Will require an external +/-15V DC power supply.
All parts available from Mouser
except the TKD main potentiometer.
There are switches that allow to choose between standard mode and Vinyltrak mode. And between "with diamond buffer" and without (I don't know the reason for that extra circuitry - I bypassed it myself).
I would love to get the gerbers and maybe also the BoM. Can you post here or should I send PM?
Cheers.
Cheers.
Hi Bob,
thank you!
May I ask you the reason for the diamond buffer when it is going straight to an opamp input?
Many thanks,
jb
Hi all,
here are the design files
(schematics (untouched apart from the configuration switches), assembly drawing, gerbers)
Let me know if you build it!
jb
here are the design files
(schematics (untouched apart from the configuration switches), assembly drawing, gerbers)
Let me know if you build it!
jb
Thanks jb,
does your design skip the vinyltrak mode circuitry? Also, any matching of transistors or other components required?
does your design skip the vinyltrak mode circuitry? Also, any matching of transistors or other components required?
Hi,
It is all optionnal : you can bypass it or not.
Same for the diamond buffer: you can have it in the pass or not.
Using configuration switches. You may want to hard wire the configuration you want (these are switches I had in the lab : I don't have a part number fo it).
The assembly drawing (PDF) should make clear how to configure the switches.
Matching transistors is not required: the LSK489 does the important job there itself.
Don't hesitate if you have mre questions,
jb
It is all optionnal : you can bypass it or not.
Same for the diamond buffer: you can have it in the pass or not.
Using configuration switches. You may want to hard wire the configuration you want (these are switches I had in the lab : I don't have a part number fo it).
The assembly drawing (PDF) should make clear how to configure the switches.
Matching transistors is not required: the LSK489 does the important job there itself.
Don't hesitate if you have mre questions,
jb
Hi all,
very interesting reading related to this:
https://dadaelectronics.com.au/doc/Audio/RIAA/MM Paper.pdf
jb
very interesting reading related to this:
https://dadaelectronics.com.au/doc/Audio/RIAA/MM Paper.pdf
jb
Thank you for posting this link. It is an interesting paper and has some good material and merit. I like the fact that the author made a convincing argument that the coupling between the cantilever bahavior and the generator is insignificant. This greatly simplifies matters of analysis.
However, the author missed the point of damped cartridge loading as described in my VinylTrak MM preamplifier.
The point of damped cartridge loading is NOT to replace the 75 uS (T3) loading that is part of the RIAA network by loading the cartridge. This missed point led to the author's conclusion that damped cartridge loading had little value. It is called damped cartridge loading for a reason. The idea is to damp the resonance formed by the cartridge and the capacitive load formed by the interconnect and input circuit of the preamp.
That resonance in a normal arrangement is part of the way that a flatter frequency response is achieved. However, that resonance results in a sharp rolloff at high frequencies, usually before 20 kHz is reached. The normal 47k cartridge load is not enough of a load to damp this resonance's peak, and that peak is normally used to keep the cartridge response reasonably flat up to the resonance frequency - but then the frequency response crashes.
With damped cartridge loading, the objective is to damp the resonance only to the point where the rolloff is essentially first order. This is significantly lighter loading than is needed to form a 75 us time constant with the cartridge inductance. This light loading does not result in any significant attenuation against the cartridge resistance, and therefore results in little flat attenuation, and virtually no reduction in net SNR.
The end result of properly-applied damped cartridge loading is the creation of what is essentially a first-order pole, often in the 8 kHz region. The 75-us pole in the RIAA equalization network is NOT thrown away or disabled. Instead, the 75 us network is given a zero at the frequency where the damped rolloff begins (e.g., in the vicinity of 8 kHz). Put another way, the 75-us 6 dB/octave rolloff is stopped at that higher frequency, thus obtaining a flat response.
Cheers,
Bob
However, the author missed the point of damped cartridge loading as described in my VinylTrak MM preamplifier.
The point of damped cartridge loading is NOT to replace the 75 uS (T3) loading that is part of the RIAA network by loading the cartridge. This missed point led to the author's conclusion that damped cartridge loading had little value. It is called damped cartridge loading for a reason. The idea is to damp the resonance formed by the cartridge and the capacitive load formed by the interconnect and input circuit of the preamp.
That resonance in a normal arrangement is part of the way that a flatter frequency response is achieved. However, that resonance results in a sharp rolloff at high frequencies, usually before 20 kHz is reached. The normal 47k cartridge load is not enough of a load to damp this resonance's peak, and that peak is normally used to keep the cartridge response reasonably flat up to the resonance frequency - but then the frequency response crashes.
With damped cartridge loading, the objective is to damp the resonance only to the point where the rolloff is essentially first order. This is significantly lighter loading than is needed to form a 75 us time constant with the cartridge inductance. This light loading does not result in any significant attenuation against the cartridge resistance, and therefore results in little flat attenuation, and virtually no reduction in net SNR.
The end result of properly-applied damped cartridge loading is the creation of what is essentially a first-order pole, often in the 8 kHz region. The 75-us pole in the RIAA equalization network is NOT thrown away or disabled. Instead, the 75 us network is given a zero at the frequency where the damped rolloff begins (e.g., in the vicinity of 8 kHz). Put another way, the 75-us 6 dB/octave rolloff is stopped at that higher frequency, thus obtaining a flat response.
Cheers,
Bob
Hi Bob,
Thx for your input, and nice to be in direct contact with you.
However to my opinion, designing an alternative for Cartridge loading without knowing the FR of the Cartridge as a whole, may lead to results that are not in line with the expectation.
In my paper I have shown that the model that van Raalte but also van Maanen where using was wrong.
In the Linear Audio article describing the Vinyltrak, an extension of the electrical response is shown in fig 5, but the expectation that damping extends the FR is based on a overly simplified RLC model.
You add to that justifiably that the contribution of the cantilever resonance is not added, which by the way is more than just resonance, but not having taken the complete mechanical part into the equation, may skew the results even further.
By using in my posting a loading that completely eliminates the 75usec pole, was just to bring the damping issue even further than the ca. 8kHz that was used for the Vinyltrak, to amplify the effect of damping even further.
Better than using words, to get this misunderstanding out of the way, I will do a few simulations with several MM Carts damped with a 8Khz loading and show the effect on FR and on rolloff behavior.
Since it´s Christmas time now, I have to spend time with my family, so it may take a few days.
So, in the meantime I wish you a merry Christmas.
Hans
Thx for your input, and nice to be in direct contact with you.
However to my opinion, designing an alternative for Cartridge loading without knowing the FR of the Cartridge as a whole, may lead to results that are not in line with the expectation.
In my paper I have shown that the model that van Raalte but also van Maanen where using was wrong.
In the Linear Audio article describing the Vinyltrak, an extension of the electrical response is shown in fig 5, but the expectation that damping extends the FR is based on a overly simplified RLC model.
You add to that justifiably that the contribution of the cantilever resonance is not added, which by the way is more than just resonance, but not having taken the complete mechanical part into the equation, may skew the results even further.
By using in my posting a loading that completely eliminates the 75usec pole, was just to bring the damping issue even further than the ca. 8kHz that was used for the Vinyltrak, to amplify the effect of damping even further.
Better than using words, to get this misunderstanding out of the way, I will do a few simulations with several MM Carts damped with a 8Khz loading and show the effect on FR and on rolloff behavior.
Since it´s Christmas time now, I have to spend time with my family, so it may take a few days.
So, in the meantime I wish you a merry Christmas.
Hans
Hi Hans,
Thanks for your comments. I think this trading of views will lead to a better understanding of the value of damped cartridge loading, and that is a good thing. You are correct that the RLC model that I used for the cartridge and its conventional loading, e.g., series cartridge inductance followed by shunt capacitance and resistance of its load (conventionally about 200 pf in parallel with 47k) is fairly simple. Your model is more complex, but one question that arizes is to what extent that increased complexity influences the behavior and benefit of damped cartridge loading.
There are 3 forms of investigation in play here. The first is simulation, which is always good for insight and sanity checking. The second is electrical measurement and experiments, such as direct measurement of the cartridge impedance and measurement of cartridge and loading when the cartridge is driven with a signal generator. The third is using a test record and looking at the system frequency response. Each of these approaches has its limitations, but when taken together can help provide an accurate overall picture. As I mentioned earlier, I think that your finding that there is little interaction between the cantilever and generator makes analysis much easier.
One thing I suggest going forward to evaluate damped cartridge loading is to not use the damping to load the cartridge to the point where the cartridge and its loading alone provide the 75 us time constant, but rather use the loading resistance only to the extent that it sifficiently damps the resonance to the point where it results in a response that is reasonably close to a first order rolloff.
Have a Merry Christmas!
Cheers,
Bob
Thanks for your comments. I think this trading of views will lead to a better understanding of the value of damped cartridge loading, and that is a good thing. You are correct that the RLC model that I used for the cartridge and its conventional loading, e.g., series cartridge inductance followed by shunt capacitance and resistance of its load (conventionally about 200 pf in parallel with 47k) is fairly simple. Your model is more complex, but one question that arizes is to what extent that increased complexity influences the behavior and benefit of damped cartridge loading.
There are 3 forms of investigation in play here. The first is simulation, which is always good for insight and sanity checking. The second is electrical measurement and experiments, such as direct measurement of the cartridge impedance and measurement of cartridge and loading when the cartridge is driven with a signal generator. The third is using a test record and looking at the system frequency response. Each of these approaches has its limitations, but when taken together can help provide an accurate overall picture. As I mentioned earlier, I think that your finding that there is little interaction between the cantilever and generator makes analysis much easier.
One thing I suggest going forward to evaluate damped cartridge loading is to not use the damping to load the cartridge to the point where the cartridge and its loading alone provide the 75 us time constant, but rather use the loading resistance only to the extent that it sifficiently damps the resonance to the point where it results in a response that is reasonably close to a first order rolloff.
Have a Merry Christmas!
Cheers,
Bob
Bob,
For replying to your posting, I used an AT150 with ATN152 Cantilever, having a comparable nominal inductance and tip resonance as the V15 that was mentioned in your article in Linear Audio.
But since the VinylTrak damping option was not just meant for a V15 type V, this AT150 may be considered a good test vehicle for examining the effect of loading with a 8kHz pole.
Just to resume, this Cart amongst many others was first measured in greatest detail, it’s electrical part translated into a replacement circuit having a frequency response FR1, the Cart’s overall frequency response FR2 recorded from a calibrated test disk, while using a calibrated load termination, enabling to make a replacement model for the mechanical part with transfer FR3, constructed from FR2 minus FR1 including the exact same load termination as during recording.
Even the disk speed and position on the disk, having their effect on response, were taken into account,
With the complete replacement model, FR1 and FR3 in succession, various capacitive and resistive loads where simulated and successively compared versus the recorded response with exact identical resistive and capacitive loadings.
The outcome was that the constructed model could give a perfect prediction of the real recordings.
So far for explaining how each Cart model was meticulously validated.
Now for the AT150 with 360mH nominal inductance and 665Ohm internal resistance, inserting a 8Khz or 19.9usec damping for this 360mH cart results in an external load of:
360mH/19.9usec minus 665R = 17K4
Simulating with the standard 47K and with this external damping of 17K4 while corrected for the 19.9usec pole resulted in the image below, this after normalizing all levels at 1Khz.
As a general experience during validating Cart’s, reducing the Cart’s load, while at the same correcting for the additionally created pole, always resulted in a strong rise at the upper frequency range.
This is no different in this case with the AT150 where a 3dB peak at 20Khz becomes visible.
To reduce this peak somewhat, a higher load capacity could be inserted, in this case 540pF just as an example to learn what impact this has.
This higher capacity made the peak drop from 3.0dB@20Khz to 2.4dB@14Khz, but at the cost of worsening the FR’s flatness that went originally up to almost 10Khz, now reduced to a much lower 2Khz.
So, in both cases the 8Khz damping with either 100pF or 560pF did not give any improvement. For that reason I repeated the previous simulation, but now added the frequency response when just using the simple model with 360mH plus 665R series resistance, loaded with the 17k4 damped pole // to 100pF like fig 4 in the VinylTrak article.
The result is visible in the image below, two curves that where already shown, but now added with the simple model’s frequency response in teal and the conventional EQ still in red.
Quite obvious is that this simple model deviates largely from reality and is therefore quite misleading indeed.
To conclude:
Did I completely miss the point of loading with a 8Khz pole ?
I think the above results speak for themselves.
That damping completely eliminates the electrical resonance resulting in a first order rolloff does not live up to the expectations.
Here the advantage of having a validated prediction model made this quite obvious.
So it’s better to stay with the 47K load that was originally selected by the Cart’s manufacturer, but finding the best fitting load capacity to get the optimal FR should be the way to go.
For completeness I have added the LTSpice models.
Hans
For replying to your posting, I used an AT150 with ATN152 Cantilever, having a comparable nominal inductance and tip resonance as the V15 that was mentioned in your article in Linear Audio.
But since the VinylTrak damping option was not just meant for a V15 type V, this AT150 may be considered a good test vehicle for examining the effect of loading with a 8kHz pole.
Just to resume, this Cart amongst many others was first measured in greatest detail, it’s electrical part translated into a replacement circuit having a frequency response FR1, the Cart’s overall frequency response FR2 recorded from a calibrated test disk, while using a calibrated load termination, enabling to make a replacement model for the mechanical part with transfer FR3, constructed from FR2 minus FR1 including the exact same load termination as during recording.
Even the disk speed and position on the disk, having their effect on response, were taken into account,
With the complete replacement model, FR1 and FR3 in succession, various capacitive and resistive loads where simulated and successively compared versus the recorded response with exact identical resistive and capacitive loadings.
The outcome was that the constructed model could give a perfect prediction of the real recordings.
So far for explaining how each Cart model was meticulously validated.
Now for the AT150 with 360mH nominal inductance and 665Ohm internal resistance, inserting a 8Khz or 19.9usec damping for this 360mH cart results in an external load of:
360mH/19.9usec minus 665R = 17K4
Simulating with the standard 47K and with this external damping of 17K4 while corrected for the 19.9usec pole resulted in the image below, this after normalizing all levels at 1Khz.
As a general experience during validating Cart’s, reducing the Cart’s load, while at the same correcting for the additionally created pole, always resulted in a strong rise at the upper frequency range.
This is no different in this case with the AT150 where a 3dB peak at 20Khz becomes visible.
To reduce this peak somewhat, a higher load capacity could be inserted, in this case 540pF just as an example to learn what impact this has.
This higher capacity made the peak drop from 3.0dB@20Khz to 2.4dB@14Khz, but at the cost of worsening the FR’s flatness that went originally up to almost 10Khz, now reduced to a much lower 2Khz.
So, in both cases the 8Khz damping with either 100pF or 560pF did not give any improvement. For that reason I repeated the previous simulation, but now added the frequency response when just using the simple model with 360mH plus 665R series resistance, loaded with the 17k4 damped pole // to 100pF like fig 4 in the VinylTrak article.
The result is visible in the image below, two curves that where already shown, but now added with the simple model’s frequency response in teal and the conventional EQ still in red.
Quite obvious is that this simple model deviates largely from reality and is therefore quite misleading indeed.
To conclude:
Did I completely miss the point of loading with a 8Khz pole ?
I think the above results speak for themselves.
That damping completely eliminates the electrical resonance resulting in a first order rolloff does not live up to the expectations.
Here the advantage of having a validated prediction model made this quite obvious.
So it’s better to stay with the 47K load that was originally selected by the Cart’s manufacturer, but finding the best fitting load capacity to get the optimal FR should be the way to go.
For completeness I have added the LTSpice models.
Hans
It seems peaking in the upper octave of 1-2 dB is a perennial problem with vinyl and a lot of work over the years has gone into trying to find a solution. But the exact amount of peaking and frequency vary considerably and most users will not have a handle on this for their particular setup unless they have access to a test record and a sound card or scope. For the most part, 1-2 dB isn’t a train crash, since there isn’t much music energy above 12 kHz, although clicks and pops energy may be significant.
On my X-Altra MC/MM design I offer switchable lower loading resistance than the normal 47k to partially address the HF peaking. It’s not a perfect solution, but does provide some mitigation. An alternative may be to just provide a switchable LP filter where the cutoff frequency can be set along with the attenuation (1-3 dB). I suspect the cutoff frequency would be > 20 kHz since you really only need a very gentle slope. Something that requires some LTspice investigation.
YMMV
😊
On my X-Altra MC/MM design I offer switchable lower loading resistance than the normal 47k to partially address the HF peaking. It’s not a perfect solution, but does provide some mitigation. An alternative may be to just provide a switchable LP filter where the cutoff frequency can be set along with the attenuation (1-3 dB). I suspect the cutoff frequency would be > 20 kHz since you really only need a very gentle slope. Something that requires some LTspice investigation.
YMMV
😊
Hello Hans,
Thank you for your detailed response regarding conventional cartridge loading versus damped cartridge loading. I have read your paper and your response carefully and still find that we disagree, and think that your findings wrongly discounted damped cartridge loading of the kind that I advocated. I believe that your analysis is flawed in at least two ways.
The first problem has to do with how you simply use cartridge impedance to predict cartridge generator response, overlooking an important aspect of how pole piece eddy current affects both impedance and response. The second problem is a result of combining cantilever response with generator response. The third problem arises when you try to compensate for cantilever response by adding capacitance to the cartridge loading in the case of damped loading and apparently not conventional loading (as I deduce from your simulation schematic), resulting in an apples-to-oranges evaluation of the two techniques.
Your cartridge generator model appears to be reasonably correct in modeling the impedance of the cartridge. The falling effective inductance of the cartridge as frequency increases in your impedance curve is something that I and others have observed before, and your model of the generator appears to follow that.
However, nowhere do you mention the cause of this as being due to eddy effect losses created in the pole pieces. These losses are reflected in the resistances that shunt 3 of the inductors in your generator model, but the way you use your impedance model to predict cartridge frequency response does not properly take these eddy current losses into account. These losses in reality decrease response in the higher frequency regions, as naturally one would expect. While the lossy resistances you put in your model correctly reduce the Q of the affected inductances, they actually increase the transmission rather than decrease it as they should.
Simulating cartridge generator frequency response by simply placing an accurate impedance model in series between a voltage source and the cartridge load does not properly account for the eddy current losses. Those shunt resistors enhance the transmission through the network when in fact their effect in the real-world cartridge generator is to exert a loss due to decreased magnetic flux impinging on the coils, reducing EMF generation.
I see that you did not reference Rod Elliot's excellent MM cartridge modeling discussion, so I must assume that you are not familiar with it. It is titled "Magnetic Phono Pickup Cartridges" and can be found at https://sound-au.com/articles/cartridge-loading.html. In it, he describes the imperfect inductance of a moving magnet cartridge that is subjected to the pole piece eddy current losses. His cartridge generator model is a split-inductor model that employs 2 inductors in series, one of which is ideal (L1) and one of which (L2) is shunted by a resistor (I'll call Rs) to take account of the eddy current losses. He refers to this second inductor L2 paralleled by a resistance Rs a semi-inductor. The presnce of the semi-inductor in the model accounts for the fact that the effective cartridge inductance falls with increasing frequency; this is not unlike your cartridge impedance model. His model is actually a bit simpler than yours, but it does the job. It is obviously more complex than my simple model that many others use as well. The shunting effect of the loss resistors responsible for the lost inductance at high frequencies will cause an unrealistic loss of attenuation when the resulting model is used to model cartridge frequency response when one end of the cartridge impedance is simply fed with the test voltage source.
He states, importantly, "Don't expect the slight loss of inductance at high frequencies to cause reduced attenuation at high frequencies - the signal amplitude will also fall as the losses increase. This too can be modelled, but to do so requires a great deal more complexity in the model, and it can't be verified by any sensible (i.e. non-destructive) test methodology that I can think of."
The key here is that the open-circuit generator EMF comes from the coil itself and is actually attenuated by the loss resistor in the model. This is not taken into account when the frequency response is evaluated by just putting the cartridge impedance in series and then shunted by the cartridge load. Indeed, one can argue that the test source should be placed directly in series with the inductance itself to properly take account of the signal loss resulting from the eddy current. Alas, it is a bit more complicated than this because signal EMF also originates with the ideal inductance part of the model.
The bottom line here is that the simple approach of putting the decreasing impedance in series with the cartridge load results in a loss of high-frequency attenuation that is not there in the real world because eddy current losses have not been properly taken into account.
Alternatively, you can continue to model the generator response the way you have, but also include in series with the test voltage source a transfer function that models the loss function created by the eddy current. The eddy currents flowing create a magnetic field that opposes the magnetic flux incident on the coil, resulting in a net reduction in the magnetic flux that creates the EMF in the coil. This effect is frequency-dependent and must be taken into account.
The simple model that just uses only an ideal inductance does not create this unrealistic boost in high-frequency response, but still lacks as much accuracy as we would desire in representing the effects of eddy current on real-world cartridge frequency response. The inductance-shunting resistors in your model create an increase in high-frequency response that tends to be opposed by the eddy current losses that increase with frequency, so their absence in the simple model does not create as much error as one might think.
The second problem in your approach has to do with your combining of the cantilever frequency response with the generator response when comparing the conventional EQ approach with the damped loading approach. It simply adds confusion and invites additional error in interpretation of results. The presence of the cantilever peaking has nothing to do with whether conventional EQ or damped EQ is better; it is there in both cases and is the same in both cases, since you admirably proved that there is no interaction between cantilever and generator. It is a separate issue to both.
Moreover, to try to mitigate cantilever peaking by adding capacitance in shunt with the cartridge output further confuses matters and is a fool's errand. In fact, it even appears that you tried to mitigate cantilever peaking that way with the damped EQ approach while not doing so with the conventional EQ approach, making for an apples-to-oranges comparison.
Finally, as you show, the damped EQ approach increases flat bandwidth as compared to conventional EQ that falls off in the vicinity of 20 kHz. This difference in amplitude at 20 kHz is why you conclude that damped EQ creates or exacerbates high-frequency peaking - it lacks the loss at 20 kHz that conventional EQ has.
I applaud your work for diligently showing that there is no interaction between cantilever and generator, and for your attempt to take into account cantilever response in the whole of the cartridge frequency response, but I think your conclusion that damped cartridge loading has nothing to offer is wrong.
Cheers,
Bob
Bob,
I´m rather disappointed in your analysis.
You keep talking about eddy currents as the reason why my models are incomplete or even wrong, thereby completely negating the fact that the models are validated against real recordings, all the time resulting in perfect matches.
You also overlook the fact that the generators where modelled after having tested them with a large spread of voltages, not giving significant impedance differences that would have occurred when eddy currents would have given a significant impact.
So, no eddy current problems whatsoever seem to introduce complications of any significance in this, resulting in overall models as accurate as the can be.
Have a look look at the huge spread in load from 48k5 to 7k1 in the image below as an example.
When eddy current would have played an important role, it would have become visible.
To criticize the attempt of trying an extra capacity when the applied 8Khz damping doesn´t bring the predicted results, and to call this a fools errand or apples to oranges is rather illustrative for your attempts to defend the damping theory with just words but without physical prove of any kind of a recording from a validated recording chain without and with damping.
That would lead to the constructive discussion it should be in the first place, a discussion for which I´m open.
So I´m looking forward to continue this discussion when real facts from recordings are available from your side.
Hans
I´m rather disappointed in your analysis.
You keep talking about eddy currents as the reason why my models are incomplete or even wrong, thereby completely negating the fact that the models are validated against real recordings, all the time resulting in perfect matches.
You also overlook the fact that the generators where modelled after having tested them with a large spread of voltages, not giving significant impedance differences that would have occurred when eddy currents would have given a significant impact.
So, no eddy current problems whatsoever seem to introduce complications of any significance in this, resulting in overall models as accurate as the can be.
Have a look look at the huge spread in load from 48k5 to 7k1 in the image below as an example.
When eddy current would have played an important role, it would have become visible.
To criticize the attempt of trying an extra capacity when the applied 8Khz damping doesn´t bring the predicted results, and to call this a fools errand or apples to oranges is rather illustrative for your attempts to defend the damping theory with just words but without physical prove of any kind of a recording from a validated recording chain without and with damping.
That would lead to the constructive discussion it should be in the first place, a discussion for which I´m open.
So I´m looking forward to continue this discussion when real facts from recordings are available from your side.
Hans
P.S. Just to add to the above, eddy currents contributing in a significant way may well be the reason why in the models the overall inductance had to be split over several sections, thereby fully including their impact.
Hans
Hans
Hans & Bob: Thanks for such an agreeable disagreement! Educational (at least for me) and role-model worthy for other discussions elsewhere on the site.
👍
👍
Hi Hans,
I'm sorry that my reply had been so long, and perhaps some of my points were unclear or misinterpreted in the clutter. I'll take a look more closely when I get a chance and give a longer reply. In the meantime, please read Rod Elliot's piece that I referred to if you have not already. Please also take another look at my lenthy response.
Briefy, however, I did not intend to say that your model was wrong or did not include effects due to eddy current. The resistors that you put in parallel with your 3 coils do take account of eddy current in causing the generator model to have decreasing impedance with frequency. As far as I know, you models are correct in modeling the effect of eddy currents on the impedance.
I'm just saying that the way that you used your generator impedance models in your simulations did not take account of the eddy current losses in signal as frequency increases that occur. My comments in that regard are based on theory and what Rod Elliott said.
I do understand that it can be difficult to separate things out, given the presence of cantilever response in a real cartridge.
Best regards,
Bob