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Post by antigua on Feb 24, 2021 22:47:14 GMT -5
I realize I'm late to the thread, but I love this: "[T]he dimensionless quantity of mojo". I also think that this is a pretty compelling analysis of the role of the electric guitar over time, and a nice explanation of how we ended up where we seem to be right now. Though I'd add that there's a distressing element of anti-science attitude, an attitude of "you have your truth and I have mine", which came out of both philosophy of science (e.g. Kuhn) and postmodernist literary theory (e.g. Derrida), and has ironically been embraced by the left and the right, at least in the US. I don't understand it, I don't know why guitarists aren't clamoring to know the inductance or functional resonant peaks, or the gauss strength of pickups. When people talk about cars, they love to talk horsepower, torque, quarter mile times. With guitar amps, people talk about wattage, whether is Class A, solid state, etc. , and with speakers it's power efficiency, cone type, and all sorts of things. But when it comes to pickups, people seem to be happier knowing less. There are so many unanswerable questions about "tone wood" that you'd think people would be happy to know there's at least this one aspect of the electric guitar that can be easily quantified with a $100 LCR meter. The few of us who care about this stuff are a tiny minority, and I have no idea why that is.
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Post by aquin43 on Feb 25, 2021 4:43:33 GMT -5
I tried an LTSpice simulation of a pair of 10 turn layers
The total currents through the capacitors are I(VSENSE_1) and I(VSENSE_2). They prove to be equal. The output voltages out and outfb differ slightly at higher frequencies and outfb seems to be the most affected.
C11 is shorted out by VSENSE_1 but is included anyway. The inductors all have resistance, the voltage sources represent the volts per turn and everything is parameterised. The values are arbitrary but chosen so that the capacitive loading on each node is negligible.
The simulation file, to be copied into a text editor by anyone interested and saved as pu-turns.asc is: ...
The next exercise would be to model the two voltage distributions in FEMM to check whether the stored charges would be equal. So this models the capacitance of two wires that are side by side, but it seems that the lumped capacitance is gradient that extends from the first wind to the very last, so the capacitance individual turns as depicted is but a small part of the lump. Maybe it's 0.1% or 10%, I have no idea. I think in the transformer designs where they use the fold back technique, there might have been a less layers, and they might have been used for RF, so the improvement would have been more meaningful. This is a naive model of the effective inter layer capacitance. It is a gross simplification of the actual layout. For example, the real turns are not face to face but nestled together. I thought it worthwhile, however, because the voltage gradient is actually similar to what would be produced by a current through the coil and it seemed reasonable to assume that the capacitances between turns would be localised to a marked degree, because capacitance falls with distance and the tightly interleaved turns shield each other . The physical layout of the turns is obviously the same for both winding methods. That leaves only the voltage distribution to make a difference. If the two winding methods were to produce different capacitive currents, one would expect to see some sign of it in even this simplified model. In the audio range, there is none. I suspect that you are right and the effects only appear at RF, where the impedance of the turns becomes significant.
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Post by ms on Feb 25, 2021 6:35:58 GMT -5
I think there is a limit to the localization. The current change due to the capacitance between turns a and b induces some voltages in all other turns because they are all magnetically coupled. It might be interesting to model a simple case, starting with low mutual inductance and increasing it until an effect is seen.
A single layer rf coil can be treated as a transmission line. The inductance and capacitance per unit distance determine the impedance. Its length is short compared to a quarter wavelength, and so it is capacitive, with the value computed from a very simple equation. I have read that this method works very well in many cases. I think that this works because the magnetic coupling is largest between turns that are close together, making this simple model possible.
But it does not work for a guitar pickup, a multi-layer coil with a huge number of turns. Perhaps a different approximation is possible taking advantage of a limit involving the large number of turns and the fact all the voltages resulting from magnetic coupling between turns appear in series.
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Post by aquin43 on Feb 25, 2021 9:51:54 GMT -5
There is, of course, also Yogi B's analysis which is based on the stored energy. While the capacitive currents may be the same, the distributions of voltages are not, so the way that the current is shared between the capacitors is different. Because the stored energy is dependent on the square of the voltage across the capacitor, the stored energy, and hence the capacitances, will differ in the bulk coil even though the current appears to be the same. This approach indicates that the foldback winding method has a lower effective capacitance than the zig zag method. I think that I am following Yogi B: in this subsequent calculation. We use the squares of the voltage differences to represent the stored energy, assuming a total of 2V applied, 1V per winding and a winding length of 1.
zig zag: delta_v = 2(1-x), delta_v^2 = 4(1 - 2x + x^2)
1 1
integral 4(1 - 2x + x^2) = [ 4(x - x^2 + x^3/3) ]
0 0
= 4/3
foldback:
delta_v = 1, so delta_v^2 and its integral from 0 to 1 also evaluates to 1
Therefore, the foldback method stores 3/4 of the energy for a given voltage applied
implying 3/4 of the capacitance
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Post by aquin43 on Feb 26, 2021 6:52:54 GMT -5
Having been convinced by Yogi B's analysis, I thought that it might be interesting to try to model a pair of coil layers in such a way that the actual capacitance could be inferred. I decided to use two resistor chains to represent the wires with ten windings per layer. The idea is to drive these resistor chains and their cross linking capacitors with a current. The voltage across the driving point would represent the impedance. Obviously, the different internal loading arrangements would upset the equal division of voltage at higher frequencies but perhaps at low frequency a similarity of input impedance could be found that would indicate the relative capacitance. The simulation contains two chains and a simple parallel RC pair. The capacitors in the foldback array are scaled by the theoretical 4/3 necessary make its low frequency behaviour the same as that of the zig zag array. The capacitor in the RC pair is chosen experimentally to match the frequency response as far as possible. The LtSpice file is given below. Version 4 SHEET 1 1268 820 WIRE -160 -128 -192 -128 WIRE 0 -128 -160 -128 WIRE 144 -128 0 -128 WIRE -192 -96 -192 -128 WIRE 0 -96 0 -128 WIRE 144 -80 144 -128 WIRE -192 16 -192 -16 WIRE 0 16 0 -16 WIRE 0 16 -192 16 WIRE 144 16 144 -16 WIRE 144 16 0 16 WIRE -192 32 -192 16 WIRE -160 112 -192 112 WIRE -32 112 -160 112 WIRE -16 112 -32 112 WIRE 80 112 64 112 WIRE 96 112 80 112 WIRE 192 112 176 112 WIRE 208 112 192 112 WIRE 304 112 288 112 WIRE 320 112 304 112 WIRE 416 112 400 112 WIRE 432 112 416 112 WIRE 528 112 512 112 WIRE 544 112 528 112 WIRE 640 112 624 112 WIRE 656 112 640 112 WIRE 752 112 736 112 WIRE 768 112 752 112 WIRE 864 112 848 112 WIRE 880 112 864 112 WIRE 976 112 960 112 WIRE 992 112 976 112 WIRE 1088 112 1072 112 WIRE 1168 112 1088 112 WIRE -192 160 -192 112 WIRE -32 176 -32 112 WIRE 80 176 80 112 WIRE 192 176 192 112 WIRE 304 176 304 112 WIRE 416 176 416 112 WIRE 528 176 528 112 WIRE 640 176 640 112 WIRE 752 176 752 112 WIRE 864 176 864 112 WIRE 976 176 976 112 WIRE 1088 176 1088 112 WIRE -192 320 -192 240 WIRE -32 320 -32 240 WIRE -32 320 -80 320 WIRE -16 320 -32 320 WIRE 80 320 80 240 WIRE 80 320 64 320 WIRE 96 320 80 320 WIRE 192 320 192 240 WIRE 192 320 176 320 WIRE 208 320 192 320 WIRE 304 320 304 240 WIRE 304 320 288 320 WIRE 320 320 304 320 WIRE 416 320 416 240 WIRE 416 320 400 320 WIRE 432 320 416 320 WIRE 528 320 528 240 WIRE 528 320 512 320 WIRE 544 320 528 320 WIRE 640 320 640 240 WIRE 640 320 624 320 WIRE 656 320 640 320 WIRE 752 320 752 240 WIRE 752 320 736 320 WIRE 768 320 752 320 WIRE 864 320 864 240 WIRE 864 320 848 320 WIRE 880 320 864 320 WIRE 976 320 976 240 WIRE 976 320 960 320 WIRE 992 320 976 320 WIRE 1088 320 1088 240 WIRE 1088 320 1072 320 WIRE 1168 320 1168 112 WIRE 1168 320 1088 320 WIRE -160 432 -192 432 WIRE -32 432 -160 432 WIRE -16 432 -32 432 WIRE 80 432 64 432 WIRE 96 432 80 432 WIRE 192 432 176 432 WIRE 208 432 192 432 WIRE 304 432 288 432 WIRE 320 432 304 432 WIRE 416 432 400 432 WIRE 432 432 416 432 WIRE 528 432 512 432 WIRE 544 432 528 432 WIRE 640 432 624 432 WIRE 656 432 640 432 WIRE 752 432 736 432 WIRE 768 432 752 432 WIRE 864 432 848 432 WIRE 880 432 864 432 WIRE 976 432 960 432 WIRE 992 432 976 432 WIRE 1088 432 1072 432 WIRE 1200 432 1088 432 WIRE -192 496 -192 432 WIRE -32 496 -32 432 WIRE 80 496 80 432 WIRE 192 496 192 432 WIRE 304 496 304 432 WIRE 416 496 416 432 WIRE 528 496 528 432 WIRE 640 496 640 432 WIRE 752 496 752 432 WIRE 864 496 864 432 WIRE 976 496 976 432 WIRE 1088 496 1088 432 WIRE -32 592 -32 560 WIRE 1200 592 1200 432 WIRE 1200 592 -32 592 WIRE -192 640 -192 576 WIRE -32 640 -32 592 WIRE -16 640 -32 640 WIRE 80 640 80 560 WIRE 80 640 64 640 WIRE 96 640 80 640 WIRE 192 640 192 560 WIRE 192 640 176 640 WIRE 208 640 192 640 WIRE 304 640 304 560 WIRE 304 640 288 640 WIRE 320 640 304 640 WIRE 416 640 416 560 WIRE 416 640 400 640 WIRE 432 640 416 640 WIRE 528 640 528 560 WIRE 528 640 512 640 WIRE 544 640 528 640 WIRE 640 640 640 560 WIRE 640 640 624 640 WIRE 656 640 640 640 WIRE 752 640 752 560 WIRE 752 640 736 640 WIRE 768 640 752 640 WIRE 864 640 864 560 WIRE 864 640 848 640 WIRE 880 640 864 640 WIRE 976 640 976 560 WIRE 976 640 960 640 WIRE 992 640 976 640 WIRE 1088 640 1088 560 WIRE 1088 640 1072 640 WIRE 1136 640 1088 640 FLAG -192 320 0 FLAG -192 640 0 FLAG 1136 640 0 FLAG -192 32 0 FLAG -160 112 zz FLAG -160 432 fb FLAG -160 -128 eq FLAG -80 320 0 SYMBOL res 80 96 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R1 SYMATTR Value {rs} SYMBOL res 192 96 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R2 SYMATTR Value {rs} SYMBOL res 304 96 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R3 SYMATTR Value {rs} SYMBOL res 416 96 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R4 SYMATTR Value {rs} SYMBOL res 528 96 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R5 SYMATTR Value {rs} SYMBOL res 640 96 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R6 SYMATTR Value {rs} SYMBOL res 752 96 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R7 SYMATTR Value {rs} SYMBOL res 864 96 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R8 SYMATTR Value {rs} SYMBOL res 976 96 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R9 SYMATTR Value {rs} SYMBOL res 1088 96 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R10 SYMATTR Value {rs} SYMBOL res 80 304 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R11 SYMATTR Value {rs} SYMBOL res 192 304 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R12 SYMATTR Value {rs} SYMBOL res 304 304 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R13 SYMATTR Value {rs} SYMBOL res 416 304 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R14 SYMATTR Value {rs} SYMBOL res 528 304 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R15 SYMATTR Value {rs} SYMBOL res 640 304 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R16 SYMATTR Value {rs} SYMBOL res 752 304 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R17 SYMATTR Value {rs} SYMBOL res 864 304 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R18 SYMATTR Value {rs} SYMBOL res 976 304 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R19 SYMATTR Value {rs} SYMBOL res 1088 304 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R20 SYMATTR Value {rs} SYMBOL cap -48 176 R0 SYMATTR InstName C1 SYMATTR Value {cp} SYMBOL cap 64 176 R0 SYMATTR InstName C2 SYMATTR Value {cp} SYMBOL cap 176 176 R0 SYMATTR InstName C3 SYMATTR Value {cp} SYMBOL cap 288 176 R0 SYMATTR InstName C4 SYMATTR Value {cp} SYMBOL cap 400 176 R0 SYMATTR InstName C5 SYMATTR Value {cp} SYMBOL cap 512 176 R0 SYMATTR InstName C6 SYMATTR Value {cp} SYMBOL cap 624 176 R0 SYMATTR InstName C7 SYMATTR Value {cp} SYMBOL cap 736 176 R0 SYMATTR InstName C8 SYMATTR Value {cp} SYMBOL cap 848 176 R0 SYMATTR InstName C9 SYMATTR Value {cp} SYMBOL current -192 240 R180 WINDOW 0 24 80 Left 2 WINDOW 3 24 0 Left 2 WINDOW 123 -107 -14 Left 2 WINDOW 39 0 0 Left 0 SYMATTR InstName I1 SYMATTR Value "" SYMATTR Value2 AC 500u SYMBOL res 80 416 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R21 SYMATTR Value {rs} SYMBOL res 192 416 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R22 SYMATTR Value {rs} SYMBOL res 304 416 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R23 SYMATTR Value {rs} SYMBOL res 416 416 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R24 SYMATTR Value {rs} SYMBOL res 528 416 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R25 SYMATTR Value {rs} SYMBOL res 640 416 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R26 SYMATTR Value {rs} SYMBOL res 752 416 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R27 SYMATTR Value {rs} SYMBOL res 864 416 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R28 SYMATTR Value {rs} SYMBOL res 976 416 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R29 SYMATTR Value {rs} SYMBOL res 1088 416 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R30 SYMATTR Value {rs} SYMBOL res 80 624 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R31 SYMATTR Value {rs} SYMBOL res 192 624 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R32 SYMATTR Value {rs} SYMBOL res 304 624 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R33 SYMATTR Value {rs} SYMBOL res 416 624 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R34 SYMATTR Value {rs} SYMBOL res 528 624 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R35 SYMATTR Value {rs} SYMBOL res 640 624 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R36 SYMATTR Value {rs} SYMBOL res 752 624 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R37 SYMATTR Value {rs} SYMBOL res 864 624 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R38 SYMATTR Value {rs} SYMBOL res 976 624 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R39 SYMATTR Value {rs} SYMBOL res 1088 624 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName R40 SYMATTR Value {rs} SYMBOL current -192 576 R180 WINDOW 0 24 80 Left 2 WINDOW 3 24 0 Left 2 WINDOW 123 -103 -36 Left 2 WINDOW 39 0 0 Left 0 SYMATTR InstName I2 SYMATTR Value "" SYMATTR Value2 AC 500u SYMBOL cap 960 176 R0 SYMATTR InstName C10 SYMATTR Value {cp} SYMBOL cap 1072 176 R0 SYMATTR InstName C11 SYMATTR Value {cp} SYMBOL cap -48 496 R0 SYMATTR InstName C12 SYMATTR Value {cp*cx} SYMBOL cap 64 496 R0 SYMATTR InstName C13 SYMATTR Value {cp*cx} SYMBOL cap 176 496 R0 SYMATTR InstName C14 SYMATTR Value {cp*cx} SYMBOL cap 288 496 R0 SYMATTR InstName C15 SYMATTR Value {cp*cx} SYMBOL cap 400 496 R0 SYMATTR InstName C16 SYMATTR Value {cp*cx} SYMBOL cap 512 496 R0 SYMATTR InstName C17 SYMATTR Value {cp*cx} SYMBOL cap 624 496 R0 SYMATTR InstName C18 SYMATTR Value {cp*cx} SYMBOL cap 736 496 R0 SYMATTR InstName C19 SYMATTR Value {cp*cx} SYMBOL cap 848 496 R0 SYMATTR InstName C20 SYMATTR Value {cp*cx} SYMBOL cap 960 496 R0 SYMATTR InstName C21 SYMATTR Value {cp*cx} SYMBOL cap 1072 496 R0 SYMATTR InstName C22 SYMATTR Value {cp*cx} SYMBOL res -16 -112 R0 SYMATTR InstName R41 SYMATTR Value {rtot} SYMBOL current -192 -16 R180 WINDOW 0 24 80 Left 2 WINDOW 3 24 0 Left 2 WINDOW 123 -112 -6 Left 2 WINDOW 39 0 0 Left 0 SYMATTR InstName I3 SYMATTR Value "" SYMATTR Value2 AC 500u SYMBOL cap 128 -80 R0 SYMATTR InstName C23 SYMATTR Value {cp*eq} TEXT 416 -8 Left 2 !.param rs = rtot/20 TEXT 416 24 Left 2 !.param cp = 100n TEXT 416 -72 Left 2 !.ac dec 20 10 1k TEXT 664 -8 Left 2 !.param cx = 4/3 TEXT 664 24 Left 2 !.param eq = 4.3 TEXT 416 -40 Left 2 !.param rtot = 2k
The results are shown below.
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