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Post by aquin43 on Apr 11, 2022 11:15:57 GMT -5
I tried a rough model of an alumitone in LTSpice to help me get an idea of how it works and why it differs from a conventional pickup. The three main characteristics are a generally falling response at low frequencies, a large variation of inductance over the audio range and a low loaded Q. I came up with the following model in which the coupling of the sensor to the output coil is not very tight as one would expect from the geometry of the transformer. I have juggled the values to roughly approximate the measured response. The AC input represents the induced voltage which reflects the string velocity so no integrator is needed.
The transformer secondary is a high inductance coupled to another inductance in series with a resistor. This L-R loop of 500u 800n has a cut off frequency of just under 100 Hz, which contributes both to the rising characteristic in the primary and the fall in the secondary inductance. LTSpice listing: Version 4 SHEET 1 1636 680 WIRE 224 -32 16 -32 WIRE 496 -32 336 -32 WIRE 736 -32 496 -32 WIRE 848 -32 736 -32 WIRE 976 -32 848 -32 WIRE 224 32 224 -32 WIRE 336 48 336 -32 WIRE 16 80 16 -32 WIRE 976 112 976 -32 WIRE 496 128 496 -32 WIRE 736 128 736 -32 WIRE 848 128 848 -32 WIRE 224 192 224 112 WIRE 336 192 336 128 WIRE 16 368 16 160 WIRE 224 368 224 272 WIRE 224 368 16 368 WIRE 336 368 336 272 WIRE 336 368 224 368 WIRE 496 368 496 192 WIRE 496 368 336 368 WIRE 736 368 736 208 WIRE 736 368 496 368 WIRE 848 368 848 192 WIRE 848 368 736 368 WIRE 976 368 976 192 WIRE 976 368 848 368 WIRE 16 400 16 368 FLAG 16 400 0 SYMBOL ind2 352 288 R180 WINDOW 0 -41 81 Left 2 WINDOW 3 -43 37 Left 2 SYMATTR InstName Ls SYMATTR Value 40 SYMATTR Type ind SYMBOL cap 480 128 R0 SYMATTR InstName C1 SYMATTR Value 30p SYMBOL res 320 32 R0 SYMATTR InstName R1 SYMATTR Value 2k5 SYMBOL res 752 224 R180 WINDOW 0 36 76 Left 2 WINDOW 3 36 40 Left 2 SYMATTR InstName R2 SYMATTR Value 1Meg SYMBOL ind2 208 288 M180 WINDOW 0 -64 76 Left 2 WINDOW 3 -67 35 Left 2 SYMATTR InstName Lstr SYMATTR Value 800n SYMATTR Type ind SYMATTR SpiceLine Rser=0 SYMBOL res 240 16 M0 SYMATTR InstName R3 SYMATTR Value 500µ SYMBOL voltage 16 64 R0 WINDOW 123 23 102 Left 2 WINDOW 39 0 0 Left 0 SYMATTR Value2 AC 120u SYMATTR InstName V1 SYMATTR Value "" SYMBOL cap 832 128 R0 SYMATTR InstName C2 SYMATTR Value 470p SYMBOL res 960 96 R0 SYMATTR InstName R4 SYMATTR Value 200k TEXT 112 408 Left 2 !.ac dec 500 80 10k TEXT 192 -64 Left 2 !Ktr Lstr Ls {kc} TEXT 656 408 Left 2 ;.step param kc list .7 .8 .9 1 TEXT 416 408 Left 2 !.param kc = 0.8 TEXT 408 448 Left 3 ;Alumitone
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Post by antigua on Apr 11, 2022 14:53:32 GMT -5
If you run the frequency sweep, does it create a plot similar to this? When I see the high pass effect, I'm thinking there has be to be some sort of parallel inductance happening.
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Post by aquin43 on Apr 11, 2022 15:23:53 GMT -5
Sorry, I left out the important bit: the curves:
The same sort of general shape. It is the cutoff frequency of the loop resistance and inductance that causes the low frequency loss.
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Post by ms on Apr 11, 2022 17:57:32 GMT -5
If I remember my transformer stuff, coupling below unity should put an inductor in series with a winding of a unity coupled transformer; you can put it in series with either the primary, the secondary (different value, of course), or split it, I suppose. So I am thinking that varying the coupling should be the same as varying the value of one of the inductors in the circuit. Is this what you see, or do I have it all wrong?
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Post by antigua on Apr 11, 2022 18:48:47 GMT -5
That's really impressive, I'm surprised to see such a high degree of matching just with such a simple model. I'm still trying to understand what's happening, I'll put this into LTSpice and see how different values affect the curve. I think I had trouble figuring out what the inductance was for the Alumitone, the LCR meter couldn't figure it out, probably because of these complicating factors, so I'm wondering if the inductance can be inferred based on this model, although 40 Henries is quite a lot.
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Post by ms on Apr 11, 2022 19:53:08 GMT -5
That's really impressive, I'm surprised to see such a high degree of matching just with such a simple model. I'm still trying to understand what's happening, I'll put this into LTSpice and see how different values affect the curve. I think I had trouble figuring out what the inductance was for the Alumitone, the LCR meter couldn't figure it out, probably because of these complicating factors, so I'm wondering if the inductance can be inferred based on this model, although 40 Henries is quite a lot. 40 H is not what sets the resonant frequency. That mostly disappears because of the coupling of the transformer, which in a sense puts a lower impedance across it. If I remember how transformers work, if it had perfect coupling the secondary inductance would not matter at all.
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Post by aquin43 on Apr 12, 2022 4:58:38 GMT -5
What I was most interested in finding out was why the low frequency roll-off and the generally rising characteristic. A normal pickup produces its output directly from the string magnetism but the alumitone has an intermediary step where the output is induced in the secondary of the transformer by the current circulating round the slot. If this were a perfect transformer, the circulating current would be governed by the output load reflected through the square of the turns ratio and the pickup would behave as usual. In the alumitone, the coupling is poor and most of the loop impedance is determined by the resistance and inductance of the loop. This provides a mechanism to affect the low frequency response. For a flat response, the current should be determined by Lstr only but at low frequencies the loop resistance dominates so there is a low frequency roll off. The turns ratio of the transformer must be around 7000 for adequate output, giving an impedance ratio of 49 million (if it were a true transformer). One extra useful thing that the alumitone allows is that because the sensing coil is a single turn its width can easily vary along its length so that it is narrower under some strings than others. This could be used give a humbucker a more single coil response.
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Post by aquin43 on Apr 12, 2022 5:20:38 GMT -5
I thought it would be worth adding here for reference a useful result for the equivalent impedance of an inductor mutually coupled to another inductor with a resistor load. This is the basis of the impedance ratio of a transformer when K and L are large and also the coupling of losses from eddy currents.
ω0 = R2/L2 ω = 2*π*frequency
U(ω) = k^2 ω^2 / (ω^2 + ω0^2) frequency dependent curve = 1/2 when ω == ω0
L = L1 ( 1 - U(ω) )
R = R1 + U(ω)* R2 * L1 / L2
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Post by ms on Apr 12, 2022 7:25:02 GMT -5
I thought it would be worth adding here for reference a useful result for the equivalent impedance of an inductor mutually coupled to another inductor with a resistor load. This is the basis of the impedance ratio of a transformer when K and L are large and also the coupling of losses from eddy currents.
ω0 = R2/L2 ω = 2*π*frequency
U(ω) = k^2 ω^2 / (ω^2 + ω0^2) frequency dependent curve = 1/2 when ω == ω0
L = L1 ( 1 - U(ω) )
R = R1 + U(ω)* R2 * L1 / L2
An alternative analysis (for example, page 213 of Jon Hagen's Radio Frequency Electronics) would avoid the variable frequency inductance. The equivalent circuit consists of an ideal transformer with turns ratio equal to the square root of L1/((k^2)*L2). A magnetizing inductance with value L1 is across the primary. A leakage inductance with value L2(1 - k^2) is in series with the secondary. I believe that this model agrees with yours for the low frequency response. It also makes it easy to see how poor coupling increases the inductance looking back into the secondary and thus lowers the resonant frequency of the system with load, causing the loss of high frequencies.
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Post by aquin43 on Apr 12, 2022 8:42:30 GMT -5
I thought it would be worth adding here for reference a useful result for the equivalent impedance of an inductor mutually coupled to another inductor with a resistor load. This is the basis of the impedance ratio of a transformer when K and L are large and also the coupling of losses from eddy currents.
ω0 = R2/L2 ω = 2*π*frequency
U(ω) = k^2 ω^2 / (ω^2 + ω0^2) frequency dependent curve = 1/2 when ω == ω0
L = L1 ( 1 - U(ω) )
R = R1 + U(ω)* R2 * L1 / L2
An alternative analysis (for example, page 213 of Jon Hagen's Radio Frequency Analysis) would avoid the variable frequency inductance. The equivalent circuit consists of an ideal transformer with turns ratio equal to the square root of L1/((k^2)*L2). A magnetizing inductance with value L1 is across the primary. A leakage inductance with value L2(1 - k^2) is in series with the secondary. I believe that this model agrees with yours for the low frequency response. It also makes it easy to see how poor coupling increases the inductance looking back into the secondary and thus lowers the resonant frequency of the system with load, causing the loss of high frequencies. Yes, there are many ways of modelling the impedance. My analysis comes directly from the voltage you get when you drive a 1A current into the terminals of the inductor and then partition that into real and imaginary parts. The point of expressing in this form is that it directly illustrates the way that the measured inductance falls and the loss resistance increases with frequency when an inductor is coupled to a lossy one.
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Post by aquin43 on Apr 13, 2022 4:38:40 GMT -5
A second look Taking a second look at this problem, I came up with the following modified version: It is clear from further consideration of the geometry of the pickup that most of the sensing loop area is not coupled to the output at all. In fact, the output coil senses only the current passing through a small part of the common connection. This suggests the diagram above in which the current through Lcom is controlled almost entirely by the loop impedances. In this version, the output impedance of the pickup is governed almost entirely by the transformer coil and the low frequency response by the geometry and resistivity of the sensing coils. The output is derived from the current through Lcom which is only loosely influenced by the load reflected back through the mutual coupling. This extra step would seem to validate the claim that the pickup is different in sensing current rather than voltage. Of course voltage is what is generated by the string in the first place and this extra step seem to be an attempt to promote and harness the ensuing eddy currents. The circulating currents in the loops will dissipate power in Rloop1 and Rloop2 in the same way as eddy currents. The extra power drawn from the string will still remain negligible. While the loop currents are controlled by inductors Loop1 and Loop2, the current will rise as the frequency falls to maintain a constant induced voltage in the sensing coil. At low frequencies, where the resistors Rloop1 and Rloop2 control the current, the output will fall at 6dB/octave. The crossover frequency will be at ω=R/L for the loop. All of the values in the model are guesses. The sensing coil and its core have been given no losses beyond Rtr so the Q is determined very much by the test set load Rtest. Rsw in the diagram connects and disconnects the load.
Version 4 SHEET 1 1636 680 WIRE 192 -144 -272 -144 WIRE 32 -112 -144 -112 WIRE 32 -80 32 -112 WIRE 192 -80 192 -144 WIRE 400 -80 352 -80 WIRE 352 -32 352 -80 WIRE 352 -32 304 -32 WIRE 416 -32 352 -32 WIRE 560 -32 416 -32 WIRE 608 -32 560 -32 WIRE 752 -32 688 -32 WIRE 864 -32 752 -32 WIRE 976 -32 864 -32 WIRE 32 32 32 0 WIRE 192 32 192 0 WIRE 304 48 304 -32 WIRE -272 80 -272 -144 WIRE -144 80 -144 -112 WIRE 752 96 752 -32 WIRE 560 112 560 -32 WIRE 976 112 976 -32 WIRE 864 128 864 -32 WIRE 32 160 32 112 WIRE 112 160 32 160 WIRE 192 160 192 112 WIRE 192 160 112 160 WIRE 304 192 304 128 WIRE 304 192 208 192 WIRE 112 224 112 160 WIRE 208 224 208 192 WIRE 416 224 416 -32 WIRE -272 288 -272 160 WIRE -208 288 -272 288 WIRE -144 288 -144 160 WIRE -144 288 -208 288 WIRE -208 368 -208 288 WIRE 112 368 112 304 WIRE 112 368 -208 368 WIRE 208 368 208 304 WIRE 208 368 112 368 WIRE 416 368 416 288 WIRE 416 368 208 368 WIRE 560 368 560 192 WIRE 560 368 416 368 WIRE 752 368 752 176 WIRE 752 368 560 368 WIRE 864 368 864 192 WIRE 864 368 752 368 WIRE 976 368 976 192 WIRE 976 368 864 368 WIRE -208 384 -208 368 FLAG -208 384 0 FLAG 400 -80 OUT SYMBOL ind2 224 320 R180 WINDOW 0 -41 81 Left 2 WINDOW 3 -43 37 Left 2 SYMATTR InstName Ltr SYMATTR Value 15 SYMATTR Type ind SYMBOL cap 400 224 R0 SYMATTR InstName C1 SYMATTR Value 30p SYMBOL res 288 32 R0 SYMATTR InstName Rtr SYMATTR Value 2k5 SYMBOL res 768 192 R180 WINDOW 0 36 76 Left 2 WINDOW 3 36 40 Left 2 SYMATTR InstName Ramp SYMATTR Value 1.111Meg SYMBOL ind2 96 320 M180 WINDOW 0 -80 68 Left 2 WINDOW 3 -67 35 Left 2 SYMATTR InstName Lcom SYMATTR Value 10n SYMATTR Type ind SYMATTR SpiceLine Rser=0 SYMBOL res 48 -96 M0 SYMATTR InstName Rloop1 SYMATTR Value 500µ SYMBOL voltage -272 64 R0 WINDOW 123 19 125 Left 2 WINDOW 39 0 0 Left 0 SYMATTR Value2 AC 120u SYMATTR InstName V1 SYMATTR Value "" SYMBOL cap 848 128 R0 SYMATTR InstName Cload SYMATTR Value 470p SYMBOL res 960 96 R0 SYMATTR InstName Rload SYMATTR Value 250k SYMBOL res 704 -48 R90 WINDOW 0 0 56 VBottom 2 WINDOW 3 32 56 VTop 2 SYMATTR InstName Rsw SYMATTR Value {rsw} SYMBOL ind2 16 128 M180 WINDOW 0 -77 90 Left 2 WINDOW 3 -67 35 Left 2 SYMATTR InstName Loop1 SYMATTR Value 800n SYMATTR Type ind SYMATTR SpiceLine Rser=0 SYMBOL res 208 -96 M0 SYMATTR InstName Rloop2 SYMATTR Value 500µ SYMBOL ind2 176 128 M180 WINDOW 0 -78 91 Left 2 WINDOW 3 -67 35 Left 2 SYMATTR InstName Loop2 SYMATTR Value 800n SYMATTR Type ind SYMATTR SpiceLine Rser=0 SYMBOL voltage -144 64 R0 WINDOW 123 13 127 Left 2 WINDOW 39 0 0 Left 0 SYMATTR Value2 AC 120u SYMATTR InstName V2 SYMATTR Value "" SYMBOL res 576 208 R180 WINDOW 0 36 76 Left 2 WINDOW 3 36 40 Left 2 SYMATTR InstName Rtest SYMATTR Value 10Meg TEXT 496 408 Left 2 !.ac dec 500 80 10k TEXT 96 400 Left 2 !Ktr Lcom Ltr {kc} TEXT 568 -128 Left 2 !.param rsw = 1m TEXT 328 448 Left 3 ;Alumitone TEXT 520 -96 Left 2 !.step param rsw list 1m 1G TEXT -152 400 Left 2 !.param kc = 0.98
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Post by antigua on Apr 13, 2022 9:33:47 GMT -5
Sorry, I left out the important bit: the curves:
The same sort of general shape. It is the cutoff frequency of the loop resistance and inductance that causes the low frequency loss.
I tried your spice file in LTSpice, but it doesn't seem to produce a curve like this one. The plot you have shows both loaded and unloaded Alumitone curves, but the spice file is loaded only. I tried it with and without the 200k and 470p cap, but in both cases it shows different curves across the 1meg resistor. How do you get it to produce the curves as shown in your screenshot?
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Post by aquin43 on Apr 13, 2022 10:10:37 GMT -5
I cheated and made a different version with a parameterised resistor that switched betwen 1m and 1G to attach the load. I wouldn't bother with that earlier version now that I have added a new twin loop version that is better thought out and represents the pickup geometry better. It includes the switch resistor to add the load.
The Q with the 10M test set load is rather high because there are no loss elements modeled for the coil. The K coupling factor has practically no effect on the frequency response but it does affect the output level of course.
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Post by ms on Apr 13, 2022 14:53:09 GMT -5
A second look Taking a second look at this problem, I came up with the following modified version: It is clear from further consideration of the geometry of the pickup that most of the sensing loop area is not coupled to the output at all. In fact, the output coil senses only the current passing through a small part of the common connection.
How did you arrive at this conclusion? I think it is clear that there is a loss of some of the sensing area, but I do not see how to decide how much. The primary loop passes through the core, a closed path of high permeability. Flux from the strings drives current around the primary loop which then creates flux in the core. The exact path through the core should not be all that critical since it is closed and high permeability. I am probably missing something; do you know what it is?
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Post by aquin43 on Apr 13, 2022 16:33:18 GMT -5
A second look Taking a second look at this problem, I came up with the following modified version: It is clear from further consideration of the geometry of the pickup that most of the sensing loop area is not coupled to the output at all. In fact, the output coil senses only the current passing through a small part of the common connection.
How did you arrive at this conclusion? I think it is clear that there is a loss of some of the sensing area, but I do not see how to decide how much. The primary loop passes through the core, a closed path of high permeability. Flux from the strings drives current around the primary loop which then creates flux in the core. The exact path through the core should not be all that critical since it is closed and high permeability. I am probably missing something; do you know what it is? Sorry, I should have said is not magnetically coupled. My reasoning was that a circulating current in the loop would generate flux mostly externally to the core with only the small stub that passes through the core being coupled so I must have been thinking of the K coupling as flux sharing. Mutual inductance itself is defined in terms of volts generated for current passed. I think that mathematically two series inductors with one tightly coupled to a third can produce the same result as one loosely coupled.
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