Over all there appear to be some real problems here. Between 100 and 300 Hz the output of the speaker is greater so it is not unexpected that the THD is greater. But then ask yourself why the distortion with eq goes down above 500 or 1k Hz when your EQ does nothing there? I think there are some problems with the measurement to say the least. Not faulting you here, fn, but the measurement looks suspect. Like Judge Judy says, if it doesn't make sense it probably not true.
I think you would do better to run a single tone sweep.
But I agree that if I go back to my results and keep the input from the signal generator then I will see higher distortion coupled to the higher SPL at the fundamental.
Back to my woofer stuff. I'm looking for significant nonlinearity and loss of control around resonance. I don't see it. I am sure HD will increase with over that 50dB range, but the nonlinearity is not a dominant factor. The SPL data scales quite nicely from one level to the next by a constant scale factor. That says the system behaves linearly.
I am also certain that if I were to test a $5 dollar woofer with poorly designed motor and suspension I might see something different. But for a respectable driver this loss of linearity and loss of control around resonance isn't a factor unless the driver is pushed to extremes, like pushing an amplifier into clipping.
I do not have an argument for your first statement.
When I think of nonlinear distortion I think of a transfer function that is not a straight line. A couple of examples; a 3/2 ‘s law for triodes and a square law for JFETS. My example of the D and D sharp keys on the piano being played together is in my mind is the mechanism of the effect we are discussing. Not the more typical nonlinear transfer function. I agree a separate thing. We do need to hurry on over to Wikipedia and change the definition of nonlinear distortion if we do not like how it is defined there now.
John k…,
Thank you for posting your plots.
Looking at the first plot, the output looks to be down about 3 db at near 60 Hz. The -3db point is typically the resonate frequency of a sealed speaker (driver in a sealed box).
The effect described by fntn shows up as increased output as 2nd and 3rd harmonics. Your plot shows peaks (small) at what would be 2nd and 3rd harmonics of a 60Hz resonance. It would be interesting to see what happens at 120Hz and 180Hz if you add (equalize) 5 db at 55hz.
All,
Again this may not be broken to the point it needs fixing. It is interesting.
DT
All just for fun!
I have now run in the SLS woofers over night. The parameters i get are again different from the data sheet. Fs went down to 26.5 Hz from 33 Hz and Qts went down from nearly 0.6 to 0.466 just to mention two changes. I asume Tymphany measured the driver without run in. I promiss that i will run in drivers in the future before i post the parameters here.
I have now simulated a 75 liter closed box with one driver and an isobaric with 40 liters. Yes, i got plausible results now with an isobaric. Maybe i put some wrong parameters into LSP-CAD yesterday. Now the isobaric option is open again. When you compare the simulations consider that the isobaric is a 4 Ohm design because the drivers are electrically in parallel.
I have now simulated a 75 liter closed box with one driver and an isobaric with 40 liters. Yes, i got plausible results now with an isobaric. Maybe i put some wrong parameters into LSP-CAD yesterday. Now the isobaric option is open again. When you compare the simulations consider that the isobaric is a 4 Ohm design because the drivers are electrically in parallel.
The distortion level for the speaker with the boosted measurement was a little bit lower at other frequencies because the drive level overall was a little bit lower. This actually heightens the argument that the boost of a few db created a substantial increase in the second harmonic. These measurements were taken many months ago and there was no intention to put the behavior under a microscope as the observed results were expected. The simple fact that overall frequency response is very similar in both and the distortion is within a few db overall with the exception of the equalized portion tells the story sufficiently for any reasonable person who is not consumed by an agenda. If you feel that the measurements presented are falsified or useless - good luck to you. I'm not losing any sleep over it. After all, it's only DIY here. 
That a driver CAN do as you suggest has never been in question - you found an example of one, OK. But what everyone keeps saying is that this IS NOT a characteristic of a loudspeaker or a resonant system or anything else. That badly designed drivers exist is certainly the case, that they all do this is absolutely incorrect.
Badly designed driver?
Vifa PL18 in MTM configuration with NEO 3 BG. "Badly designed" doesn't seem to be the consensus of everyone I've come in contact with in this business but again, I'm on DIY here so there are bound to be a variety of perspectives and you are certainly entitled to yours.
The distortion level for the speaker with the boosted measurement was a little bit lower at other frequencies because the drive level overall was a little bit lower. This actually heightens the argument that the boost of a few db created a substantial increase in the second harmonic. These measurements were taken many months ago and there was no intention to put the behavior under a microscope as the observed results were expected. The simple fact that overall frequency response is very similar in both and the distortion is within a few db overall with the exception of the equalized portion tells the story sufficiently for any reasonable person who is not consumed by an agenda. If you feel that the measurements presented are falsified or useless - good luck to you. I'm not losing any sleep over it. After all, it's only DIY here.
I don't think the measurement are toyed with. I just suggested there may be an issue that should be examined.
Perhaps we are looking through the same tunnel but from different ends. You take your speaker and sweep it with 1 V RMS and say, "here is the distortion with and w/o the EQ in the circuit". The distortion comes out higher in the region of the EQ boost. You say, EQ causes distortion. Fine.
I look at this and say yes, higher distortion but it is not because of the EQ. It is because the operating point has changed when EQ is applied and the change in operating point is the cause of the increase distortion. The nonlinear characteristics of the driver vs. the amplitude of the applied signal do not changed, the applied signal has.
If you take you speaker with or without the EQ applied and measure it when playing at 80dB and then again at 90 dB you expect to see higher distortion at 90 dB. The nonlinearity of the system has not changed, the result of that nonlinearity has. For example BL(x) is still the same. The driver is just operating over a range with the nonlinearity in BL(x) has a bigger effect on the output.
May I suggest you take a look at the SoundEasy web site and down load chapter 17 of the manual on nonlinear modeling?
The point was that it was previously posted (way back now) that the response around resonance was highly nonlinear and that there was a loss of control and that the amplitude response as resonance would not scale linearly with input. It was suggest such measurements would show this. The plots show quite the contrary. They clearly show the dominant behavior is linear. I am sure that THD sweeps at the different levels would be very different, but there is no gross nonlinearity, like an unstable oscillator where the response at resonance grows exponentially with input, indicated. Everything is very nicely behaved.
If everything deviated from dominantly linear behavior the average DIY speaker designer would not have a change of designing anything worth a dam. Certainly some of the HT woofer system employ motional feedback but, I suspect that is more because at the limits they are operation it is just cheaper to introduce feedback than to design a driver which maintains linearity at such high excursion levels. Motional feedback at low frequency isn't that difficult. I think GR Research even sells a subwoofer amp with it build in, or at least they used to.
Hello john k…,
Go out to your shop and test the null hypothesis.
Take the speaker tested in your first plot in post 880 and equalize / boost only a narrow frequency band at the resonate frequency of the speaker not the overall input and report what happens at the 2nd and 3rd harmonics.
It may not be broken.
The rest is dismissive hand waving.
DT
All just for fun!
That's not reflected in the graphs. It has all the appearance of no change in drive level. The only significant change is from 100-250Hz where there's an increase in output of up to 5db. The rest is so close as to be almost a perfect overlay, so it's an indication of no drive level change. I'm still looking for the high-Q change made. What was the Q of the change? How can there have been a high-Q change, yet the resultant FR change shows low Q?
In addition, though I've never looked into the HOLM info for this, your measurements have values that differ in the HOLM display. Maybe someone more familiar with HOLM will explain.
Left (LogSweep):
Unboosted: +35.9db
Boosted: +45.5db
Yet the overlays are nearly perfect in most areas.
Dave
It's a waste of time. What will hapen to the distortion if I eq it will be the same thing as is I just increase the gain when testthing those frequencies. You haven't been paying attention. The driver is the driver. What ever its nonlinearity is, however it maps with amplitude and frequency, does not change by such manipulations.
Sorry john k…,
I missed your post 897 while I was pecking at 898.
Perhaps there is instability at resonance in a sealed speaker. Not to the point of needing repair in my mind.
The discussion has opened my mind about the assumption of Q:=0.707 being optimum especially now with more watts to use and DSP to implement.
For Single End Triodes with only a few watts to work with Q:=0.707 is best to optimize the limited power at hand.
It is not broken to the point it needs fixing.
DT
All just for fun!
There is no instability with any reasonable driver. Don't you think driver manufactures would have addressed this by now if it were so? Audio is not exactly new science.
A problem with SET amps is they typically have high output impedance. Like the case of a cap in series with the woofer impedance peak, a resistor in series also has an affect. It is not a resonance but rather a voltage divider which can alter the response across the complete audio band. With any amp with high output impedance it is best to try to add impedance comp to make the entire speaker, at its terminals, look like a resistive load of constant value.
...or go active and remove most of the reactive elements from the loudspeaker.
Or, better yet, go active and use ribbons or planars in place of the moving coils, with SS amplification for bass in both instances.
Horses for courses.
John - perhaps a misleading example. If the masses are all the same as well as the springs, then the motion will appear quite "orderly" - think of a standing wave. If, however, all of the masses are a little different and the springs as well, then this motion will not appear to have any order to it, even though the "order" could be analyzed with measurements to show that it was perfectly predictable and coherent.
Now add some nonlinearity to the above and after a little time all order is destroyed and even measurements could not find any coherence from the chaos.
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