar tendencies as those from the tests, up to around 10khz or so, including their general curvature and the way they merge into the plots with C at low frequency. The differences above 10khz are interesting because they might relate to why often a model that works well below that frequency tends to deviate above the highest peak, often not falling quite so steeply. These are the loaded and unloaded outputs for the tests and the model: You can see there, where the solid green line from the unloaded model declines slightly less steeply at 9khz and above compared to the dashed lines traced from Antigua's test. At these high frequencies, such deviations are of theoretical interest but not really of practical significance. That's good. I think now I have to run the eddy current model (time permitting) to see if it is possible to use just one parameter in the range of values normally encountered with pickups. (I mentioned in that other discussion that it is hard to fit for both parameters at once. That might mean that one parameter, set up in some way to be determined, would be enough.) Of course, even if one parameter is enough, that does not mean that one real component would be enough to make your model work well. We are dealing with mutual induction; it is a bit special. Who knows? it might be convenient to invent a mutual inductistor with some useful characteristic.
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Post by ms on Jan 7, 2017 10:37:01 GMT -5
Here is a block diagram of the current setup: It works better with the signal into input 2 attenuated; also the level controls should be adjusted well back from where the overload indicators come on. Both inputs are set up for instrument, not line.
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Post by ms on Jan 7, 2017 8:20:04 GMT -5
Here are some results from a coil using ferrite cores. It is low resistance and inductance, but surprisingly high capacitance. (must be wound very tight and evenly, I do not remember) The ferrite material is the highest permeability commonly available, about 3000, I believe. It is thus high loss for a ferrite. It appears that this loss can be measured at the top of the audio range, but it is a lot less than alnico. I suspect that the method for finding the coil inductance needs a bit of work.
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Post by ms on Jan 7, 2017 8:12:11 GMT -5
An interesting effect appears when you measure a humbucker. In this case, we measure one coil with the other coil open. This is an SD pickup; the sticker on the bottom reads "SH1N Neck". This is the so called PAF replacement that does not carry the SD label on top. Here are the measurements: Of course the peak is lower and broader as expected, compared to the tele pickup, but it also has a funny shape above the peak. Apparently the open second coil, which resonates with its own capacitance, is stealing some energy from the coil under measurement. This is quite high in frequency and should have no practical effect, but it does suggest that there could be even more coupling when both coils are connect together. I had a thread on this topic a few months ago guitarnuts2.proboards.com/thread/7769/damping-caused-unused-splitting-humbucker The unused coil sucks from the active coil different depending on whether it's open or closed. If it's closed, it's an inductive load, if it's open, it's faintly capacitive. Another thing to note about 4 conductor humbuckers is that there is a 40pF capacitance, give or take, between the series coils as a result of the two way run through the shielded hookup wire. If the shield is left disconnected, usually an braided wire with not insulator, that capacitance mostly goes away. Interesting, this is a mutual inductance effect, related to eddy currents, not sure how the term should be used technically. This brings up again the possibility of "shaping" the resonant peak by the use of an extra coil with a particular kind of loading. It need not have a lot of turns if the right size wire and load are used. It would be most conveniently put around the main coil like a transformer secondary.
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Post by ms on Jan 7, 2017 8:06:12 GMT -5
Here are the impedance measurements for the SN1 Neck connected as a normal humbucker. With the two coils in series, the inductance is higher, and, with the high capacitance connecting cable, the resonance frequency comes down a lot. The funny coupling effects at the top are even more apparent. Here's something I found interesting. I took one of the 6-part theoretical models, and extracted impedance results in the same form as in your tests. This one is for a 8.04k 4.83H uncovered '57 Classic (recently tweaked as in previous posts.) Compared to SD '59's, these seem to be slightly less lively, but the form of the graphs are very similar indeed, up to above 10khZ where your measured results start to show extra wiggles. You can see the low frequency reactance aligning to the gradient of the Lcoil impedance, and also it has a similar effect whereby the imaginary impedance sneaks slightly above the Lcoil impedance, before reaching a maximum and then dropping. Encouraging I think. Yes, it is. It might be interesting to 'unparallel' the C and see how the eddy current effects show up.
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Post by ms on Jan 6, 2017 15:04:13 GMT -5
Here are the impedance measurements for the SN1 Neck connected as a normal humbucker. With the two coils in series, the inductance is higher, and, with the high capacitance connecting cable, the resonance frequency comes down a lot. The funny coupling effects at the top are even more apparent.
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Post by ms on Jan 6, 2017 13:57:41 GMT -5
An interesting effect appears when you measure a humbucker. In this case, we measure one coil with the other coil open. This is an SD pickup; the sticker on the bottom reads "SH1N Neck". This is the so called PAF replacement that does not carry the SD label on top. Here are the measurements: Of course the peak is lower and broader as expected, compared to the tele pickup, but it also has a funny shape above the peak. Apparently the open second coil, which resonates with its own capacitance, is stealing some energy from the coil under measurement. This is quite high in frequency and should have no practical effect, but it does suggest that there could be even more coupling when both coils are connect together.
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Post by ms on Jan 6, 2017 13:26:08 GMT -5
I find what you're doing with these signals very interesting, but what is the reason to consider using them vs. the common swept sine wave? Thanks for your interest! Measuring all the parameters at once avoids various small problems that arise in non-simultaneous measurements, and also, when information is used in a near optimum fashion, results in very fast complete measurements, done before any conditions can change. Also one thing I do professionally is radar coding techniques, and there is that old thing about everything looking like a nail to a hammer.
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Post by ms on Jan 6, 2017 13:19:42 GMT -5
Now look at some results. This test pickup is an old tele bridge (no base plate) I wound sometime ago with #43 wire, loose and scattered, giving low capacitance. The attachment shows the results. The measurement required about 3.5 seconds of integration. The instrument was calibrated (at Stratotart's suggestion), and the following means was used: 1. The pickup is measured with the Extech (120 Hz), and the resulting series resistance is input to the software. 2. The inductance is also input for comparison with the results. 3. When the measurement integration is complete, lines are fit to the low frequency real and imaginary parts, and results are evaluated at 120 Hz. 4. A scale factor is derived so that the measured real part at 120 becomes equal to that of the Extech. 5. The scale factor is saved and printed, and it is used in further measurements instead of a value from the Extech. There are 513 points in the spectra, with about 256 independent points, and so the smoothness of the measurement is a result of low noise, not digital post processing. The value of the resonant frequency is derived by fitting a line in the neighborhood of the zero crossing of the imaginary part. Not only is this consistent with the formal definition of resonance, it is more accurate than looking using the peak of the real part. I will discuss how the value of C is derived some time in the future, but for now it is easy to verify that the value is accurate. The green and yellowish lines are the impedance with the C "unparalleled". The purpose of these lines is to show the effect of eddy currents, by comparison to the gray dashed and dot dashed lines, which are the case for no eddy currents. Eddy currents are low in this pickup because there is little deviation from those lines, as a result of alnico magnets. However, the main point here is that there is no sign of the peak in the yellowish and green curves, and therefore an accurate value of C was removed. A sequence of measurements was made in order to look at noise on the measurements and at drifting, a result of temperature change affecting both the pickup and the instrument. This attachment shows three parameters on a zoomed in scale so that changes are easily seen: The inductance differs from the Extech value by about .16%. I was hoping for better, but I guess it will do. The noise is dominated by mH size spikes; I do not know the cause, but speculate some kind of transient magnetic noise. The resistance is very close because that is what we are calibrating to. The value decreases as the temperature increases in the morning. The standard deviation is way under 1 ohm, better than needed. The frequency shows a more complicated drift, apparently because there are multiple factors involved. The standard deviation is less than 1 Hz, also more than good enough.
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Post by ms on Jan 6, 2017 12:30:46 GMT -5
What wave form to use? A bit of an aha! moment: Golay complementary sequences, used for radars sometimes, but I had not thought about them for some time (decades). For purposes here, these are a pair of sequences of +1 and -1 such that if you add the two power spectra, the result is flat, that is independent of frequency, even though individually they are not flat. We do not really need perfectly flat, but it is convenient, and these codes come in all powers of two. Also, they are generated by a simple recursive algorithm:
# Complementary codes # l is the length (must be power of two) def ccode(l): lc = 2 c0 = np.array([1,1]) c1 = np.array([1,-1]) cs0 = c0 cs1 = c1 lc *= 2 while lc <= l: c0 = np.append(cs0, cs1) c1 = np.append(cs0, -cs1) cs0 = c0 cs1 = c1 lc *= 2 return c0, c1
The attachment () shows a small part of the measurement stream, about one code pair. The codes (blue) have passed through the anti aliasing filter after the DAC, and so they are no longer constant amplitude. The red shows the voltage across the sensing resistor, that is, proportional to the current, and it has greatly reduced high frequencies since the impedance of a pickup increases with frequency. The codes have 512 samples and are separated by another 512 samples. This is to allow the correlation introduced by the pickup to die down. This condition is not met at very low frequencies, of course, and so a ripple is introduced in the spectra, but this does not hurt the measurement because it involves taking the ratio.
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Post by ms on Jan 5, 2017 12:40:08 GMT -5
Of course most of the difference is the result of different frequency response in the pickup circuit. But the effects of the two regions of sampling in a humbucker are both measurable and audible in a consistent way. After all, bridge and neck pickups do sound grossly different because they sample the string in different locations and thus have different ratios of harmonics. Considering closer spacing is just an extension of this to more subtle effects. Yes, but subtlety can extend to imperceptibility. I've taken an unmounted pickup and held it over the strings, moved it up and down the strings. I think if you try this, you will not be able to detect a difference of one inch. But that is the wrong test. What matters is what happens when you have two sampling windows both present at the same time with the responses adding. Then you have a kind of funny low pass filter that takes out some of the picking transients. You can hear this on the low E because the string makes these harmonics and they lie within the bandpass of the system. You cannot hear it on the high E because those harmonics lie outside the bandpass of the system (primarily the guitar speaker, which falls like a ton of bricks near 5 KHz), and the sting has fewer of the harmonics to start with.
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Post by ms on Jan 5, 2017 6:23:54 GMT -5
I think it's a case where Occam's Razor applies... a typical humbucker has a notably lower Q and loaded resonant frequency than a typical single coil. It's amply sufficient to explain the difference. It's also easy to demonstrate, unlike the aperture phenomenon which is a perfectly plausible theory with almost no experimental validation. What we need to know, is the magnitude of the effect. There are too many physical variables feeding into it to trust math alone. Of course most of the difference is the result of different frequency response in the pickup circuit. But the effects of the two regions of sampling in a humbucker are both measurable and audible in a consistent way. After all, bridge and neck pickups do sound grossly different because they sample the string in different locations and thus have different ratios of harmonics. Considering closer spacing is just an extension of this to more subtle effects.
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Post by ms on Jan 4, 2017 17:42:56 GMT -5
One thing that might bias intuitive interpretations here is that when eddy current losses are low, inductance measurement at 1KHz can be about 1.5% high because of the effect of the capacitance. It only takes 100pf to screw things up that much.
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Post by ms on Jan 4, 2017 17:35:59 GMT -5
Ferromagnetic material does not have to be conductive. There are ferrites that can do the job with any permeability that you want. If you want to get permanent field to the strings in an air core pickup, just use Neo magnets inside the coil under the strings. Neo's permeability is about 2% higher; so it is effectively the same. If you want such an air core pickup for some reason, use very fine wire. The basic idea is to reduce inductance increase caused by the magnet and magnetic structure, so we can get more turns on the coil and get more output. I think you are seriously confused. Permeability that increases the inductance also increases the output.
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Post by ms on Jan 4, 2017 15:10:01 GMT -5
Yes, exactly. That is how I use it, and I have not seen any pickups for which it is not true. (But always on the look out for exceptions and improvements!) In the low frequency range eddy current effects should fall off with the square of frequency, and thus go away fast as the frequency goes down (). There's a powerful result there if I'm understanding it right. In equation 8, setting aside capacitance, the pickup seems to be represented by just 4 variables, being resistance and inductance as measured, plus hidden parameters Rse and T representing eddy currents. Presumably these could be derived from measurements too? Add another parameter which is a capacitance, to make 5 variables. It is not quite that simple since both Rse and k can vary slowly with frequency. The skin effect, or rather its variations with frequency, is the culprit, changing Rse directly, and k through changes in the current flow geometry. But this should still be useful. For example, suppose you have Lcoil, Rcoil, and the impedance as a function of frequency and want C. You can use the impedance measurements well above resonance where C dominates the impedance, over a limited range where k and Rse can be considered constant. I use non linear least squares fitting to do this, getting the C values on the plots that I show. They seem good, but I do not consider any of this proven yet.
Also, k and Rse are very hard to measure accurately. The errors are correlated, etc. I think the best way to judge the effect of eddy currents is to measure the deviations of the impedance vs frequency from the values that would exist with just Lcoil and Rcoil. That is, find the capacitance, take out its effect, and plot the modified impedance. Then look at the decrease in the imaginary part and the increase in the real part compared to the impedance without eddy currents, that is, just the inductor with its series resistance. This is also on my plots, but how accurate is it?
Then you want to translate all that into the addition of the fewest possible ideal components. I think this is an interesting challenge.
I have been working on my pickup impedance meter, and will have some more to say in that discussion soon.
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