Hello @lrisbo and All,
I have been away to scout camp for a week.
After a little studying and head scratching I have come up with a few insights.
@b_force if a formula or simulation model does not have a S(d)x factor the simulation / computer animation will not generate S(d) low frequency HD or any 2 tone IMD. The model is incomplete.
For a Two-Tone IMD test f1 is the lower frequency and f2 is the higher frequency. Just for grins for this discussion:
f1 := 50Hz
f2 := 1000Hz
For a symmetrical B field with a centered Voice Coil the Bl curve will cycle at 2 times f1. 100Hz
For f1 there will be 3rd HD and perhaps 5th HD. There will be no even HD’s for f1.
For f2 there will be side bands at + / - 100Hz. F1 is 1000Hz and the side bands will be at 900Hz and 1100Hz. Or f2 +/- 2 x f1
For S(d)x the S(d) curve will cycle between min and Max at 50Hz the same rate as f1.
For the same conditions as Bl above S(d) will produce only even HD’s.
f1 will produce 2nd HD perhaps 4th HD.
f2 at 1000Hz will have side bands at 950Hz and 1050Hz. Or f2 +/- f1.
S(d) distortion will have side bands +/- f1. (even)
B(l) distortion will have side bands +/- 2 x f1. (odd)
Thanks DT
I have been away to scout camp for a week.
After a little studying and head scratching I have come up with a few insights.
@b_force if a formula or simulation model does not have a S(d)x factor the simulation / computer animation will not generate S(d) low frequency HD or any 2 tone IMD. The model is incomplete.
For a Two-Tone IMD test f1 is the lower frequency and f2 is the higher frequency. Just for grins for this discussion:
f1 := 50Hz
f2 := 1000Hz
For a symmetrical B field with a centered Voice Coil the Bl curve will cycle at 2 times f1. 100Hz
For f1 there will be 3rd HD and perhaps 5th HD. There will be no even HD’s for f1.
For f2 there will be side bands at + / - 100Hz. F1 is 1000Hz and the side bands will be at 900Hz and 1100Hz. Or f2 +/- 2 x f1
For S(d)x the S(d) curve will cycle between min and Max at 50Hz the same rate as f1.
For the same conditions as Bl above S(d) will produce only even HD’s.
f1 will produce 2nd HD perhaps 4th HD.
f2 at 1000Hz will have side bands at 950Hz and 1050Hz. Or f2 +/- f1.
S(d) distortion will have side bands +/- f1. (even)
B(l) distortion will have side bands +/- 2 x f1. (odd)
Thanks DT
I don't understand where you get the impression from that the formula/simulation doesn't have Sd(x) ?
About the rest, yes it's clear what it can do.
Thank you for writing it out.
It only still doesn't give us any idea about how significant it is.
Only if it's even or odd.
I do believe that you understand that S(d)x is a function of the position of the voice coil in the B field as B(l)x is a function of the position of the voice coil.
You are a advocate of formulas, the last 2 formulas that I see you posted do not show Sd(x) as a function of x. (posts 243 and 251)
Thanks DT
hi DT,
Yes, that is correct if we assume that Sd(x) is just a linear function of x and if Bl(x) is symmetric and parabolic (1-x^2).
However, Bl(x) is also often not symmetric so we get f1 side bands too. Conversely, Sd(x) may have higher order terms too.
cheers,
Lars
Hi B_force,
I am not sure what you mean by the above? you mean when we have the general case where both Bl and Sd have both even and odd components?
cheers,
Lars
D
Deleted member 375592
2c from a mathematician.
The speculations on the importance of Bl(x) /Sd(x) /etc for midrange are not supported by real-world measurements and therefore have nothing to do with science. The amplitude of vibration shall decrease ~1/f^2 for the same SPL. Thus, the 2nd-order distortions shall decrease same speed with f, 3rd - even faster. For a given frequency, 2nd order distortions shall decrease x dB with amplitude decreasing by x dB. 3rd order - by 2x dB, etc. Alas, this is not what is observed.
I do not claim to know the "right" theory. afaik, it does not exist - yet.
The speculations on the importance of Bl(x) /Sd(x) /etc for midrange are not supported by real-world measurements and therefore have nothing to do with science. The amplitude of vibration shall decrease ~1/f^2 for the same SPL. Thus, the 2nd-order distortions shall decrease same speed with f, 3rd - even faster. For a given frequency, 2nd order distortions shall decrease x dB with amplitude decreasing by x dB. 3rd order - by 2x dB, etc. Alas, this is not what is observed.
I do not claim to know the "right" theory. afaik, it does not exist - yet.
^Hi, I think your example shows the opposite, why it matters: Since output is not just the excursion, but volume displacement, the higher the frequency the more Sd matters for output. Output at frequency f relies to x*Sd, and as x goes towards zero Sd matters more.
You are right when thinking output at only single frequency f, the higher the frequency the less it would make excursion and the less modulate itself. Same is true for Bl(x) and any x related distortion mechanism. The second you imagine low frequency content with the high frequecy you'll see the problem, low frequencies that really make excursion now modulates Sd (or any other x related parameter) for the whole bandwidth, it's the same cone/motor/driver outputting all the input at once.
You would measure this stuff with some multitone setup to bring it from imagination to reality.
You are right when thinking output at only single frequency f, the higher the frequency the less it would make excursion and the less modulate itself. Same is true for Bl(x) and any x related distortion mechanism. The second you imagine low frequency content with the high frequecy you'll see the problem, low frequencies that really make excursion now modulates Sd (or any other x related parameter) for the whole bandwidth, it's the same cone/motor/driver outputting all the input at once.
You would measure this stuff with some multitone setup to bring it from imagination to reality.
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Yes, but with higher frequency Sd is modulated much less because of low X.
Edit/correction:
However a low frequency high excursion signal does indeed modulate higher frequency contents with modulation of Sd.
The question is probably wether acoustic impedance counteracts modulation of Sd.
yeah, except the modulation (x) is not dominated by the f but any signal at lower frequency than f.
Say there is 50Hz and 1000Hz tone at once both at 90db for example, the 1000Hz tone makes fraction of total x while 50Hz tone makes huge x. So output is dominated by Sd much more at 1000hz than at 50Hz. At the same time x, so Sd or any other x related parameter*, modulates greatly by the 50Hz. Its the lows that make the whole bandwidth suffer, IMD.
*Kms(x) being the exception, stiffness of spring doesn't matter much above resonance. In this sense Sd(x) feels more significan issue of the two except for subs. The Sd gets more significant the wider the bandwidth, has most significant effect at the top end of the bandwidth.
Say there is 50Hz and 1000Hz tone at once both at 90db for example, the 1000Hz tone makes fraction of total x while 50Hz tone makes huge x. So output is dominated by Sd much more at 1000hz than at 50Hz. At the same time x, so Sd or any other x related parameter*, modulates greatly by the 50Hz. Its the lows that make the whole bandwidth suffer, IMD.
*Kms(x) being the exception, stiffness of spring doesn't matter much above resonance. In this sense Sd(x) feels more significan issue of the two except for subs. The Sd gets more significant the wider the bandwidth, has most significant effect at the top end of the bandwidth.
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D
Deleted member 375592
Here you are...
I did, quite a few times. The reality is : IMD on Vifa/Peerless TC9, 1450 & 1550, sweeping up from ~55 dB SPL to 100 dB SPL and back.
Go figure out how to explain it🙂
BTW, You may want to read the publications of Pascal Brunet, PhD , Research Director of Samsung Audio Lab
I did, quite a few times. The reality is : IMD on Vifa/Peerless TC9, 1450 & 1550, sweeping up from ~55 dB SPL to 100 dB SPL and back.
Go figure out how to explain it🙂
BTW, You may want to read the publications of Pascal Brunet, PhD , Research Director of Samsung Audio Lab
Cool graph, could you expand what the dF in legend means? Is it 100Hz in this case so F1-dF is 1350Hz side tone? Why there is no F1+xdF and no F2-xdF plots?
hi Mikets42,
That is indeed an intriguing graph!
I know you are familiar with the magnetic hysteresis distortion which shows up as odd harmonics that decay slower with level than expected. You pointed out that we see a slower harmonic decay vs frequency some posts above. We did some research here together with DTU and believe the reason is hysteresis in the suspension. A simple dry friction model explain the observations very well.
One thing we noted is that there seems to be a cut off points below which the material is linear elastic.
your graph shows knee points where the slope changes which indicates similar cut off points.
We ran out of funding for the project so no paper was published. The candidate got a new job so writing the paper is a spare time thing now.
cheers
Lars
That is indeed an intriguing graph!
I know you are familiar with the magnetic hysteresis distortion which shows up as odd harmonics that decay slower with level than expected. You pointed out that we see a slower harmonic decay vs frequency some posts above. We did some research here together with DTU and believe the reason is hysteresis in the suspension. A simple dry friction model explain the observations very well.
One thing we noted is that there seems to be a cut off points below which the material is linear elastic.
your graph shows knee points where the slope changes which indicates similar cut off points.
We ran out of funding for the project so no paper was published. The candidate got a new job so writing the paper is a spare time thing now.
cheers
Lars
I thing it is about the viscoelastic creep phenomena in the suspention. There is a theoretical approach developed by Antoine Falaize and Thomas Helie using port-Halmiltonian formalism to model the viscoelastic creep.
https://www.diyaudio.com/community/threads/the-significance-of-high-qms.120505/page-9#post-6859726
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Deleted member 375592
visco elastic creep is a fractional order response. It’s not necessarily nonlinear.
D
Deleted member 375592
"I thing it is about the viscoelastic creep phenomena in the suspension." - Alas, it is not.
Here is the plot of the 3rd harmonic on the same TC9, on 80 dB SPL (exactly the same coil/cone/suspension movement) for the varying series resistors.
The picture becomes even more mysterious when you try music as excitation. There appears to be a distortion peak on ~1.5kHz (any musical content)
While there is nothing to indicate any abnormalities on the sine sweep excitation:
Here is the plot of the 3rd harmonic on the same TC9, on 80 dB SPL (exactly the same coil/cone/suspension movement) for the varying series resistors.
The picture becomes even more mysterious when you try music as excitation. There appears to be a distortion peak on ~1.5kHz (any musical content)
While there is nothing to indicate any abnormalities on the sine sweep excitation:
The strange thing is that this phenomenon in loudsspeakers is little studied. Djurek et al. believed that the viscoelastic creep is responsible for some loudspeakers poor performance at low levels.
I am not sure that I have correctly understood your arguments against viscoelastic creep. Lisbo correctly noted that viscoelastic creep does not necessarily manifest itself as a nonlinear phenomenon.
D
Deleted member 375592
"I am not sure that I have correctly understood your arguments against viscoelastic creep."
If any mechanical effects were responsible for the observable non-linearities, there would be no differences in measurements for the amplitude of vibration was maintained the same for all (current linearizing) series resistors. But the differences are clearly observed.
If any mechanical effects were responsible for the observable non-linearities, there would be no differences in measurements for the amplitude of vibration was maintained the same for all (current linearizing) series resistors. But the differences are clearly observed.
