A new model.

[aquin43]

I have been playing about with the mutually coupled eddy current losses idea and I tried to fit the model to a Seymour Duncan Phat Cat bridge pickup. This is a metal cased supposed P90 replacement in a standard hum bucker case.

The idea was to match the output impedance and Q at several frequencies.

In the end, I matched peak impedance unloaded and loaded with 10n and corrected the excess overshoot of the resulting model with the pre-filter. The pre-filter represents the screening effect of the case plus the eddy current losses which add up to a downward step in the frequency response. The model assumes that the velocity excitation by the string has been integrated for a more intuitive response curve.

The way the model works is that, as the frequency rises, the inductance falls and the series resistance rises, due to the mutually coupled loop. We can thus model the way that the impedance and Q vary with frequency without introducing external damping elements. Indeed, the principal virtue of this model is that it has close to the correct output impedance.

The choice of a unity coupled coil equal to the main coil is arbitrary and makes the calculations easier. In the real case the parasitic inductance will be very small and the resistance correspondingly so. What I have done here, in effect, is to introduce a virtual ideal transformer coupling the actual loss loop to the main coil.

Arthur

[JohnH]

Very interesting! can you explain a bit more about how this LTSpice model works? I use a different Spice software. What is the component E1 doing? and if there is a change in inductance or resistance values with frequency, what are the parameters? Is the transformer assumed to be a perfect one?

It would be great to take one known and tested, pickup, do output tests as Antigua and others have done, test impedance and phase vs frequency, then put all that up against the best model equivalents with this, and with 3, 4 and 6 part fixed models.

[aquin43]

Hello JohnH,

For a circuit as simple as this all Spices are the same.

The netlist is:

Phatcat Bridge
Lc N002 N003 3.83
C1 out 0 200p
R1 out N003 8.6k
R3 N001 0 350k
Le N001 0 3.83
V1 string-int 0 AC 1
E1 N002 0 N004 0 1
R5 N005 0 2k
R4 N004 string-int 10k
C2 N004 N005 3.6n
.ac dec 500 80 20k
K1 Lc Le 1
.end

E1 is a standard spice voltage controlled voltage source which acts as a unity gain buffer between the pre-filter and the main coil model.

The two coils represent the pickup coil and a conveniently scaled version of the eddy current loop, coupled by the factor K1, which in this case just happens to be one (some versions of Spice will only accept 0.999). The variation of the main coil resistance and inductance with frequency arise naturally from this coupling -  see my contribution to the "higher impedance at lower frequencies" thread.

In the final version of this model, I expect that the most important parameters will be Le, which will determine how far the coil inductance will fall, K1 and R3.

The basic coil parameters for this model were derived from an accurate impedance plot with a 10Meg feed resistor plus computed correction.  Having adjusted R3 to make the unloaded response and that with a 10n load match as closely as possible, the pre-filter was adjusted by hand to reduce the step-response overshoot of the unloaded pickup to the correct level and the final response was compared with the pickup response using an exciter coil followed by computed integration. The step response was determined using a triangle wave into the exciter coil,

Arthur

[ms]

Suppose the coupling K goes to unity and the resistance R3 goes to zero.  This shorts Lc and E1 operates into a divider composed of R1 in series and C1 in shunt.  I think what should happen is that E1 is shorted; that is, the pickup should have no output, just as the pickup would have no output if C1 goes to infinity.

[aquin43]

ms -

The choice of one as the value for k is somewhat unrealistic. This was a quick first attempt and it appeared from the computed impedance plot that the inductance fell to pretty well zero above the resonant frequency so I chose k=1, which allows that. The actual coupling must be quite close to unity in this particular case.

The induction of the signal from the strings is via another magnetic route, part of which is direct and part via an eddy current loop. This gives a response that is diminished at high frequencies in a similar fashion to a simple R-C filter. In the model, this is  a completely separate network that is isolated from the main coil so as not to affect its impedance.

In reality, the filter and the eddy current loop are related and, yes, in extremis a shorted coil will give no output. The reason why this model doesn't cover this is that it models the pickup as it is. The pre-filter values depend on the properties of the pickup as measured; there is no attempt to model the internal dependencies from which the parameters are derived. This is legitimate because the only access we have to the pickup is via its terminals. There is no way we can short just Lc, for example. If we get the value and phase of both the forward response and the output impedance correct, then the pickup is complete, from the electrical point of view.

So, if we want a shorted coil, we would have to change the model values, but if we want to know how the pickup will behave with its terminals shorted, then this model will deliver the correct current into the short. As a matter of interest, a model that puts all of the frequency dependencies into shunt elements would get the short circuit current completely wrong.

Arthur

[JohnH]

Ok Im catching up!, thanks for the explanations. I tried modelling it in 5Spice. I couldn't find/get the E1 component to work, so instead I used a perfect opamp as a x1 buffer. I think that is a valid swap?

Then I plotted output from the model, and it certainly looks credible. The pre-input filtering does bring the peak down, and so does the damping component.


The model below replicates your diagram, and then repeats it (from after the buffer) without the transformer and instead using a simple inductor with the damping referred to it directly (which I believe is supported by general transformer theory, but Im not an EE). The results from test points Tv1 and Tv2 are identical (see plot at lower right). so for this model, a transformer is not needed (unless you have some other tricks to add to it later?)

Then, I ran it with extra 470pF and 200k load, as we do around here. Again, the results are credible and the two versions are identical (plot at lower left).





Seems good!

[aquin43]

Yes, your modified circuit is directly equivalent to the original. I am surprised that 5Spice doesn't have the E device, since it is a basic spice element.

Do they perhaps call it a VCVS or something similar? Anyway, the unity gain buffer is an exact equivalent.

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:

So, with tightly coupled loss, the inductance effectively disappears at a high enough frequency, to be replaced by R, but with looser coupling, there is always a residual inductance in series with R.

In the real pickup, the coupling is between the coil and a much smaller inductive loop with a very low resistance. The decision to make the coupled coil equal to the main coil is justified by the fact that the R and L in the eddy current loop can be scaled equally by any amount without altering the impedance of the main a-b branch.

Arthur

[JohnH]

A couple more thoughts and questions:

When you were tuning the prefiltering, how important was the second (grounded) resistor and how does the model interpret the two values listed 5k and 2k? Does it change with frequency? in which case in what range and what basis? Im wondering hiw many independent variables are needed to adequately characterise a pickup with this model. The fewer needed, then the better it is as a concept.

Im thinking that if the main components the other side of the buffer get the impedance and damping right (4 variables currently), then could a single prefiltering variable defining the corner frequency of a simple low-pass (RC like, -6db per ictave) filter provide the rest of the shaping? Depending on this frequency, it could be set to have little effect (alnico single), carve rhe rising slope of a resonanr peak (most hb's), or by setting it lower, provide the mid-dip and low peak that we see in some covered pickups. That would just be 5 varaiables.

[perfboardpatcher]

I can only express myself in layman's terms. But to me it seems that there is the power plant, which consists of the magnet, iron core, the strings and the person who plucks the strings. Unfortunately the power plant isn't perfect, energy is dissipated (eddy current loss). The pickup coil isn't the cause of the losses but as sensor it will detect less (signal) because what has been lost before can not be detected. (Also the losses have to catch the eye, if the losses were equal across the frequency range, how would you notice!)

There must be something similar going on for the Q of the resonance peak of the pickup. At least when I create a fake pickup configuration with a signal generator and a guitar pickup acting as R and L - & yes I know there is also a C! - together with a resistor and cap then the Q is higher then when measuring with the excitation coil.

The way I see it you need to select the excitation coil instead of the guitar coil if you want to simulate the eddy current losses.

Cheers,
PP

[aquin43]

Nov 25, 2018 15:31:18 GMT -5 JohnH said:

A couple more thoughts and questions:

When you were tuning the prefiltering, how important was the second (grounded) resistor and how does the model interpret the two values listed 5k and 2k? Does it change with frequency? in which case in what range and what basis? Im wondering hiw many independent variables are needed to adequately characterise a pickup with this model. The fewer needed, then the better it is as a concept.

Im thinking that if the main components the other side of the buffer get the impedance and damping right (4 variables currently), then could a single prefiltering variable defining the corner frequency of a simple low-pass (RC like, -6db per ictave) filter provide the rest of the shaping? Depending on this frequency, it could be set to have little effect (alnico single), carve rhe rising slope of a resonanr peak (most hb's), or by setting it lower, provide the mid-dip and low peak that we see in some covered pickups. That would just be 5 varaiables.

The pre-filter is a simple step that begins to roll off at w = 1/(2*pi*C*(Rin+Rgnd)) and has maximum attenuation of Rgnd/(Rin+Rgnd).

In this case, since the losses appeared high, I made Rgnd small, so we have a deep roll off and I tweaked the capacitor until the model had the same percentage overshoot to a step as the real pickup. Frequency response matching might have been more accurate, but frequency response and step response are equivalent. The impedance level of the filter is unimportant so it is possible to choose a fixed Rin and adjust the other components for the desired effect.

When the real pickup is driven by a step of current through its terminals via a 10M resistor, the ringing is much more extended than when it is driven via the coil exciter, confirming that the intrinsic Q is higher than that seen in the overall frequency response.

In this case, by tweaking the filter capacitor, I was essentially doing what you suggest. Whether this simplification would be valid for lower loss pickups I don't know at this stage.

Of course, a lot of the difference between the pure roll off and the step may occur above resonance, where the accuracy of the model becomes less important.

Arthur

[aquin43]

Nov 25, 2018 15:41:00 GMT -5 perfboardpatcher said:

I can only express myself in layman's terms. But to me it seems that there is the power plant, which consists of the magnet, iron core, the strings and the person who plucks the strings. Unfortunately the power plant isn't perfect, energy is dissipated (eddy current loss). The pickup coil isn't the cause of the losses but as sensor it will detect less (signal) because what has been lost before can not be detected. (Also the losses have to catch the eye, if the losses were equal across the frequency range, how would you notice!)

There must be something similar going on for the Q of the resonance peak of the pickup. At least when I create a fake pickup configuration with a signal generator and a guitar pickup acting as R and L - & yes I know there is also a C! - together with a resistor and cap then the Q is higher then when measuring with the excitation coil.

The way I see it you need to select the excitation coil instead of the guitar coil if you want to simulate the eddy current losses.

Cheers,
PP

The Q of the pickup coil is higher than the Q measured via the exciter because the path from exciter to coil includes a frequency dependent eddy current loss which, here,  is modelled by the pre-filter. The magnetic signal from the strings also passes through this filter. The magnetic signal from the string is represented as the input voltage to the filter. It is presumed that the signal currents in the pickup have no effect at all on the string or the exciter. As I have pointed out in another thread, a properly designed exciter coil is essentially open circuit and it is weakly coupled to the pickup coil.

Of course, the static magnetic field can affect the string, but this is a different matter altogether.

Arthur

[antigua]

I'm not sure what's going on here; but I know there are two types of "models" in general; those which attempt to accurately describe reality, and those which do no represent reality, but pragmatically yield "realistic" results none the less. Is this the former or the later? I hear it described as the former, yet this spice model has a VCVS, so I'm not sure. I see an LtSpice model, but no simulation curves. 

One thing I'd be interested in is curve matching a pickup that shows high eddy losses, and for a known L, C, and series R, calculating the effective series or parallel R, maybe at a given frequency, for a particular pickup, say, a Filter'tron. If we supposed that eddy currents are analogous to a transformer with a resistor across the secondary, it should be possible to figure out what the values would be for that resistance, the mutual inductance, or the coupling coefficient. 

[JohnH]

Nov 26, 2018 12:52:31 GMT -5 antigua said:

I'm not sure what's going on here; but I know there are two types of "models" in general; those which attempt to accurately describe reality, and those which do no represent reality, but pragmatically yield "realistic" results none the less. Is this the former or the later? I hear it described as the former, yet this spice model has a VCVS, so I'm not sure. I see an LtSpice model, but no simulation curves. 

One thing I'd be interested in is curve matching a pickup that shows high eddy losses, and for a known L, C, and series R, calculating the effective series or parallel R, maybe at a given frequency, for a particular pickup, say, a Filter'tron. If we supposed that eddy currents are analogous to a transformer with a resistor across the secondary, it should be possible to figure out what the values would be for that resistance, the mutual inductance, or the coupling coefficient. 

Hi Antigua - this may potentially be a form of model that is both pragmatic and theory based. The example by aquin43 is based on a bridge Phatcat. In my post above I used this to make loaded and unloaded plots. Do you think they look feasible for such a pickup?

The transformer idea seems like a valid theory, and then you can take one more theoretical step and it seems we can eliminate the transformer, so simplifying the model. If this model works well to match other pickups (particularly the tricky filtertron types!), then it may be the next step in this field. Aquin43 has shown how it can go into Spice models, and I could also easily build it in spreadsheets too such as GuitarFreak. Potentially, it has 5 variables, which is one better than the 6 part models that I use and easier to derive.

[perfboardpatcher]

Nov 26, 2018 12:52:31 GMT -5 antigua said:

If we supposed that eddy currents are analogous to a transformer with a resistor across the secondary, ... . 

 No! I say it must be an impedance across the excitation coil. Well it could have been a resistor if the excitation coil was the primary of an ideal transformer.

[antigua]

Nov 26, 2018 13:52:31 GMT -5 JohnH said:

Nov 26, 2018 12:52:31 GMT -5 antigua said:

I'm not sure what's going on here; but I know there are two types of "models" in general; those which attempt to accurately describe reality, and those which do no represent reality, but pragmatically yield "realistic" results none the less. Is this the former or the later? I hear it described as the former, yet this spice model has a VCVS, so I'm not sure. I see an LtSpice model, but no simulation curves. 

One thing I'd be interested in is curve matching a pickup that shows high eddy losses, and for a known L, C, and series R, calculating the effective series or parallel R, maybe at a given frequency, for a particular pickup, say, a Filter'tron. If we supposed that eddy currents are analogous to a transformer with a resistor across the secondary, it should be possible to figure out what the values would be for that resistance, the mutual inductance, or the coupling coefficient. 

Hi Antigua - this may potentially be a form of model that is both pragmatic and theory based. The example by aquin43 is based on a bridge Phatcat. In my post above I used this to make loaded and unloaded plots. Do you think they look feasible for such a pickup?

The transformer idea seems like a valid theory, and then you can take one more theoretical step and it seems we can eliminate the transformer, so simplifying the model. If this model works well to match other pickups (particularly the tricky filtertron types!), then it may be the next step in this field. Aquin43 has shown how it can go into Spice models, and I could also easily build it in spreadsheets too such as GuitarFreak. Potentially, it has 5 variables, which is one better than the 6 part models that I use and easier to derive.

Thanks for the summary. I will do some eddy current testing this week which might provide some useful test data. 

For the Tri Sonic pickups guitarnuts2.proboards.com/thread/8438/burns-sonic-strat-analysis-review there was clearly eddy current losses associated with the cover:



These are the known values:

Burns London Mini Tri-Sonic Neck

- DC Resistance: 8.59K ohms
- Measured L: 0.73H
- Calculated C: 310pF (320 - 10)
- Gauss: 1250G

So if the "without cover" plot can be curve matched assuming no eddy currents, and then the "with cover" plot can be matched with eddies added, it might serve as a demonstration for how the model can yield relative values for eddy losses. 

[perfboardpatcher]

aquin43, I think I understand
You're modeling that part I booked in my worksheet as a parallel resistance under
L_coil / (C_coil+C_cable) * R_coil) * factor to dampen the resonance peak at different resonance frequencies?

[ms]

Let's consider how the physics  tells us to construct a model with eddy current loss.

First consider an air core coil with time varying magnetic flux passing through it from a vibrating string.  Ignore the C, but put an external load ZL across the terminals.

The coil has a resistance R.

The law of magnetic induction says that a voltage is developed around each turn of the coil.  Following the usual practice, we take the many small voltage sources in series and slide them to one end of the coil and replace them with a single source.  A current flows through the coil, the resistance R, and the load.


Now add a steel core to the coil.  The ac current in the coil causes a magnetic field that induces a current around the core.  Assume that the current flows in a thin sheet at the surface of the core.  Thus we can think of the core with its current as the secondary of a transformer.

Normally we apply a voltage to the terminals of the transformer; here we have a load across the terminals and the voltage is generated inside the coil.  But this does not matter: it is the same series circuit.

As with a normal transformer, the secondary load goes across the coil with the R in series.  That is, it is in parallel with the external load ZL.

The model follows directly from this: the R and coil in series make the series leg of a voltage divider, and the secondary load (transformer secondary including poor coupling) is the shunt leg.

We have read that you cannot get the correct output impedance with this model.  That is not true; a direct model based on the physics must give the correct output impedance.

[antigua]

I haven't had a chance to get into the spice model proposed on TDPRI that blamed, and supposedly demonstrated how "the dip" was due to the presence of the exciter coil itself, but supposing that the exciter causes the dip, where as eddy currents merely result in a reduced Q, then I think we've probably correctly modeled eddies in the past with the transformer model, but didn't recognize it for what it was, since we were under the impression that it had to also have "the dip", when in reality "the dip" is quite possibly unrelated. 

[JohnH]

Nov 26, 2018 17:30:17 GMT -5 antigua said:

I haven't had a chance to get into the spice model proposed on TDPRI that blamed, and supposedly demonstrated how "the dip" was due to the presence of the exciter coil itself, but supposing that the exciter causes the dip, where as eddy currents merely result in a reduced Q, then I think we've probably correctly modeled eddies in the past with the transformer model, but didn't recognize it for what it was, since we were under the impression that it had to also have "the dip", when in reality "the dip" is quite possibly unrelated. 

Do you have a link to that TDPRI post? Lets give it some critical assessment!

My expectation would be that similar factors apply to the exciter coil as to a variable flux due to string vibration.

Also, an actual dip is just an extreme version of a family of curves where the rise of the peak towards resonance is pulled down by eddys.

[antigua]

Nov 26, 2018 17:53:34 GMT -5 JohnH said:

Nov 26, 2018 17:30:17 GMT -5 antigua said:

I haven't had a chance to get into the spice model proposed on TDPRI that blamed, and supposedly demonstrated how "the dip" was due to the presence of the exciter coil itself, but supposing that the exciter causes the dip, where as eddy currents merely result in a reduced Q, then I think we've probably correctly modeled eddies in the past with the transformer model, but didn't recognize it for what it was, since we were under the impression that it had to also have "the dip", when in reality "the dip" is quite possibly unrelated. 

Do you have a link to that TDPRI post? Lets give it some critical assessment!

My expectation would be that similar factors apply to the exciter coil as to a variable flux due to string vibration.

Also, an actual dip is just an extreme version of a family of curves where the rise of the peak towards resonance is pulled down by eddys.

It starts about here www.tdpri.com/threads/physically-based-eddy-current-equivalent-circuit.846745/page-3#post-8531564 

If the dip is associated with eddies and not the exciter coil, then we should see the dip with all inductors that have steel parts in their midst, because a pickup is not unique from an inductor otherwise. It should be a somewhat common manifestation in electronics in general, but it seems to me that it's somewhat case specific to this pickup testing involving a second coil. AFAIK the dip was first observed by Lemme, who also used an exciter coil. My testing with the 1 meg resistor has flaws, as noted in the other thread, but so far I haven't observed any dipping in those tests. 

[JohnH]

The TPDRI thread is a good one.

But there's a difference between the model discussed there and the one here above: Above, aquin43's model has a fully buffered seperation between the exciter section and the pickup main and eddy coils. On TPDRI, tele-tuscon's one has three inductively coupled coils.

What do we think? can one be turned into an equivalenr if the other? or is this a fundamental difference?

[aquin43]

Nov 28, 2018 3:16:00 GMT -5 JohnH said:

The TPDRI thread is a good one.

But there's a difference between the model discussed there and the one here above: Above, aquin43's model has a fully buffered seperation between the exciter section and the pickup main and eddy coils. On TPDRI, tele-tuscon's one has three inductively coupled coils.

What do we think? can one be turned into an equivalenr if the other? or is this a fundamental difference?

The two models can be equivalent if the time constants are matched. The sum  of the two forward paths from the exciter to the main coil in the pure inductance model, directly and via the eddy current loop, amounts to a frequency step that I model with the RC pre-filter. My model has an extra degree of freedom in that the exciter time constant can be chosen separately. I am speculating that the magnetic input from the strings can be coupled more strongly than the main coil to other eddy current losses, such as the cover.

If you look closely at the pure inductance model you see that the exciter coil, being driven by a current source, is open circuit. There is, therefore no reverse path because the only way that the exciter coil can interact with the other coils is via a circulating current. So, while the pickup and eddy current coils can induce voltages in the exciter coil, they can't change the current through it. There can, therefore, be no mutual action via the exciter. This was the inspiration for the separation in my model.

It is vital, when making the measurements that the exciter coil is driven via a resistance that is large compared with its reactance at the highest frequency of interest. Otherwise it might interact with the pickup coil and, anyway, there will be a large phase error long before any frequency response error.

The only direct access we have to the pickup coil is via the terminals. The route via the exciter is subject to the unknown eddy current loss so neither amplitude nor phase can be relied upon. This is why I based my modelling process on getting the output impedance correct first and then refining the frequency response with the pre-filter.

I have noticed, also, that in some humbuckers the two coils have different eddy current losses. They are also mutually coupled. Whether this simple model will be able to emulate this with any accuracy is unknown at the moment.

Arthur

[JohnH]

That all sounds good to me. The thing is, your model, with the extra step of converting the eddy secondary into an equivalent load on the primary, is very easy to calculate as well as to model. Once it is accepted that it is a reasonable model arrangement, there are several ways to derive the parameters. You can go via basic testing of impedance phase and transient response (ie, what you have done?), or you can take loaded and unloaded frequency response curves and derive values by matching those, or maybe you could work it all out by pure calculation.

The best demonstration of its merits and limitations would be to work with tested impedances etc and hence derive predicted frequency response outputs, and then work back from tested frequency response outputs to work out the values and so calculate impedances, then compare it all. If it is a good concept then these two directions will correlate to a reasonable extent, and deviate to an acceptable extent. Then given that it is only a model of something more complex, which set of values are best? This would depend on what the model is for. If (as I would use), it is more generating predicted frequency outputs, then I would tweak values to get the best match possible to tests near to its real operating conditions inside a guitar.

[aquin43]

I have written a program that lets me superimpose the modelled impedance on the measured both with and without a 10n load.

I have noticed that with the 10n load the phase response turns towards zero as the frequency rises, instead of staying around -90 degrees. This implies that part of the basic resistance of the pickup is not coupled to the coil capacitance - it seems to be of the order of 10%.

I have added this to the model, so there is another parameter, Rx, which is the fraction of R that is uncoupled.

I haven't done the frequency response measurement yet.

Arthur

[JohnH]

How does that look on an equivalent schematic?

When I make models by fitting to response, I find I need some resistance that bypasses the cap, and the main R adjusted to compensate.

[aquin43]

The circuit is as follows:

and the spice listing, written by the program is:

pickup
R1 in 1 1.0e4
C1 1 2 2.803e-09
R2 2 0 9.775e+03
E1 pref 0 1 0 1
L1a pref 3 3.412e+00
Rp pref 3 1.427e+05
L1b 3 4 1.662e+00
Rl 4 res 8.918e+03
C2 res 0 1.804e-10
Rx res out 8.284e+02

The pre-filter values are OK for the overshoot but will need to be checked when I plot the frequency response.

Arthur

[JohnH]

I see, that Rx position seems credible, since C is distributed through the coil. So it makes sense that if you have to chose one position to lump all of it, its not necessarily right at the far end. So by similar reasoning, should part of the inductance also be outside of C?

I was also thinking about your model in comparison to the 3-winding transformer model by tele-tuscon on tpdri. In that model, signals are induced into the coils of the output side, to get directly loaded by the eddy damping. Yours puts the signal input outside of the coil, so Rp is there for impedance but it may not be responding to the signal in the same way. I think there may be a consequence particularly for a very light load. If you set aside the effect of C and the prefilter, the current model as shown will flat-line with no eddy effect if load is very small. So, im suggesting the signal should perhapa be within the eddy loop, such as if Rp went to ground.

[aquin43]

Actually, Rx seems to have been a mistake. I put it in to account for the 10n loaded phase gradually heading away from -90 at high frequencies but it only seemed to work because I had added the 10n in the wrong position in the netlist. I think that the phase shift must be caused by another low Q resonance, but I have decided that it is not worth modelling because it occurs where the attenuation is high.

Both this and the three coil model buffer the drive voltage from the main coil, in the one case by an explicit VCVS buffer and in the other by driving the exciter coil by a current source. This is in accordance with the assumption that the pickup loading cannot affect the strings.

In my model the drive voltage is applied to L and R instead of just to L. I can try it the other way.

I have found that the simple RC filter is unable to model the frequency response to within 1 dB so I have added another section. This adds to the complexity a little, but the program makes the curve fitting quit easy. The physical justification for the added complexity is that the actual eddy current shielding effect is not a simple roll off but involves the variation of skin depth with frequency and the summation of multiple paths.

The final model comes in the form of a spice subcircuit file where none of the input parameters appears explicitly - a black box, in effect.

Arthur

[ms]

Dec 3, 2018 5:54:22 GMT -5 aquin43 said:

Actually, Rx seems to have been a mistake. I put it in to account for the 10n loaded phase gradually heading away from -90 at high frequencies but it only seemed to work because I had added the 10n in the wrong position in the netlist. I think that the phase shift must be caused by another low Q resonance, but I have decided that it is not worth modelling because it occurs where the attenuation is high.

Both this and the three coil model buffer the drive voltage from the main coil, in the one case by an explicit VCVS buffer and in the other by driving the exciter coil by a current source. This is in accordance with the assumption that the pickup loading cannot affect the strings.

In my model the drive voltage is applied to L and R instead of just to L. I can try it the other way.

I have found that the simple RC filter is unable to model the frequency response to within 1 dB so I have added another section. This adds to the complexity a little, but the program makes the curve fitting quit easy. The physical justification for the added complexity is that the actual eddy current shielding effect is not a simple roll off but involves the variation of skin depth with frequency and the summation of multiple paths.

The final model comes in the form of a spice subcircuit file where none of the input parameters appears explicitly - a black box, in effect.

Arthur

Have you tried putting Rx in series with the C?  It makes sense that the coil capacitance  is lossy since the charge has to go through so much fine wire to be redistributed.  Another possibility is that the eddy current loss is involved.

[ms]

Dec 2, 2018 16:21:23 GMT -5 JohnH said:

should part of the inductance also be outside of C?

Inductance results from the voltage induced around each turn by the changing magnetic flux resulting from the current in each other turn.  Each turn has resistance, and so each induced voltage can cause current to flow only around a path that includes series resistance.