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Post by stratotarts on Dec 19, 2018 8:29:19 GMT -5
I'm relieved now that I gave up on precise modeling.  |
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Post by aquin43 on Dec 19, 2018 8:55:22 GMT -5
I found an old Dimarzio PAF style pickup and have modelled that with what I think may be the final version of the model. I have reverted to the two coils which can be either a coupled pair or a lossy and lossless in series. The matching program uses the coupled coils, because that arrangement seems easier to optimise by intuition, but It can write the spice file in either form. How does the model fare in cases where the resonance frequency is shifted upwards? For instance, what happens when the load is changed into 10M || 17pF || 1.28H + 1880ohms ? According to LTSpice:
Whether that is like the real pickup I don't know. All of the twin coil pickups have an extra resonance above the main one where the two coupled coils interact.
Arthur
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Post by JohnH on Dec 19, 2018 15:50:26 GMT -5
Hello, Sorry I forgot Rdc which is 7k688. The data are test data. The responses are normalized at 100 Hz so the loaded one doesn't include the 0.3 dB overall loss. The impedance data have all test set loading effects factored out. The plots look good, obviously good enough for practical use. Essentially, you are adjusting the split between the two LR series branches to perform the double duty of making the impedance right and making the frequency response right. In the range of impedances and frequencies in the guitar simulation this works amply well enough for practical use. The short-circuit current will be wrong, but this is of little interest.
Arthur Thanks. BTW, which DiMarzio pickup model is this? I readjusted my model to match the dcR, but it really made no difference. Then cycled a little more around the optimisation, to confirm that id reached the limit of matchting accuracy for the 6P model. I got peak frequencies and gain exact, with about 0.2db deviation around the droops. Here's an image of my modelling spreadsheet, it shows the output plots, with a blow up around the dips to show the deviations, and the impedance magnitudes below. Model values are in green at top, with some previous trial sets next to them:  While this is accurate enough for its purpose, I can see that your plots are closer. |
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Post by aquin43 on Dec 19, 2018 17:05:33 GMT -5
The pickup has no type name on it, just Dimarzio Pickups Made In USA. It dates from the mid 80's and has a metal magnet so it is probably their equivalent of a PAF.
Arthur
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Post by perfboardpatcher on Dec 20, 2018 15:41:10 GMT -5
How does the model fare in cases where the resonance frequency is shifted upwards? For instance, what happens when the load is changed into 10M || 17pF || 1.28H + 1880ohms ? According to LTSpice: Whether that is like the real pickup I don't know. All of the twin coil pickups have an extra resonance above the main one where the two coupled coils interact. Arthur Thanks for the chart, aquin43! I just wanted to mention this option because perhaps it could show some unexpected effect, perhaps somewhere in the mid frequencies. I leave it up to you, I have no ambitions in the modeling business. |
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Post by aquin43 on Dec 22, 2018 7:17:16 GMT -5
Shielding without much coupling.
I did a little experiment which I think provides some justification for the separate pre-filter in the model. I plotted a high Q single coil (plastic cover, alnico magnets) with the exciter on a wooden spacer placed 15mm above the poles. Then I inserted a piece of aluminium 100 X 140 mm X 1.6mm thick on top of the poles with the exciter on the spacer on top. The two plots superimposed show the enormous shielding loss through the aluminium and yet the pickup retains a high Q as shown by the peak and the steepness of the phase curve at resonance. I'm sure that if the aluminium had been folded round the coil there would have been more coupling so this is just an indication of the effect of the top plate of a cover.
Arthur
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Post by ms on Dec 22, 2018 11:21:45 GMT -5
Those curves belong to that class of pickups with the thick covers and the useless holes.
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Post by antigua on Dec 22, 2018 20:52:43 GMT -5
Shielding without much coupling.
I did a little experiment which I think provides some justification for the separate pre-filter in the model. I plotted a high Q single coil (plastic cover, alnico magnets) with the exciter on a wooden spacer placed 15mm above the poles. Then I inserted a piece of aluminium 100 X 140 mm X 1.6mm thick on top of the poles with the exciter on the spacer on top. The two plots superimposed show the enormous shielding loss through the aluminium and yet the pickup retains a high Q as shown by the peak and the steepness of the phase curve at resonance. I'm sure that if the aluminium had been folded round the coil there would have been more coupling so this is just an indication of the effect of the top plate of a cover.
Arthur
It doesn't look like the high Q is totally retained, the higher peak appears to rise about 20dB, but the lower peak only rises about 10dB. With the Filter'tron it looked like the big screws were the primary cause of the losses, the H cover was less significant, and the H cut does reduce the eddy current losses to some extent, compared to covers with no cuts. stratotarts did an experiment with eddy currents kenwillmott.com/blog/archives/246 showing that the wider the conductive pathway, the greater the losses in the cover, so breaks in the path reduce eddy currents, but to fully break the path, the "hole" would have to extend all the way to the base of the cover, which greatly reduced the rigidity of the structure. I'm not sure how to explain why this happens from a circuit analysis perspective, but the simple three coil Tuscon model is able to replicate this effect by simply adjusting the coupling between the pickup coil and the eddy current coil. As far as I know, this model accounts for the physically present factors, so unless I'm missing something there, it's a open and shut case.  I guess the eddy currents are able to attenuate the amplitude across the pickup without impeding the LC resonance. If you vary the resistance across the entire pickup, you get the usual tone control curves, which obliterates the Q, which just goes to show that eddy current losses and parallel load are not particularly alike. The parallel load also maintains a particular downward slope, but the eddy current cases the slop to decline progressively.  |
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Post by perfboardpatcher on Dec 23, 2018 7:48:04 GMT -5
Yes but,
if Lstr is magnetically coupled to Lcoil and Lcoil is coupled to Leddy doesn't that imply that Leddy is coupled to Lstr? What if there is a combination of Reddy and Leddy that's coupled to Lstr (+Rstr?) in the simulation that gives the same graphic results?
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Post by aquin43 on Dec 23, 2018 7:52:39 GMT -5
The point I was trying to make is that you can still have quite a high Q in the core of the pickup even the presence of a large high frequency loss caused by the shielding effect of the cover. I saw that as a small justification for the pre filter in my model.
My model and the Tucson one are equivalent to the extent that the Tucson model includes a low pass step in the response caused by the summing of two K couplings to the coil - directly and via the eddy current loop.
I considered that model to be difficult to visualise, so I separated the step out into a simple pre-filter. I also discovered that a single step is not generally sufficient to describe real pickups.
Arthur
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Post by aquin43 on Dec 23, 2018 7:59:20 GMT -5
Yes but, if Lstr is magnetically coupled to Lcoil and Lcoil is coupled to Leddy doesn't that imply that Leddy is coupled to Lstr? What if there is a combination of Reddy and Leddy that's coupled to Lstr (+Rstr?) in the simulation that gives the same graphic results? There is no back coupling via Lstr because it is open circuit. There are only the two forward paths, direct and via the eddy current loop.
Arthur.
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Post by perfboardpatcher on Dec 23, 2018 8:28:51 GMT -5
Yes but, if Lstr is magnetically coupled to Lcoil and Lcoil is coupled to Leddy doesn't that imply that Leddy is coupled to Lstr? What if there is a combination of Reddy and Leddy that's coupled to Lstr (+Rstr?) in the simulation that gives the same graphic results? There is no back coupling via Lstr because it is open circuit. There are only the two forward paths, direct and via the eddy current loop. Arthur. I didn't propose any back coupling. |
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Post by aquin43 on Dec 23, 2018 8:52:03 GMT -5
I'm sorry,
I thought that you were proposing the path Leddy -> Lcoil -> Lstr, which exists but is frustrated by Lstr being current driven.
The step in response is caused by Lstr -> Lcoil in parallel with Lstr -> Leddy -> Lcoil.
Leddy -> Lstr also exists but it too is frustrated by Lstr being current driven.
Arthur
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Post by perfboardpatcher on Dec 23, 2018 9:45:15 GMT -5
I'm sorry, I thought that you were proposing the path Leddy -> Lcoil -> Lstr, which exists but is frustrated by Lstr being current driven. The step in response is caused by Lstr -> Lcoil in parallel with Lstr -> Leddy -> Lcoil. Leddy -> Lstr also exists but it too is frustrated by Lstr being current driven.
Arthur Actually I thought I was coming to your defense, in support of your reply #65.  (yes, I proposed Lstr->Leddy) |
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Post by aquin43 on Dec 23, 2018 11:02:03 GMT -5
I must be getting a bit confused. I've been round the houses so many times on the Tucson model which is no longer at the forefront of my mind.
Arthur
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Post by antigua on Dec 23, 2018 15:12:53 GMT -5
My model and the Tucson one are equivalent to the extent that the Tucson model includes a low pass step in the response caused by the summing of two K couplings to the coil - directly and via the eddy current loop.
I considered that model to be difficult to visualise, so I separated the step out into a simple pre-filter. I also discovered that a single step is not generally sufficient to describe real pickups.
I'm not sure what you mean by "low pass step in the response caused by the summing of two K couplings to the coil", because if you eliminate the "eddy current coil" circuit from the three-way transformer, leaving only the current source and pickup portions, you still get the same overall curve. It sounds like you're saying there's an additional low pass represented by the three way coupling itself, but I don't see that happening.  |
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Post by aquin43 on Dec 30, 2018 8:36:06 GMT -5
My model and the Tucson one are equivalent to the extent that the Tucson model includes a low pass step in the response caused by the summing of two K couplings to the coil - directly and via the eddy current loop.
I considered that model to be difficult to visualise, so I separated the step out into a simple pre-filter. I also discovered that a single step is not generally sufficient to describe real pickups.
I'm not sure what you mean by "low pass step in the response caused by the summing of two K couplings to the coil", because if you eliminate the "eddy current coil" circuit from the three-way transformer, leaving only the current source and pickup portions, you still get the same overall curve. It sounds like you're saying there's an additional low pass represented by the three way coupling itself, but I don't see that happening. Go back to one of your earlier spice simulations with an obvious dip before the resonance and break the circuit just after Rcoil so that Rcoil is working into an open circuit. The voltage on the end of Rcoil will then be the total voltage induced in the main coil by the two forward paths. One path is direct and one is via the current induced in the eddy current loop then coupling onwards to the main coil. This latter current falls with frequency so the sum of the two couplings behaves like a low pass shelving filter. The roll off time constant is Leddy /Reddy.
In other words, the step in response is caused by Lstr -> Lcoil in parallel with Lstr -> Leddy -> Lcoil.
I have incorporated this filter into my model as a separate RC pre-filter.
This arrangement can adequately describe simple strat type pickups, but the single step or shelving filter is not sufficient to describe other pickups. You will soon find that it can't match the detail of the rise to the peak, nor can it describe the ultimate rate of fall after the peak. Remember that in this simple model, the time constant Leddy /Reddy is already fixed by the need to match the output impedance.
Arthur
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Post by antigua on Jan 5, 2019 13:25:04 GMT -5
I'm not sure what you mean by "low pass step in the response caused by the summing of two K couplings to the coil", because if you eliminate the "eddy current coil" circuit from the three-way transformer, leaving only the current source and pickup portions, you still get the same overall curve. It sounds like you're saying there's an additional low pass represented by the three way coupling itself, but I don't see that happening. Go back to one of your earlier spice simulations with an obvious dip before the resonance and break the circuit just after Rcoil so that Rcoil is working into an open circuit. The voltage on the end of Rcoil will then be the total voltage induced in the main coil by the two forward paths. One path is direct and one is via the current induced in the eddy current loop then coupling onwards to the main coil. This latter current falls with frequency so the sum of the two couplings behaves like a low pass shelving filter. The roll off time constant is Leddy /Reddy.
In other words, the step in response is caused by Lstr -> Lcoil in parallel with Lstr -> Leddy -> Lcoil.
I have incorporated this filter into my model as a separate RC pre-filter.
This arrangement can adequately describe simple strat type pickups, but the single step or shelving filter is not sufficient to describe other pickups. You will soon find that it can't match the detail of the rise to the peak, nor can it describe the ultimate rate of fall after the peak. Remember that in this simple model, the time constant Leddy /Reddy is already fixed by the need to match the output impedance.
Arthur
Thanks for the explanation. I might have missed it if you explained it before, but do you happen to know or have an idea why the actual slope, or detail, of pickups with steel parts doesn't conform to the three coil model? If the eddy currents are analogous to a transformer and a resistor, is it because there are numerous, independent steel parts each causing eddy currents, leading to a model with many "eddy coils"? |
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Post by Yogi B on Sept 22, 2019 23:49:30 GMT -5
My model and the Tucson one are equivalent to the extent that the Tucson model includes a low pass step in the response caused by the summing of two K couplings to the coil - directly and via the eddy current loop. I considered that model to be difficult to visualise, so I separated the step out into a simple pre-filter. I also discovered that a single step is not generally sufficient to describe real pickups. For god knows what reason, I've had this rattling around my head today. With models based around the coupling of coils, I also find it difficult to intuit what effect changing the various parameters will have. However, I'll also say that your separated pre-filtering, to me, seems a bit overly complicated, in addition I'm not convinced by its use of VCVSes -- to me it feels like cheating 😜.
As noted previously, the key difference between the 'normal' 6-part model and both your model, Tucson's model, and what is apparent in the measured data is the additional 6dB/octave roll off after the peak. While, as JohnH has shown the 6-part model can get close in terms of magnitude up to about 10kHz, after which the difference in roll off becomes significant, but the phase starts diverging from the measurements a while before that point. Also while the output plot is damn close, I think the matching of the impedance could be closer overall. For Reference here's a comparison plot of John's values for the 6-part model (orange) vs. the measured pickup data (red), first voltage output: 
and then impedance: 
In order to combat the difference between the 2nd order filters of the 3 and 6 part models and the apparent 3rd order filter, we need to add another (1 st order) LPF. So, using the the 6-part model as a base, because I find pretty intuitive to hand-tweak in order to match curves, I set about trying to modify it to include another LPF with as few additions as possible. The result is as follows: 
(I've split the primary inductance of the 6-part model in half and added a new resistor from that tap point to ground) Why split the inductor into exact halves? I have no clever scientific insight, it just seemed appropriate as we're modelling a humbucker. I haven't done a great deal of testing, but it seems as though this choice is somewhat arbitrary as similar results can be had by adjusting the values of the other components to compensate. If you want to run the above in LTspice, here's the sub-circuit: .subckt tapped6part POS NEG
.param V = 1
.param resDC=7k688 resD=140k resL=1100k resT=140k
.param ind1=4.7 indD=11
.param capP=130p
; calculate value for R1
.param _resP = 1/(1/resD + 1/resL)
.param _res1 = 1/(1/resDC - 1/_resP)
; offset to 0dB @ 0Hz
V1 N001 NEG AC {V * (_res1 + _resP) / _resP} Rser=1m
L1 N001 N002 {ind1 / 2}
R_tap N002 NEG {resT}
L2 N002 POS {ind1 / 2} RSer={_res1}
L_damp POS NEG {indD} RSer={resD} CPar={capP} RPar={resL}
.ends
So what does that actually look like? Well, below are a couple of comparison plots, first showing the output, then the impedance. For each there's a standard plots looking at the overall shape and, because they're so close, a plot of the models as a ratio to the measured data (i.e. the closer to 0dB & 0° the better), to better illustrate their difference. Arthur's model is shown in blue, mine in green, and as before the measured data is in red. |
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Post by aquin43 on Sept 23, 2019 6:11:55 GMT -5
Hello, Yogi B,
My simple idea of a pickup is an inductor and resistor in series with a capacitor to ground. A voltage is induced in the inductor by the magnetic field of the string. The generator of this voltage is in series with the inductor and resistor. There are two extra factors. First, the inductance and resistance vary with frequency and second, there is a frequency dependence in the path from the string to the induced voltage. The frequency dependence of the path from the string can be assumed to be independent of any loading on the pickup. The interaction of the inductance, the capacitance and any load produces its own frequency response. The two frequency responses are in cascade.
This is why I model the pickup with only series blocks and also separate the magnetic path frequency response from the inductor/capacitor one. When the pickup is loaded, only the second, coil derived, contribution to the frequency response will change.
Thus, the ideal modelling procedure would be to first get the pickup impedance correct, which will ensure correct response to loading and then to adjust the filter representing the magnetic path to make the overall response correct. This simplifies the problem by separating the two matches. It also mirrors the separation of much of the forward path frequency response from the impedance, particularly in pickups that contain lots of iron and shielding covers.
It is possible to model the inductor that varies with frequency by splitting the low frequency inductor into parts which then have resistors placed in parallel with them. For many pickups, a single split is sufficient but some, notably humbuckers, would benefit from an extra split. In the case of a single split, the impedance result can be shown to be equivalent to placing a resistor across a coil which is less than unity coupled to the pickup coil. Such an arrangement also contributes to the magnetic path frequency response. This is the essence of the Tucson model.
I have found that most pickups can be modelled tolerably well using a single coil split, two low pass steps and a low pass roll off. One of the low pass steps is related to the step response of the split coil. Not all pickups need the full armoury of filters. I particular, strat type pickups seem to need only the single low pass step locked to the coil split.
Separating the filter sections by VCVS buffers eliminates the interaction between the filter elements, very much simplifying calculations.
The model itself consists of a Spice subcircuit containing only the essential elements.
Arthur
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Post by JohnH on Sept 23, 2019 16:43:32 GMT -5
Yogi's pickup model has 8 components, but since the main inductor is in 2 equal parts, it has just 7 variables So with one extra variable beyond my 6 part model, it should be able to achieve better accuracy, and indeed it does. So that extra component is pulling its weight effectively!
I like these purely RLC versions of a model because they are very easy to set up all the maths explicitly in a spreasheet, matlab script or code, and hence customise processing of results, run multiple scenarios optimize, goal-seek etc, without relying on a Spice model.
But, Im curious about, without going to that 7th variable, is there a better 6 variable version? The key move that Yogi made was to split the main coil. Could that assumption with its resistor at the tap, allow another component such as Rload to be omitted? the remaining parts to be adjusted for best fit.
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Post by aquin43 on Sept 24, 2019 4:10:43 GMT -5
The difficulty I have with the six part model is that the impedance and the frequency response are intimately connected. Once you have optimised the impedance, you are forced to accept the frequency response that the network produces, or vice versa. A fair number of real pickups do behave like that but many have extra losses in the forward path that are not reflected in the measured impedance. Also, I just find it easier to visualise the simple series L, parallel C with the separate forward losses.
The spice subcircuit is just one way of expressing the result. It is perfectly possible to write equations for the impedance and frequency response that are hardly more complex than those for the six part model. The pre filter is defined purely in terms of the roll off frequencies and step depths (or poles and zeros). The VCVS isolators between the sections of the pre-filter in the subcircuit are introduced so that the individual sections do not load each other thus simplifying calculations in specifying the spice components.
Arthur
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Post by Yogi B on Nov 8, 2021 0:42:40 GMT -5
You spotted that in this particular case of unity coupling, the coupled coil is redundant. In fact, I have just noticed that it can always be eliminated. There is a simple equivalent circuit with two inductors which I think makes the circuit more intuitive:  Not sure this is the best place to reply, but I thought I'd give a heads-up of something to watch out for when eliminating coupled inductors in LTSpice — from the manual:That extra 1mΩ can be significant when working, for example, with TeleTuscon's model where the given value for R eddy is 340μΩ. I wasn't doubting my sanity, having just been bitten by this, honestly  . |
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(yes, I proposed Lstr->Leddy)
.