hi, I would very like to understand why you think it makes little difference?
the sound pressure reproduced is proportional to i(t)•Bl(x,i)•Sd(x). This means that both Bl and Sd scale the pressure and thus makes amplitude modulation if not constant. Hence, Sd being constant is just as important as Bl being constant.
cheers
Lars
the sound pressure reproduced is proportional to i(t)•Bl(x,i)•Sd(x). This means that both Bl and Sd scale the pressure and thus makes amplitude modulation if not constant. Hence, Sd being constant is just as important as Bl being constant.
cheers
Lars
I think I am starting to repeat myself 🙁
Absolutely no offense.
Again, because of the shape of the Sd(x) curve IMD products don't add up like the other ones do.
That is obviously true, but not all of these parameters will be of the same order of magnitude.
So saying that things are directly proportional doesn't say much.
Would you care to elaborate on this since I have no idea what it means? Does the same apply to Bl(x)?
In big round figures, both Bl(x) and Sd(x) can vary 10% across the operating area.
it says that the system is linear if the proportionality is constant and otherwise nonlinear (amplitude modulation IMD)
I already did this very extensively in the last couple of posts/pages.
Actually already before that, when showing the Sd vs excursion graph from that paper.
No, because the BL drops on both ends.
we have discussed that in another thread: the Bl(x) or Sd(x) curve being even or odd only determines if we have even or odd distortion products. The fact remains that linearity requires constant Sd and Bl.
Yes, that is know.
But it doesn't tell us the significance of it.
Or in other words, how it mathematically sums up.
Because of the shape of Sd vs excursion curve , I just don't see it would be summing the same way, therefore resulting in an equal amount of distortion.
That totally depends on context how much of that is required.
But that's not the question and discussion here.
We're looking at fundamentals.
what does this mean? is there an innocuous shape ? what is meant by summing up?
Again, anything but a constant Sd and Bl gives distortion.
Yes, but some things give more distortion than other.
I assume you understand how intermodulation products sum up?
Hello Lars,
Yes, but the Million Dollar question is still how e.g. 5% Sd variation translates in a distortion percentage. So far that question does not seem to be answered.
Could you shed some light on the Delta Sd vs distortion relationship?
Hello Boden,
It’s quite simple: 5% Sd or Bl modulation turns roughly into 2.5% distortion.
if Sd varies harmonically with frequency f1 and the speaker plays back another harmonic with frequency f2 then we get harmonic components at the sum (f1+f2) and difference (f1-f2) frequencies. The amplitude splits equally on these components. In the simple case where Sd(x)=1+a•x then a harmonic x(t)=cos(ω•t) played back results in 2nd harmonic distortion with amplitude a/2 and a DC component (difference frequency is zero). however the dc component does not produce acoustic pressure. so if a=5% then the second harmonic has amplitude of 2.5%.
if the signal has a bass components and a voice components then we get IMD, ie the bass tone modulates the voice tone. That is the most problematic with both Bl(x) and Sd(x) (they are both multipliers in the signal chain).
cheers
Lars
It’s quite simple: 5% Sd or Bl modulation turns roughly into 2.5% distortion.
if Sd varies harmonically with frequency f1 and the speaker plays back another harmonic with frequency f2 then we get harmonic components at the sum (f1+f2) and difference (f1-f2) frequencies. The amplitude splits equally on these components. In the simple case where Sd(x)=1+a•x then a harmonic x(t)=cos(ω•t) played back results in 2nd harmonic distortion with amplitude a/2 and a DC component (difference frequency is zero). however the dc component does not produce acoustic pressure. so if a=5% then the second harmonic has amplitude of 2.5%.
if the signal has a bass components and a voice components then we get IMD, ie the bass tone modulates the voice tone. That is the most problematic with both Bl(x) and Sd(x) (they are both multipliers in the signal chain).
cheers
Lars
sure but Sd and Bl are both multipliers in the signal chain and produce similar distortion.
I’m not sure what you mean here so please enlighten me
How many angles can dance on the head of the pin discussion here.
Fact: It can matter. Sd does change and Lars gave a number. Agreed.
Fact: That massive 5% change is only at peak amplitude. How often do you get this in the real world? And in the bass that that full excursion requires will it even be noticed that you have 2.5% distortion?
Just trying to keep it real.
As for variable BL, design an underhung. If you do it properly the BL is quite linear from top to bottom excursions.
Fact: It can matter. Sd does change and Lars gave a number. Agreed.
Fact: That massive 5% change is only at peak amplitude. How often do you get this in the real world? And in the bass that that full excursion requires will it even be noticed that you have 2.5% distortion?
Just trying to keep it real.
As for variable BL, design an underhung. If you do it properly the BL is quite linear from top to bottom excursions.
When you speak of imagination I like to call it visualization, the kind of thing you would see with a computer animation.
For a perfect mid-bass driver with a 40 Hz signal applied; at 0 degrees both Force Factor and Stiffness are neutral, at 90 degrees both Force Factor and Stiffness are at a maximum. At 180 degrees both Force Factor and Stiffness are back to neutral. At 270 degrees both Force Factor and Stiffness are close to a maximum near where they were at 90 degrees, an equal and opposite sort of symmetry. There is no IMD, both Force Factor and Stiffness are balanced and symmetrical.
Now visualize the same mid-bass driver with a cone that has a half round rubber surround. This driver has the same Force Factor and Stiffness symmetry. So what is different? The output SPL waveform at 90 degrees and 270 degrees will be anything but symmetrical. Because of modulating effective driver area the SPL at 90 degrees will be larger than at 270 degrees. That is what you call amplitude modulation. That is what shows up as bass distortion and side bands in the two-tone FFT.
Thanks DT
Just a fun fact, the position of the Voice Coil in the magnetic gap will change all that symmetry.
For a perfect mid-bass driver with a 40 Hz signal applied; at 0 degrees both Force Factor and Stiffness are neutral, at 90 degrees both Force Factor and Stiffness are at a maximum. At 180 degrees both Force Factor and Stiffness are back to neutral. At 270 degrees both Force Factor and Stiffness are close to a maximum near where they were at 90 degrees, an equal and opposite sort of symmetry. There is no IMD, both Force Factor and Stiffness are balanced and symmetrical.
Now visualize the same mid-bass driver with a cone that has a half round rubber surround. This driver has the same Force Factor and Stiffness symmetry. So what is different? The output SPL waveform at 90 degrees and 270 degrees will be anything but symmetrical. Because of modulating effective driver area the SPL at 90 degrees will be larger than at 270 degrees. That is what you call amplitude modulation. That is what shows up as bass distortion and side bands in the two-tone FFT.
Thanks DT
Just a fun fact, the position of the Voice Coil in the magnetic gap will change all that symmetry.
@lrisbo ,
Thanks for answering the question without a question mark "?" in my post above.
While I was thinking of, visualizations / simulations, I had a copy of AES "Convention Paper 5640", laying open on my desk.
"The Effects of Voice-Coil Axial Rest Position on Amplitude Modulation Distortion in Loudspeakers"
https://secure.aes.org/forum/pubs/conventions/?elib=11286
For All the other readers, this "Convention Paper 5640" is well worth the price of admission. There are many Models and Figures that show amplitude Modulation graphs and FFT plots of the various combinations of possible symmetry and asymmetry.
Thanks DT
Le(x) is dominant as well as qts and tuning until the volume gets really high.
Tuning for sound quality at low volume is essential.
Tuning for sound quality at low volume is essential.
Why not just enlighten us with some data?
If it's that obvious, that shouldn't be a problem?
If a midrange driver can be considered to be a mass–spring system with damping, an input signal consisting of a 1/2 cycle of a sine wave will generally produce significant displacement after the input signal itself has stopped. To ensure that the response is linear, then Bl(x) and Kms(x) need to be constant, of course. If they aren't, distortion will result.
Large displacements occur in the vicinity of the resonance frequency of the driver for relatively small input signal levels. Hence, a 1/2 cycle pulse waveform with frequency equal to Fs can produce a displacement that extends into the nonlinear regions of operation. I guess that's why the high-pass section of a crossover filter has a –3dB point that is at least one octave higher than the Fs of the midrange.
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