I think that you've raised an important point, that many different groups of values lead to similar simulated impedance curves. This seems to imply that there are a few local minima in the least squares objective function. This may be indicative of the fact that the model is an over-parameterization of the impedance for the Lavoce SAF184.03.
The fact that Rss can tend to a large value if the estimation process is restarted from a given solution is also indicative of the model over-parameterizing the impedance behaviour. When I set Rss = 10,000 ohms, essentially removing it from the circuit, the other component values were adjusted a little, and subsequently, a very good impedance fit was once again obtained.
Keeping in mind that the initial equivalent circuit model proposed by Thorborg and Unruh (JAES, 2008) did not include Rss but still produced good curve fits, then it seems entirely reasonable to set Rss = 10,000 ohms and to remove it from the parameter estimation process.
As you've noted, different estimated values usually produce very similar simulations in the 30–100Hz range, which is your primary range of interest. I also note your observation that, when there is no impedance data below 20Hz, the curve fitter regularly produces values of Re' < Rvc.
You've taken an entirely reasonable approach to set a fixed value of Re' under these circumstances, as otherwise there is nothing to guide the optimizer and keep it on a good estimation path. It's simply the nature of the problem, and one needs to use experience from other simulations to provide some sort of empirical guidance when real data is lacking.
One example of this approach is to set Re' = 1.10Rvc, as per the suggestion of bolserst. Based on some results published by Thorborg and Unruh (JAES, 2008), I'd suggest that it might be more appropriate to use Re' = 1.07Rvc under these circumstances. In any case, a very good curve-fit of the impedance peak of the Lavoce SAF184.03 is obtained when setting Re' = Rvc = 5.8 ohms, and this also carries over into the higher frequency range
However, I am aware that my digitization is of course approximate. Against my best efforts, it seems to me that I may have produced regions of somewhat biased impedance data, which will of course bias the nonlinear optimizer in its search for a solution.
Hence, @DerKalle, are you able to obtain from Lavoce the set of impedance measurements of Lavoce SAF184.03 that were used to produce the impedance curve shown in the datasheet? That would help to get rid of some of the niggling little inaccuracies that are being inadvertently introduced.
The fact that Rss can tend to a large value if the estimation process is restarted from a given solution is also indicative of the model over-parameterizing the impedance behaviour. When I set Rss = 10,000 ohms, essentially removing it from the circuit, the other component values were adjusted a little, and subsequently, a very good impedance fit was once again obtained.
Keeping in mind that the initial equivalent circuit model proposed by Thorborg and Unruh (JAES, 2008) did not include Rss but still produced good curve fits, then it seems entirely reasonable to set Rss = 10,000 ohms and to remove it from the parameter estimation process.
As you've noted, different estimated values usually produce very similar simulations in the 30–100Hz range, which is your primary range of interest. I also note your observation that, when there is no impedance data below 20Hz, the curve fitter regularly produces values of Re' < Rvc.
You've taken an entirely reasonable approach to set a fixed value of Re' under these circumstances, as otherwise there is nothing to guide the optimizer and keep it on a good estimation path. It's simply the nature of the problem, and one needs to use experience from other simulations to provide some sort of empirical guidance when real data is lacking.
One example of this approach is to set Re' = 1.10Rvc, as per the suggestion of bolserst. Based on some results published by Thorborg and Unruh (JAES, 2008), I'd suggest that it might be more appropriate to use Re' = 1.07Rvc under these circumstances. In any case, a very good curve-fit of the impedance peak of the Lavoce SAF184.03 is obtained when setting Re' = Rvc = 5.8 ohms, and this also carries over into the higher frequency range
However, I am aware that my digitization is of course approximate. Against my best efforts, it seems to me that I may have produced regions of somewhat biased impedance data, which will of course bias the nonlinear optimizer in its search for a solution.
Hence, @DerKalle, are you able to obtain from Lavoce the set of impedance measurements of Lavoce SAF184.03 that were used to produce the impedance curve shown in the datasheet? That would help to get rid of some of the niggling little inaccuracies that are being inadvertently introduced.
First of all, thank you very much for your support! Given the good results, we actually only have minor problems that have little impact in practice; the software is already extremely helpful. I think it's great that we still exchange ideas so intensively. If we can improve the software, other users will certainly be happy in the future. I will try to do my part and write to sales to ask whether the data for the original impedance curve is available.
My current approach is to set Re' to Re*1.07 and then start with a very narrow frequency range, e.g. 20-150Hz. This gives me a very good approximation of the measurement curve. Then I increase the range a little at a time until I reach 10k. This has produced the best value for "LS-fit" so far. What makes me a little suspicious are the graphs on the right-hand side. I'm just starting to get a basic understanding of the meaning of the individual parameters, but the curve at Zmotional seems strange to me...?
If I then tick the box to automatically determine Re', I get an even better value for LS-fit - but a Re' lower than Re and an Rss of over 4000.
Is there perhaps something suspicious about LaVoce's impedance curve; are any of the other manufacturer's specifications incorrect or why is the program doing strange things here?
Is there perhaps something suspicious about LaVoce's impedance curve; are any of the other manufacturer's specifications incorrect or why is the program doing strange things here?
The "program doing strange things" seems to be more or less par for the course when running a nonlinear least squares estimation code to solve a complex approximation problem. Most of the issues that have been encountered (e.g., Rss > 4000, and therefore not contributing much to the circuit's impedance response), seem to be a result of the model being an approximation of the true multiphysics of the driver's response.
The generated impedance curve fits are generally a good fit to the data, but the fits obtained with a wide variety of parameters can all be regarded as being similarly good. I know that some lead to a lower error term, but the differences in the quality of the fits is visually hard to discern, so they are essentially equivalent, to all intents and purposes.
The generated impedance curve fits are generally a good fit to the data, but the fits obtained with a wide variety of parameters can all be regarded as being similarly good. I know that some lead to a lower error term, but the differences in the quality of the fits is visually hard to discern, so they are essentially equivalent, to all intents and purposes.
In practice quantifying the error in terms of db difference in a target crossover might be more valuable.
Has anyone tried verifying the model through blocked impedance subtraction? IE take a cheap speaker, remove the dustcap and do an impedance measurement, then drop hard epoxy into the gap and do another impedance sweep after it sets? It may help if there are Rms effects that mimic semi-inductance effects?
Has anyone tried verifying the model through blocked impedance subtraction? IE take a cheap speaker, remove the dustcap and do an impedance measurement, then drop hard epoxy into the gap and do another impedance sweep after it sets? It may help if there are Rms effects that mimic semi-inductance effects?
I didn't get any data from LaVoce.
After many more simulations, I came to the conclusion that the main problem is the manufacturers' impedance graphs. Most of the manufacturers' diagrams are estimates at best, the scales and grids are simply wrong or pure fantasy. The impedance peaks often do not match the resonance frequency; the height of the impedance minima does not match the information in the data sheet. Some kind of grid has been placed over the impedance curves and you can only guess how the values should be assigned. With RCF, the X-scale is often not usable because the grid spacing is not logical, there are often seven instead of nine sections between factors of 10 and the distances between 100Hz and 1000Hz are different than between 1000Hz and 10000Hz. With PD, the "logarithmic" impedance axis is often divided into equal distances.
Without your own measurements, it's all just a guessing game. So it's no wonder that I can't get any meaningful values.
After many more simulations, I came to the conclusion that the main problem is the manufacturers' impedance graphs. Most of the manufacturers' diagrams are estimates at best, the scales and grids are simply wrong or pure fantasy. The impedance peaks often do not match the resonance frequency; the height of the impedance minima does not match the information in the data sheet. Some kind of grid has been placed over the impedance curves and you can only guess how the values should be assigned. With RCF, the X-scale is often not usable because the grid spacing is not logical, there are often seven instead of nine sections between factors of 10 and the distances between 100Hz and 1000Hz are different than between 1000Hz and 10000Hz. With PD, the "logarithmic" impedance axis is often divided into equal distances.
Without your own measurements, it's all just a guessing game. So it's no wonder that I can't get any meaningful values.
I understand your frustration with the impedance curves. The mismatch between the plotted resonance frequency and the published Fs is not uncommon, but the ones that I've seen where this happens aren't really out by that much when it comes to Fs.
As for the logarithmic scales having incorrect spacing, I must admit that I've never come across that sort of problem. Some old datasheets do need some careful interpretation, as the impedance curves are inverted, but even those are very rare.
I'd be interested in seeing an example or two of these types of issues that you've identified in plots of impedance data.
As for the logarithmic scales having incorrect spacing, I must admit that I've never come across that sort of problem. Some old datasheets do need some careful interpretation, as the impedance curves are inverted, but even those are very rare.
I'd be interested in seeing an example or two of these types of issues that you've identified in plots of impedance data.
It is very mysterious that the semi-inductance blends so well with Re that you can get a near perfect fit by excluding Re above Fs. This suggests to me that our assumptions about suspension behavior above Fs may not hold. Or possibly change in excursion during the measurement is modifying the result depending on what source impedance and amplitude is used.
PD 185C001: https://www.precision-devices.com/products/all-products/pd-185c001/
Rs 32Hz; graph shows something around 42Hz.
Even spacings 5-10 + 50-100 ohm, but logarithmic numbers
RCF 18N405: https://www.rcf.it/de/products/product-detail/lf18n405
Minimum impedance: 6,0 ohm; graph (PDF download) is close to 7 ohm
7 spaces between 100-1000 and 1000 - 10000Hz. What do the lines stand for? And why is 1000 closer to 100 than to 10.000?
Many RCF graphs are this way.
I stumbled over a lot of such examples... :-(
Rs 32Hz; graph shows something around 42Hz.
Even spacings 5-10 + 50-100 ohm, but logarithmic numbers
RCF 18N405: https://www.rcf.it/de/products/product-detail/lf18n405
Minimum impedance: 6,0 ohm; graph (PDF download) is close to 7 ohm
7 spaces between 100-1000 and 1000 - 10000Hz. What do the lines stand for? And why is 1000 closer to 100 than to 10.000?
Many RCF graphs are this way.
I stumbled over a lot of such examples... :-(
Those examples that you kindly provided do have very glaring faults. It's hard to believe that those sorts of issues would exist for long without being fixed.🙁 That 32Hz-listed versus 42Hz-plotted resonance frequency issue seems terribly bad. I wonder what happened there?
there is 8. 200,300,400,500,600,700,800,900.
Because it is a 18" sub driver that has a quoted range of 30-1000hz ?
You get "precision" in the measurements where it is of interest kind of.
10k is far outside usable range, and will be out of a xo.
Thanks for bringing my attention to that. The 950-litre enclosure would cause the free-air resonance frequency to be increased by a factor of sqrt(1+302/950) = 1.148 when the PD 185C001 driver is mounted in that enclosure. Hence, Fc = 1.148*Fs = 1.148*32 = 36.7 Hz, whereas the impedance graph shows the peak to be something in the range 41–42Hz. That's still a big discrepancy of about 12–14%.
Next point is that they're impedance plots are clearly not accurate measurements. Go through they're whole line of cones, and find a single impedance spike/resonance anywhere, good luck🙂
And wether the driver is properly broken broken in during the measurement.
And then the 2-4% off from "accepted" is not do bad.
And wether the driver is properly broken broken in during the measurement.
And then the 2-4% off from "accepted" is not do bad.
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