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Post by aquin43 on Mar 17, 2019 6:22:02 GMT -5
The magnetised string has been simulated as a twin array of small magnets with different magnetisations to reproduce the pattern of magnetisation found in a string above a stratocaster type pickup. The axial field produced by the simulated string in the coil and magnet space has been plotted. This is purely the field due to the string, without the field due to the magnet. The accuracy and resolution of FEMM type analysis plots is not high enough to isolate the field due to the string directly. The magnet is dummy Alnico with a mu of 1.5, length 17mm, width 4.75mm. The string is 3mm above the magnet pole. The magnetisation pattern of the of the string was found from an earlier simulation and the magnet array was adjusted by hand to match it. In the earlier simulation it became clear that the string captures both radial and axial flux from the magnet which then becomes directed along the string, so that it is the total flux, not just the axially directed flux from the magnet that contributes to the string field and hence to the output. Flux Pattern: Flux in string: Flux in coil and magnet:
Arthur
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Post by antigua on Mar 17, 2019 21:22:34 GMT -5
Is the inference that the window is more narrow towards the top of the coil, and wider towards the bottom of the coil?
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Post by aquin43 on Mar 18, 2019 4:30:09 GMT -5
Is the inference that the window is more narrow towards the top of the coil, and wider towards the bottom of the coil? It looks like it, but the flux level at the bottom of the coil is so low that it would contribute only a small rounding to the window. Notice how much of the flux is concentrated in the magnet, even with mu as low as 1.5 and the flux reversal beyond 10mm.
Arthur
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Post by ms on Mar 18, 2019 6:43:59 GMT -5
In this rectangular 2D simulation the string is an infinite sheet and the dummy magnet extends into and out of the page for an infinite distance. I think in the previous simulation the magnetization of the string used the same approximate geometry. I think that this approach exaggerates the interaction of the string with the permanent field, and also overestimates the effect of the string away from the center has on the returning flux.
Another approximation you can use (that I did several years ago) is to represent the string by a small cylinder magnet with its axis aligned with the axis of the dummy magnet. Then you use FEMM in the cylindrical mode. You can vary the diameter of the string magnet, giving different kinds of inaccuracies. This has the advantage of giving an actual 3D field even if the string is not accurately represented.
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Post by aquin43 on Mar 18, 2019 9:08:22 GMT -5
In this rectangular 2D simulation the string is an infinite sheet and the dummy magnet extends into and out of the page for an infinite distance. I think in the previous simulation the magnetization of the string used the same approximate geometry. I think that this approach exaggerates the interaction of the string with the permanent field, and also overestimates the effect of the string away from the center has on the returning flux. Another approximation you can use (that I did several years ago) is to represent the string by a small cylinder magnet with its axis aligned with the axis of the dummy magnet. Then you use FEMM in the cylindrical mode. You can vary the diameter of the string magnet, giving different kinds of inaccuracies. This has the advantage of giving an actual 3D field even if the string is not accurately represented. In my earlier simulation, for working out the total flux intercepted by the string, I used the axisymmetric mode of FEMM which can model a cylindrical magnet effectively in 3D by using symmetry. From that analysis it is possible to calculate the flux seen by any part of the string but it is not possible to represent the string itself in any way, because of the radial symmetry. That is why I used the other, 2D mode for this simulation. The question is, does the lack of the third dimension alter the field pattern? Well, yes it does, but what remains is similar enough to the true 3D case to give a good qualitative insight into the string magnetisation. At first I was worried that the "string" by intercepting too much of the flux would have a totally unrepresentative magnetisation pattern. I tried reducing the permeability to allow flux to leak through in an attempt to approximate the situation where the string is only part of the path above the pole and I found that the magnetisation pattern remained the same. Still, I considered it a mere curiosity, not worth sharing until I saw the measurements of actual string magnetisation made by Manfred Zollner www.gitec-forum-eng.de/wp-content/uploads/2019/03/poteg-5-4-2-static-magnetic-field-with-string.pdfThe patterns match tolerably well. As I see it, the string is turned into two long, back to back, leaky magnets oriented along its length and meeting over the magnet centre. The magnetising flux is gathered from the static magnetic field indiscriminately; both axial and radial fluxes from the magnet contribute equally so that radially directed flux from the magnet also contributes to the axial signal flux. The magnetisation pattern stays roughly the same as the string moves but varies enough that a separate time consuming match would have to be made at each millimetre or so of distance. I think that this visualisation of the field, which represents something between a strat pickup and the middle of a single coil rail, can be useful in illustrating how unevenly the flux is distributed within the coil and also the flux reversal in coil turns too far from the magnet. It also makes clear how the flux pattern that makes the signal is very different from the static field of the magnet. In particular, the main axis of the string magnetisation is at right angles to the coil axis so the coil is weakly excited by the fringe of the string's field, which is why so many turns are required even though we start off with a large static field. The absolute flux levels in the simulation are arbitrary. In reality, the flux perturbations caused by the string are below one percent of the static field, which is why they are out of reach of direct calculation by FEMM. Arthur
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Post by ms on Mar 18, 2019 15:11:36 GMT -5
Each magnetic dipole in the string responds to both the externally applied field and the field caused by all the other dipoles responding to that field. The strength of the latter, and so its importance, depends on how many dipoles are nearby to a given dipole. This would seem to be much greater when the string is represented by a sheet rather than a string. Thus I would expect significant differences, with the dipoles in the the sheet model changing direction over a shorter distance near the center.
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Post by aquin43 on Mar 18, 2019 17:03:07 GMT -5
Each magnetic dipole in the string responds to both the externally applied field and the field caused by all the other dipoles responding to that field. The strength of the latter, and so its importance, depends on how many dipoles are nearby to a given dipole. This would seem to be much greater when the string is represented by a sheet rather than a string. Thus I would expect significant differences, with the dipoles in the the sheet model changing direction over a shorter distance near the center. Yes, this is more like a ribbon over a rectangular magnet so it cannot reproduce the round string over a circular magnet exactly. It does, however, provide an illustration of every measurable characteristic of the real pickup. Usually, the field interaction with the cylindrical magnet falls of more quickly towards the magnet edge, simply because there is less material at the cylinder edge compared with the square section. This effect diminishes with height above the pole. The string magnetisation pattern is artificially constructed and its accuracy is simply a matter of patience in adjusting the values of the sub-magnets.
Arthur
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Post by ms on Mar 19, 2019 14:35:40 GMT -5
Edit: Sorry, I missed the scale on figure 1 above. I think the answer to my question is that you are not predicting saturation, far from it.
The chapter of Zollner's book that you refer to above indicates that the string is saturated, or nearly so depending on its distance, as you pointed out. Does your simulation saturate? I am wondering because my gut feeling is that is that a magnetic field of a few hundred Gauss (3mm from the string) does not saturate it. His measurement technique is extraordinarily elegant, but I think there is a simple check on this. The flux density in the string directed along it is about 1 Tesla (10,000 Gauss) by his measurement. The tangential component of H does not change at a boundary, and B = mu*H. Also the relative mu of the string is probably about 100, typical for carbon steel (as opposed to "electrical steel", used for transformers, which is a few thousand). So, using the ratio of the permeabilities, the field along the string just outside it should be about 100 Gauss. For attracting steel, it is the change in the field that matters, and the figure shows that the change remains high almost 1 cm from the magnet. I think it should be possible to feel this field with a jeweler's screw driver, a smaller force than near the magnet itself, but I think it should be there. I do not feel it. But I need to get a Gauss(Tesla)meter with reasonable spatial resolution to be able to measure this better.
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Post by antigua on Mar 19, 2019 22:54:39 GMT -5
But I need to get a Gauss(Tesla)meter with reasonable spatial resolution to be able to measure this better. Have you seen the WT10A model? It's just over $100 USD in the US.
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Post by ms on Mar 20, 2019 6:04:27 GMT -5
But I need to get a Gauss(Tesla)meter with reasonable spatial resolution to be able to measure this better. Have you seen the WT10A model? It's just over $100 USD in the US. That looks like a good one, but I ordered a TD8620
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Post by aquin43 on Mar 20, 2019 11:30:20 GMT -5
FEMM can calculate these fields quite well, using the axisymmetric mode so that the result is like a 3D model.
The Alnico 5 material model is taken from the FEMM standard library.
A caveat, when measuring as far as 10mm from the magnet axis is that in a real pickup there is at least one other magnet not that much further away
Arthur
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Post by antigua on Mar 20, 2019 14:53:34 GMT -5
Have you seen the WT10A model? It's just over $100 USD in the US. That looks like a good one, but I ordered a TD8620 Not to derail, but I ordered that one was well, and my only gripe is that the probe is flexible, so the elevation of the tip is hard to control, and it also has a measuring reference built in that doesn't make much sense since the Hall effect sensor itself is not located at zero. I also see the SJ200 in the same price range, but it just looks to me like the WT10A with a different form factor. Im looking forward to seeing if your mental model of the magnetic field is confirmed or invalidated with measurements.
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Post by aquin43 on Mar 21, 2019 5:40:18 GMT -5
Trying to think of a simpler way than Zollner's of carrying out a direct measurement of the flux pattern in the string; if the magnet flux could be modulated by an ac signal, then it could be picked up directly in a static coil wrapped round the string. Since the signal would be ac of a known frequency and with a phase reference from the modulation source, there would be no dc offset problems and it would be possible to make the measurement bandwidth very small e.g. by averaging on a phase locked digital scope so it would be possible to work with microvolt signals. The Hc value for Alnico 5 is 50kA/m and rod magnets in a pickup probably don't achieve this, so it might be feasible to modulate the magnetisation of the magnet using a single layer coil wrapped around it, driven by a few amps ac. The presumption would be, of course, that the added field would be distributed in the same way as the static field. The static field is distributed according to the spatial pattern of the reluctance as determined by the static field itself and the hysteresis curve of the magnet. Would this idea fail because the dynamic hysteresis curve is not the same as traversing the static one so that the modulating flux would simply end up being distributed as if by a low mu pole piece? The detailed variation of mu
caused by the static magnetisation would still be in place.
Arthur
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Post by ms on Mar 21, 2019 7:02:43 GMT -5
Trying to think of a simpler way than Zollner's of carrying out a direct measurement of the flux pattern in the string; if the magnet flux could be modulated by an ac signal, then it could be picked up directly in a static coil wrapped round the string. Since the signal would be ac of a known frequency and with a phase reference from the modulation source, there would be no dc offset problems and it would be possible to make the measurement bandwidth very small e.g. by averaging on a phase locked digital scope so it would be possible to work with microvolt signals. The Hc value for Alnico 5 is 50kA/m and rod magnets in a pickup probably don't achieve this, so it might be feasible to modulate the magnetisation of the magnet using a single layer coil wrapped around it, driven by a few amps ac. The presumption would be, of course, that the added field would be distributed in the same way as the static field. The static field is distributed according to the spatial pattern of the reluctance as determined by the static field itself and the hysteresis curve of the magnet. Would this idea fail because the dynamic hysteresis curve is not the same as traversing the static one so that the modulating flux would simply end up being distributed as if by a low mu pole piece? The detailed variation of mu
caused by the static magnetisation would still be in place.
Arthur
I think that is a great idea that would take some experimentation. But I think it would be easy to use it just to determine if the string saturates in the presence of the magnet. You need a driver coil and a sensor coil around the string, separated by maybe 3 cm. Use just enough drive level to get a solidly detectable signal, that is, well below saturation. (A long FFT for detection is almost as good as true phase locking, and a lot easier.) Maybe 1 KHz? Then move the magnet close to the string in between the two coils. If the string saturates, then the detected signal should decrease a lot. I do not think it would it would take very many turns on either coil. I would start by wrapping the wire right around a plain G string supported by a couple of blocks separated by maybe 10 cm. As a test to see if this works, a larger neo magnet in contact with the string would certainly cause saturation. There are many variations that would be lots of fun. Suppose that you mounted several magnets on a disk, facing to to the rim, alternating which pole is radially outward from the shaft. Then put the disk on the shaft of a motor and rotate the magnets so that they pass by the string with closest approach adjustable by the location of the disk/motor. You could measure permeability changes in the string and plot out the hysteresis curve if you are clever.
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Post by aquin43 on Mar 21, 2019 12:41:28 GMT -5
I just tried a quick experiment using a FeCrCo magnet taken from a Creamery strat pickup. I wound 100 turns of 0.2mm wire on the magnet and drove it with 70mA rms sine wave - so 7AT of mmf. The string was a 12 thou plain steel with two turns of 0.2mm wire. All leads were twisted tight and led off as far as possible at right angles to each other. A 2mm pick was used as a spacer between magnet and string. Amplification was via the monitor output of an old Radford noise meter on the 10uV range with a nominal 1V for full scale output so a gain of of 100k and a DIN audio bandwidth into a Phillips PM3394 digital scope with 2mV/div sensitivity and capable of averaging up to 4096 times. The scope was triggered directly by the signal generator. One mV on the scope represents 10 nV at the input. The readings were of the order of a few mV but the low source resistance and the averaging gave a clear signal. The frequency was 320Hz - not too high and not a multiple of 50Hz. The averaging improves the signal to noise by 64 times, but it would still be better to limit the bandwidth in the amplifier stage. This was a very crude experiment but it did seem to agree with expectations. A null with the magnet centred over the coil, a peak just past the magnet edge and a gradual decay beyond. I'll have to make a proper test rig to get useful readings, but the idea does seem to work.
Arthur
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Post by ms on Mar 21, 2019 15:03:52 GMT -5
That was fast! So I think this implies that the string is not saturated. The null in the middle occurs because there is no component of flux along the string. As the observation point moves away from the middle, the flux switches to along the string. If the string were saturated, the signal should drop abruptly, not gradually, since the saturation should start right outside the boundary of the magnet. I am assuming that the ac drive makes an ac field small compared to the steady field from the rare earth magnet, and so if saturated, it would remain so during the entire ac cycle. I think my conclusion needs some discussion and questioning.
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Post by aquin43 on Mar 22, 2019 5:26:11 GMT -5
I am pretty sure that the string is not saturated - aren't lower permeability materials hard to saturate anyway? I suspect that what Zollner means is that the string is pushed into a region where the mu starts to diminish, but from the simulation the magnetisation pattern of the string remains more or less the same with mu from 10 upwards. Higher mu tends to spread the pattern along the string rather more. I think that FeCrCo has similar properties to Alnico but I would get some Alnico magnets for a proper test rig. I am not sure that this trick would work with Neo but I would expect it to work even better with a humbucker where more of the magnetic circuit is in iron. There is a real difficulty in measuring the magnet position with meaningful accuracy. The whole system is so small and tenths of a millimetre count.
An interesting observation; the magnet that I took out of the Creamery pickup for this experiment was under the second string of a nickel wound 12-56 set. Normally it is necessary to compensate for the excessively loud second string. Removing the magnet only slightly over compensates, so the second string is working on the leakage field from the first and third and the guitar is perfectly playable.
Arthur
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Post by ms on Mar 22, 2019 6:52:03 GMT -5
I am pretty sure that the string is not saturated - aren't lower permeability materials hard to saturate anyway? I suspect that what Zollner means is that the string is pushed into a region where the mu starts to diminish, but from the simulation the magnetisation pattern of the string remains more or less the same with mu from 10 upwards. Higher mu tends to spread the pattern along the string rather more. I think that FeCrCo has similar properties to Alnico but I would get some Alnico magnets for a proper test rig. I am not sure that this trick would work with Neo but I would expect it to work even better with a humbucker where more of the magnetic circuit is in iron. There is a real difficulty in measuring the magnet position with meaningful accuracy. The whole system is so small and tenths of a millimetre count.
An interesting observation; the magnet that I took out of the Creamery pickup for this experiment was under the second string of a nickel wound 12-56 set. Normally it is necessary to compensate for the excessively loud second string. Removing the magnet only slightly over compensates, so the second string is working on the leakage field from the first and third and the guitar is perfectly playable. Arthur I think he means actual saturation: "Just a few millimeters away from the magnetic axis, the string already loses its good conductivity for alternating magnetic flux and barely differs from air in that way!" page 5-27 I think that the evidence for this is Fig. 5-4.10, where the measured flux is nearly the same for d = 2 and 5 mm. Also the flux density (~1.5 TGesla) seems about right for saturation. But it would appear that you are measuring a signal that indicates significant string permeability. (If you measure with an identical coil not enclosing the string, you should see a lot less.)
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Post by aquin43 on Mar 22, 2019 10:07:40 GMT -5
I am pretty sure that the string is not saturated - aren't lower permeability materials hard to saturate anyway? I suspect that what Zollner means is that the string is pushed into a region where the mu starts to diminish, but from the simulation the magnetisation pattern of the string remains more or less the same with mu from 10 upwards. Higher mu tends to spread the pattern along the string rather more. I think that FeCrCo has similar properties to Alnico but I would get some Alnico magnets for a proper test rig. I am not sure that this trick would work with Neo but I would expect it to work even better with a humbucker where more of the magnetic circuit is in iron. There is a real difficulty in measuring the magnet position with meaningful accuracy. The whole system is so small and tenths of a millimetre count.
An interesting observation; the magnet that I took out of the Creamery pickup for this experiment was under the second string of a nickel wound 12-56 set. Normally it is necessary to compensate for the excessively loud second string. Removing the magnet only slightly over compensates, so the second string is working on the leakage field from the first and third and the guitar is perfectly playable. Arthur I think he means actual saturation: "Just a few millimeters away from the magnetic axis, the string already loses its good conductivity for alternating magnetic flux and barely differs from air in that way!" page 5-27 I think that the evidence for this is Fig. 5-4.10, where the measured flux is nearly the same for d = 2 and 5 mm. Also the flux density (~1.5 TGesla) seems about right for saturation. But it would appear that you are measuring a signal that indicates significant string permeability. (If you measure with an identical coil not enclosing the string, you should see a lot less.) My little experiment could do no more than show that the flux distribution was of the same general shape as expected, even with saturation.
The coil of two turns was tight round the string of 0.3mm diameter and the generated voltage was 40nV at 320 Hz or 20nV per turn at omega = 2k011 so the alternating flux was 20n/2k011 ~ 10pWb. The string cross section was pi*(3e-4)^2/4 ~ 70nm^2, so the alternating B was 10p/70n = 140uT.
If the magnet is supposed to be able to induce 1T into the string, then the flux modulation achieved in the magnet is a tiny part of its magnetisation and there is room for more turns and much higher current without disturbing the magnet unduly.
Arthur
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Post by ms on Mar 26, 2019 17:27:38 GMT -5
I am pretty sure that the string is not saturated - aren't lower permeability materials hard to saturate anyway? I suspect that what Zollner means is that the string is pushed into a region where the mu starts to diminish, but from the simulation the magnetisation pattern of the string remains more or less the same with mu from 10 upwards. Higher mu tends to spread the pattern along the string rather more. I think that FeCrCo has similar properties to Alnico but I would get some Alnico magnets for a proper test rig. I am not sure that this trick would work with Neo but I would expect it to work even better with a humbucker where more of the magnetic circuit is in iron. There is a real difficulty in measuring the magnet position with meaningful accuracy. The whole system is so small and tenths of a millimetre count.
An interesting observation; the magnet that I took out of the Creamery pickup for this experiment was under the second string of a nickel wound 12-56 set. Normally it is necessary to compensate for the excessively loud second string. Removing the magnet only slightly over compensates, so the second string is working on the leakage field from the first and third and the guitar is perfectly playable.
Arthur
The article you referred to in another discussion, the one on straits, (https://asa.scitation.org/doi/10.1121/1.5080465) has some information on string saturation. "Our plain (non-wire-wrapped) steel guitar G string6 (diameter = 0.51 mm, length L = 653 mm, mass density = 1.58 mg/mm) exhibits magnetic hysteresis. With the string oriented parallel to a magnetic field B, the induced magnetic moment saturates for B > 0.1 T; for the perpendicular orientation the induced moment is still increasing for B = 1 T." With the neo magnet, which is 3 to six times stronger than typical for pickups, the transverse field does not exceed .03T, while the perpendicular to the string it does not exceed .35T, both below saturation. So if this is correct, we should be well below saturation in the usual case.
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Post by stratotarts on Apr 19, 2019 9:41:37 GMT -5
The accuracy and resolution of FEMM type analysis plots is not high enough to isolate the field due to the string directly.
I tried enabling B vector labeling on the plots, selecting a scale factor of 100. That seems to magnify the field enough to see what's going on, unless I'm missing something? I modeled the string as two tiny Neo's back to back in line with a steel string, 2mm from a steel pole. The idea is to show the increase in string field intensity in the coil region due to the steel pole.
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Post by aquin43 on Apr 19, 2019 12:19:21 GMT -5
The accuracy and resolution of FEMM type analysis plots is not high enough to isolate the field due to the string directly. I tried enabling B vector labeling on the plots, selecting a scale factor of 100. That seems to magnify the field enough to see what's going on, unless I'm missing something? I modeled the string as two tiny Neo's back to back in line with a steel string, 2mm from a steel pole. The idea is to show the increase in string field intensity in the coil region due to the steel pole. When I wrote "directly", I really meant "in the presence of the field from the magnet". My analysis is similar to yours except that I have modelled the string in more detail using many small magnets with selected degrees of magnetisation and used a polepiece of low mu to represent the magnet acting as the coil core.
Try this code: string-sim.fem It was created by an Octave program that also draws the graphs. I find FEMM a bit difficult to use on its own.
[Format] = 4.0 [Frequency] = 0 [Precision] = 1e-008 [MinAngle] = 30 [DoSmartMesh] = 1 [Depth] = 10 [LengthUnits] = millimeters [ProblemType] = planar [Coordinates] = cartesian [ACSolver] = 0 [PrevType] = 0 [PrevSoln] = "" [Comment] = "Add comments here." [PointProps] = 1 <BeginPoint> <PointName> = "NP" <I_re> = 0 <I_im> = 0 <A_re> = 0 <A_im> = 0 <EndPoint> [BdryProps] = 2 <BeginBdry> <BdryName> = "Periodic1" <BdryType> = 4 <A_0> = 0 <A_1> = 0 <A_2> = 0 <Phi> = 0 <c0> = 0 <c0i> = 0 <c1> = 0 <c1i> = 0 <Mu_ssd> = 0 <Sigma_ssd> = 0 <innerangle> = 0 <outerangle> = 0 <EndBdry> <BeginBdry> <BdryName> = "Periodic2" <BdryType> = 4 <A_0> = 0 <A_1> = 0 <A_2> = 0 <Phi> = 0 <c0> = 0 <c0i> = 0 <c1> = 0 <c1i> = 0 <Mu_ssd> = 0 <Sigma_ssd> = 0 <innerangle> = 0 <outerangle> = 0 <EndBdry> [BlockProps] = 13 <BeginBlock> <BlockName> = "Air" <Mu_x> = 1 <Mu_y> = 1 <H_c> = 0 <H_cAngle> = 0 <J_re> = 0 <J_im> = 0 <Sigma> = 0 <d_lam> = 0 <Phi_h> = 0 <Phi_hx> = 0 <Phi_hy> = 0 <LamType> = 0 <LamFill> = 1 <NStrands> = 0 <WireD> = 0 <BHPoints> = 0 <EndBlock> <BeginBlock> <BlockName> = "blank" <Mu_x> = 500 <Mu_y> = 500 <H_c> = 0 <H_cAngle> = 0 <J_re> = 0 <J_im> = 0 <Sigma> = 0 <d_lam> = 0 <Phi_h> = 0 <Phi_hx> = 0 <Phi_hy> = 0 <LamType> = 0 <LamFill> = 1 <NStrands> = 0 <WireD> = 0 <BHPoints> = 0 <EndBlock> <BeginBlock> <BlockName> = "mag1" <Mu_x> = 20 <Mu_y> = 20 <H_c> = 1860 <H_cAngle> = 0 <J_re> = 0 <J_im> = 0 <Sigma> = 0 <d_lam> = 0 <Phi_h> = 0 <Phi_hx> = 0 <Phi_hy> = 0 <LamType> = 0 <LamFill> = 1 <NStrands> = 0 <WireD> = 0 <BHPoints> = 0 <EndBlock> <BeginBlock> <BlockName> = "mag2" <Mu_x> = 20 <Mu_y> = 20 <H_c> = 7068 <H_cAngle> = 0 <J_re> = 0 <J_im> = 0 <Sigma> = 0 <d_lam> = 0 <Phi_h> = 0 <Phi_hx> = 0 <Phi_hy> = 0 <LamType> = 0 <LamFill> = 1 <NStrands> = 0 <WireD> = 0 <BHPoints> = 0 <EndBlock> <BeginBlock> <BlockName> = "mag3" <Mu_x> = 20 <Mu_y> = 20 <H_c> = 6882 <H_cAngle> = 0 <J_re> = 0 <J_im> = 0 <Sigma> = 0 <d_lam> = 0 <Phi_h> = 0 <Phi_hx> = 0 <Phi_hy> = 0 <LamType> = 0 <LamFill> = 1 <NStrands> = 0 <WireD> = 0 <BHPoints> = 0 <EndBlock> <BeginBlock> <BlockName> = "mag4" <Mu_x> = 20 <Mu_y> = 20 <H_c> = 6324 <H_cAngle> = 0 <J_re> = 0 <J_im> = 0 <Sigma> = 0 <d_lam> = 0 <Phi_h> = 0 <Phi_hx> = 0 <Phi_hy> = 0 <LamType> = 0 <LamFill> = 1 <NStrands> = 0 <WireD> = 0 <BHPoints> = 0 <EndBlock> <BeginBlock> <BlockName> = "mag5" <Mu_x> = 20 <Mu_y> = 20 <H_c> = 5022 <H_cAngle> = 0 <J_re> = 0 <J_im> = 0 <Sigma> = 0 <d_lam> = 0 <Phi_h> = 0 <Phi_hx> = 0 <Phi_hy> = 0 <LamType> = 0 <LamFill> = 1 <NStrands> = 0 <WireD> = 0 <BHPoints> = 0 <EndBlock> <BeginBlock> <BlockName> = "mag6" <Mu_x> = 20 <Mu_y> = 20 <H_c> = 3906 <H_cAngle> = 0 <J_re> = 0 <J_im> = 0 <Sigma> = 0 <d_lam> = 0 <Phi_h> = 0 <Phi_hx> = 0 <Phi_hy> = 0 <LamType> = 0 <LamFill> = 1 <NStrands> = 0 <WireD> = 0 <BHPoints> = 0 <EndBlock> <BeginBlock> <BlockName> = "mag7" <Mu_x> = 20 <Mu_y> = 20 <H_c> = 2790 <H_cAngle> = 0 <J_re> = 0 <J_im> = 0 <Sigma> = 0 <d_lam> = 0 <Phi_h> = 0 <Phi_hx> = 0 <Phi_hy> = 0 <LamType> = 0 <LamFill> = 1 <NStrands> = 0 <WireD> = 0 <BHPoints> = 0 <EndBlock> <BeginBlock> <BlockName> = "mag8" <Mu_x> = 20 <Mu_y> = 20 <H_c> = 2232 <H_cAngle> = 0 <J_re> = 0 <J_im> = 0 <Sigma> = 0 <d_lam> = 0 <Phi_h> = 0 <Phi_hx> = 0 <Phi_hy> = 0 <LamType> = 0 <LamFill> = 1 <NStrands> = 0 <WireD> = 0 <BHPoints> = 0 <EndBlock> <BeginBlock> <BlockName> = "mag9" <Mu_x> = 20 <Mu_y> = 20 <H_c> = 1488 <H_cAngle> = 0 <J_re> = 0 <J_im> = 0 <Sigma> = 0 <d_lam> = 0 <Phi_h> = 0 <Phi_hx> = 0 <Phi_hy> = 0 <LamType> = 0 <LamFill> = 1 <NStrands> = 0 <WireD> = 0 <BHPoints> = 0 <EndBlock> <BeginBlock> <BlockName> = "mag10" <Mu_x> = 20 <Mu_y> = 20 <H_c> = 1116 <H_cAngle> = 0 <J_re> = 0 <J_im> = 0 <Sigma> = 0 <d_lam> = 0 <Phi_h> = 0 <Phi_hx> = 0 <Phi_hy> = 0 <LamType> = 0 <LamFill> = 1 <NStrands> = 0 <WireD> = 0 <BHPoints> = 0 <EndBlock> <BeginBlock> <BlockName> = "mag11" <Mu_x> = 20 <Mu_y> = 20 <H_c> = 744 <H_cAngle> = 0 <J_re> = 0 <J_im> = 0 <Sigma> = 0 <d_lam> = 0 <Phi_h> = 0 <Phi_hx> = 0 <Phi_hy> = 0 <LamType> = 0 <LamFill> = 1 <NStrands> = 0 <WireD> = 0 <BHPoints> = 0 <EndBlock> [CircuitProps] = 0 [NumPoints] = 63 -55 0 0 0 55 0 0 0 75 0 0 0 111.66666666666666 0 0 0 93.333333333333329 0 1 0 -2.375 -8.5 0 0 -2.375 8.5 0 0 2.375 8.5 0 0 2.375 -8.5 0 0 2.625 -7 0 0 2.625 7 0 0 4.625 7 0 0 4.625 -7 0 0 -2.625 -7 0 0 -2.625 7 0 0 -4.625 7 0 0 -4.625 -7 0 0 0 11.5 0 0 0 12.5 0 0 2.2000000000000002 12.5 0 0 2.2000000000000002 11.5 0 0 -2.2000000000000002 12.5 0 0 -2.2000000000000002 11.5 0 0 4.4000000000000004 12.5 0 0 4.4000000000000004 11.5 0 0 -4.4000000000000004 12.5 0 0 -4.4000000000000004 11.5 0 0 6.6000000000000005 12.5 0 0 6.6000000000000005 11.5 0 0 -6.6000000000000005 12.5 0 0 -6.6000000000000005 11.5 0 0 8.8000000000000007 12.5 0 0 8.8000000000000007 11.5 0 0 -8.8000000000000007 12.5 0 0 -8.8000000000000007 11.5 0 0 11 12.5 0 0 11 11.5 0 0 -11 12.5 0 0 -11 11.5 0 0 13.199999999999999 12.5 0 0 13.199999999999999 11.5 0 0 -13.199999999999999 12.5 0 0 -13.199999999999999 11.5 0 0 15.400000000000002 12.5 0 0 15.400000000000002 11.5 0 0 -15.400000000000002 12.5 0 0 -15.400000000000002 11.5 0 0 17.600000000000001 12.5 0 0 17.600000000000001 11.5 0 0 -17.600000000000001 12.5 0 0 -17.600000000000001 11.5 0 0 19.800000000000001 12.5 0 0 19.800000000000001 11.5 0 0 -19.800000000000001 12.5 0 0 -19.800000000000001 11.5 0 0 22 12.5 0 0 22 11.5 0 0 -22 12.5 0 0 -22 11.5 0 0 49.799999999999997 12.5 0 0 49.799999999999997 11.5 0 0 -49.799999999999997 12.5 0 0 -49.799999999999997 11.5 0 0 [NumSegments] = 79 5 6 -1 0 0 0 6 7 -1 0 0 0 7 8 -1 0 0 0 5 8 -1 0 0 0 9 10 -1 0 0 0 10 11 -1 0 0 0 11 12 -1 0 0 0 9 12 -1 0 0 0 13 14 -1 0 0 0 14 15 -1 0 0 0 15 16 -1 0 0 0 13 16 -1 0 0 0 17 18 -1 0 0 0 18 19 -1 0 0 0 19 20 -1 0 0 0 17 20 -1 0 0 0 18 21 -1 0 0 0 21 22 -1 0 0 0 17 22 -1 0 0 0 19 23 -1 0 0 0 23 24 -1 0 0 0 20 24 -1 0 0 0 21 25 -1 0 0 0 25 26 -1 0 0 0 22 26 -1 0 0 0 23 27 -1 0 0 0 27 28 -1 0 0 0 24 28 -1 0 0 0 25 29 -1 0 0 0 29 30 -1 0 0 0 26 30 -1 0 0 0 27 31 -1 0 0 0 31 32 -1 0 0 0 28 32 -1 0 0 0 29 33 -1 0 0 0 33 34 -1 0 0 0 30 34 -1 0 0 0 31 35 -1 0 0 0 35 36 -1 0 0 0 32 36 -1 0 0 0 33 37 -1 0 0 0 37 38 -1 0 0 0 34 38 -1 0 0 0 35 39 -1 0 0 0 39 40 -1 0 0 0 36 40 -1 0 0 0 37 41 -1 0 0 0 41 42 -1 0 0 0 38 42 -1 0 0 0 39 43 -1 0 0 0 43 44 -1 0 0 0 40 44 -1 0 0 0 41 45 -1 0 0 0 45 46 -1 0 0 0 42 46 -1 0 0 0 43 47 -1 0 0 0 47 48 -1 0 0 0 44 48 -1 0 0 0 45 49 -1 0 0 0 49 50 -1 0 0 0 46 50 -1 0 0 0 47 51 -1 0 0 0 51 52 -1 0 0 0 48 52 -1 0 0 0 49 53 -1 0 0 0 53 54 -1 0 0 0 50 54 -1 0 0 0 51 55 -1 0 0 0 55 56 -1 0 0 0 52 56 -1 0 0 0 53 57 -1 0 0 0 57 58 -1 0 0 0 54 58 -1 0 0 0 55 59 -1 0 0 0 59 60 -1 0 0 0 56 60 -1 0 0 0 57 61 -1 0 0 0 61 62 -1 0 0 0 58 62 -1 0 0 0 [NumArcSegments] = 4 0 1 180 2.5 1 0 0 0.62 1 0 180 2.5 2 0 0 0.62 2 3 180 2.5 1 0 0 0.62 3 2 180 2.5 2 0 0 0.62 [NumHoles] = 0 [NumBlockLabels] = 27 0 50 1 0.5 0 0 0 1 0 93.333333333333329 9.1666666666666661 1 0.5 0 0 0 1 0 0 0 2 1 0 0 0 1 0 3.625 0 1 1 0 0 0 1 0 -3.625 0 1 1 0 0 0 1 0 1.1000000000000001 12 3 0.10000000000000001 0 0 0 1 0 -1.1000000000000001 12 3 0.10000000000000001 0 180 0 1 0 3.3000000000000003 12 4 0.10000000000000001 0 0 0 1 0 -3.3000000000000003 12 4 0.10000000000000001 0 180 0 1 0 5.5 12 5 0.10000000000000001 0 0 0 1 0 -5.5 12 5 0.10000000000000001 0 180 0 1 0 7.7000000000000011 12 6 0.10000000000000001 0 0 0 1 0 -7.7000000000000011 12 6 0.10000000000000001 0 180 0 1 0 9.9000000000000004 12 7 0.10000000000000001 0 0 0 1 0 -9.9000000000000004 12 7 0.10000000000000001 0 180 0 1 0 12.1 12 8 0.10000000000000001 0 0 0 1 0 -12.1 12 8 0.10000000000000001 0 180 0 1 0 14.300000000000001 12 9 0.10000000000000001 0 0 0 1 0 -14.300000000000001 12 9 0.10000000000000001 0 180 0 1 0 16.500000000000004 12 10 0.10000000000000001 0 0 0 1 0 -16.500000000000004 12 10 0.10000000000000001 0 180 0 1 0 18.700000000000003 12 11 0.10000000000000001 0 0 0 1 0 -18.700000000000003 12 11 0.10000000000000001 0 180 0 1 0 20.900000000000002 12 12 0.10000000000000001 0 0 0 1 0 -20.900000000000002 12 12 0.10000000000000001 0 180 0 1 0 34.799999999999997 12 13 0.10000000000000001 0 0 0 1 0 -34.799999999999997 12 13 0.10000000000000001 0 180 0 1 0
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