Thank you again for your thoughts @b_force Yes I do mean distortion in general. I think the easiest way ask my question, and once again I asked here, because I just it seemed BL would be a major factor. The higher the BL the less it is affected by the loading is my guess, and here it is;
In the case the midrange doubles as the subwoofer....and during playback as a sealed woofer has no issue of high excursion....everything is kept near 2mm...would the introduction of a vent tuned to system cutoff, affect midrange quality in anyway. Essentially would the loading that takes place while playing near Fb affect midrange quality in anyway?
In the case the midrange doubles as the subwoofer....and during playback as a sealed woofer has no issue of high excursion....everything is kept near 2mm...would the introduction of a vent tuned to system cutoff, affect midrange quality in anyway. Essentially would the loading that takes place while playing near Fb affect midrange quality in anyway?
I think this is the answer I was looking for.... Don't you think a stronger motor would also affect the out come of this situation?
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I don’t think it would get any better. Why would it? The stronger motor would also increase the excursion and therefore the distortion.
Of course it will for a given Fs, Cms since it will lower Qes, Qts = a higher upper mass corner (Fhm = 2*Fs/Qts), which is similar to the bass 'shy' woman likely hearing it up in the mids.
The easy way to get around it is do like the pioneers did and use a high effective Qt driver (low Qt driver + high output/matching impedance amp), i.e. the lower Fhm, the quicker any resonances decay away.
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Well, yes and no. lol
It kinda depends how you look at this problem.
A stronger motor will raise the sensitivity, which could lead to less excursion actually.
The problem in this case is that the same woofer has to do the lower end as well.
But by increasing the BL, basically the -3dB point shifts up in frequency.
(see that wonderful Eargle book, somewhere in the beginning, described very well).
Which effectively means, lowering the output of the lower frequencies.
But yeah, compression always produces more distortion in general, since you're quite literally squeezing those since waves.
Luckily this is mostly 2nd order, so meh, who cares?
I had the thought that possibly while dealing with the pressure near Fb, the midrange itself, might distort itself. 2nd order distortion with the midrange as the fundamental, then it would be audible yes?
It is an interesting balance...throws me off...High Bl, lowering sensitivity on the bass side....I understand the more you can get the system to what you want it to do without additional filtering the better. Yet a higher BL motor with the FR adjusted by EQ is not the better option vs lowering the BL in order to increase low end Sensitivity?
The system ís a bunch of ‘filters’. You only need to optimize them.
But still, why throw up this small signal TSP wisdom in a topic that actually is about serious cone excursions and the (non)linearity of those, including varying Bl? Or did I miss something?
like I said, I was interested in how BL(x) might be affected by pressure. We've talked about reasons to stay away from F in regards to increased excursion.... but we haven't talked about Fb where excursion has an dip before response falls off....where excursion is no longer the consequence, but pressure is....Until now lol...
BL(x) is affected by cone excursion, hence the name BL (x), or in other words, the BL as function of x (x = excursion).
So as long as something else affects the cone excursion, the answer is yes.
Drastically simplified obviously, given that those other parameters don't cause other issues (which is very unlikely in practice)
One note about Sd modulation.
I found it a little far fetched to be perfectly honest.
In the worst case scenario the difference would be the entire size of the surround.
So lets assume that the surround is 10mm wide for a 6 inch woofer. (which is very substantial)
So if we take a 6 inch woofer with an Sd of 133 cm²
10mm extra on this will give us a Sd of 154 cm²
Which results in a difference of 20*log(154/133) = 1.27dB
This is really worst case, because even a very poor surround would not be that extreme.
In practice this means a very thick and wide surround, which is a extremely bad choice for a mid-woofer to begin with.
Again for situation with no or very limited excursion, this whole Sd story is non-existing.
Another very important point, we haven't ANY objective data and measurements that backup this theory to begin with.
If they want to make a convincing point, please just show us the same driver with just different surrounds.
And I am more than happy to change my skepticism in less than a heart-beat.
Because at this point the whole Sd modulation story, is nothing more than just a little theoretical thought.
Which is fine, but it doesn't hold any conclusions, nor any scientific value.
I found it a little far fetched to be perfectly honest.
In the worst case scenario the difference would be the entire size of the surround.
So lets assume that the surround is 10mm wide for a 6 inch woofer. (which is very substantial)
So if we take a 6 inch woofer with an Sd of 133 cm²
10mm extra on this will give us a Sd of 154 cm²
Which results in a difference of 20*log(154/133) = 1.27dB
This is really worst case, because even a very poor surround would not be that extreme.
In practice this means a very thick and wide surround, which is a extremely bad choice for a mid-woofer to begin with.
Again for situation with no or very limited excursion, this whole Sd story is non-existing.
Another very important point, we haven't ANY objective data and measurements that backup this theory to begin with.
If they want to make a convincing point, please just show us the same driver with just different surrounds.
And I am more than happy to change my skepticism in less than a heart-beat.
Because at this point the whole Sd modulation story, is nothing more than just a little theoretical thought.
Which is fine, but it doesn't hold any conclusions, nor any scientific value.
It is always wise to match a driver's parameters to suitable applications (horn loading, BR, closed, OB, etc.), even though there are ways to make mismatches work.
The resonance frequency fs for a driver is related to Mmt and Cms. It's inversely proportional to the square root of both quantities: total moving mass and suspension compliance:
fs = 1/ ( 2π√(Mmt*Cms) )
When the driver is mounted on a closed box a new resonance frequency fo is created for the oscillating loudspeaker diaphragm (Cmt instead of Cms):
fo= 1/ ( 2π√(Mmt*Cmt) ).
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note that whilst 1.27dB may sound innocuous it represents a gain modulation of around 15%, similar to Bl(x) and Bl(i) modulation - both directly controlling the gain. In other words, 15% wide band IMD.
Sd modulation has been confirmed experimentally by changing only the surround and by a general measurement setup. Near field measurements close to a normal half roll is higher than close to the cone. Moreover, Sd modulation is confirmed by finite element simulation. It was first analysed in AES papers from 1994 and 1995. Technics invented a surround that reduces Sd modulation back in 1992.
Ok, let's revive this thread, now with a lot more technical knowledge and understanding for many of us.
I particularly want to dive into two things, let's start with one first, The importance of Kms(x)
We all want to strive for best possible performance and a good bang for the buck.
Currently, the general approach for some people, is just to go for lower distortion = more better.
Which on itself is fine, but it doesn't hold much real scientific foundation.
Besides, it often comes with a price, which doesn't make all projects very practical.
Let's recap first;
Obviously there are a bunch of parameters that will be influenced by the cone excursion.
Those are BL(x), Kms(X), Le(x) and in theory also Sd(x)
(although its significance has never been proven with objective data, in theory it's there).
Rms(x) is often not being considered and Mmd (not Mms, since this is connected to Sd!) is deemed to be a constant.
Just for simplicity, I will leave out other things like Le(i), Re(i) and Re(T) as well as Kms(T)
Those things are also not connected to the excursion, so they won't produce and intermodulation products.
We can quickly see what influence most of those parameters have by just looking at the definitions of the model of a driver.
In case of the compliance, there are only two that come to mind.
The resonance frequency, since;
As well as the Vas;
To a much lower extend also the Qms, therefor the Qts, although very limited.
If we compare this to the BL for example, we can already see that BL(x) has a much greater influence.
Mostly because in most (all) definitions, we are dealing with BL² (squared).
So any chance in BL will have a much bigger impact.
As well as in;
Meaning that BL doesn't only has an affect on the low-end, near Fs.
Since it's changes the height of the impedance peak drastically, therefor the overal Q of the system.
But it actual changes the overal sensitivity of the driver as well = modulation.
We can actually simulate this to visualize this a bit more. (although steady state)
In this case a ported system is being used to amplify those changes a bit.
Gray = original, no changes, Yellow = 50% Cms (20% distortion), Green = 82% BL (10% dist)
All other things are being kept equal.
From this graph, it can be seen that even BL at just 82% has a very drastic effect on the overal system response!
Fyi, we are not even talking about distortion numbers at this point!
On the other hand, even a drop of 50% of the compliance doesn't show a very big difference.
Anyway, back to compliance.
This kept me thinking.
Because this suggest that compliance only has a very limited performance penalty.
1 - only at the low-end, up till say about 2*Fs
2 - little change in overal system performance
3 - therefor, there is barely any intermodulation going on (IMD)
So I decided to dive a bit deeper into this.
A good start can be found in;
"Loudspeaker Distortion – Measurement and Perception Part 1: Regular distortion defined by design"
https://www.klippel.de/fileadmin/klippel/Files/Know_How/Literature/Papers/Loudspeaker regular signal distortion caused by design_part 1_Klippel_Werner.pdf
On page 8 the following can be found;
As well as the case for a multi-tone signal;
Searching a bit more, we can find some more clues in the by now famous document;
"Loudspeaker Nonlinearities – Causes, Parameters, Symptoms" by Klippel
https://www.klippel.de/fileadmin/klippel/Files/Know_How/Literature/Papers/Loudspeaker Nonlinearities_Causes,Parameters,Symptoms_06.pdf
(people should know that thing by heart by now ! )
Although this document doesn't give much direct proof of things, it at least gives us a nice summary.
On page 36 the following table can be found;
So this basically proves my suspicion, that the impact of a non-linear compliance is very limited.
Not only that, but the symptoms of it only result in HD products and no IMD products.
But that leaves a question open.
Many of us look and compare those wonderful LSI Kms(x) and BL(x) graphs.
Using either 10% distortion or 20% distortion limits as guidelines.
However, that is clearly not the entire story I think?
Because it's obvious from everything above that a drop in BL is FAR more significant then just a drop in compliance?
In that case we are not just talking about HD distortion, but IMD as well as change of the actual system response.
The last one is I think maybe even the most audible of all of these things!
We are talking 3dB difference here as well as changing the Q of the system drastically!
The compliance is only responsible for some HD distortion below, near and around Fs.
At the same time, from the field of psycho-acoustics we know that the distortion threshold is much higher at those lower frequencies.
(btw, I am NOT talking about IMD products FROM those lower frequencies, that's a different thing!)
This would suggest that we can't just conclude that the 20% distortion limit of compliance is as important as the same distortion level of BL?
Which brings me to the second subject;
If we practically remove any excursion, I think we are basically only left with HD distortion products?
Or in more simple words, just the THD graph we can measure.
Again for simplicity, we keep Le(i) and all other non-excursion issues out of this, because those still exist.
I particularly want to dive into two things, let's start with one first, The importance of Kms(x)
We all want to strive for best possible performance and a good bang for the buck.
Currently, the general approach for some people, is just to go for lower distortion = more better.
Which on itself is fine, but it doesn't hold much real scientific foundation.
Besides, it often comes with a price, which doesn't make all projects very practical.
Let's recap first;
Obviously there are a bunch of parameters that will be influenced by the cone excursion.
Those are BL(x), Kms(X), Le(x) and in theory also Sd(x)
(although its significance has never been proven with objective data, in theory it's there).
Rms(x) is often not being considered and Mmd (not Mms, since this is connected to Sd!) is deemed to be a constant.
Just for simplicity, I will leave out other things like Le(i), Re(i) and Re(T) as well as Kms(T)
Those things are also not connected to the excursion, so they won't produce and intermodulation products.
We can quickly see what influence most of those parameters have by just looking at the definitions of the model of a driver.
In case of the compliance, there are only two that come to mind.
The resonance frequency, since;
As well as the Vas;
To a much lower extend also the Qms, therefor the Qts, although very limited.
If we compare this to the BL for example, we can already see that BL(x) has a much greater influence.
Mostly because in most (all) definitions, we are dealing with BL² (squared).
So any chance in BL will have a much bigger impact.
As well as in;
Meaning that BL doesn't only has an affect on the low-end, near Fs.
Since it's changes the height of the impedance peak drastically, therefor the overal Q of the system.
But it actual changes the overal sensitivity of the driver as well = modulation.
We can actually simulate this to visualize this a bit more. (although steady state)
In this case a ported system is being used to amplify those changes a bit.
Gray = original, no changes, Yellow = 50% Cms (20% distortion), Green = 82% BL (10% dist)
All other things are being kept equal.
From this graph, it can be seen that even BL at just 82% has a very drastic effect on the overal system response!
Fyi, we are not even talking about distortion numbers at this point!
On the other hand, even a drop of 50% of the compliance doesn't show a very big difference.
Anyway, back to compliance.
This kept me thinking.
Because this suggest that compliance only has a very limited performance penalty.
1 - only at the low-end, up till say about 2*Fs
2 - little change in overal system performance
3 - therefor, there is barely any intermodulation going on (IMD)
So I decided to dive a bit deeper into this.
A good start can be found in;
"Loudspeaker Distortion – Measurement and Perception Part 1: Regular distortion defined by design"
https://www.klippel.de/fileadmin/klippel/Files/Know_How/Literature/Papers/Loudspeaker regular signal distortion caused by design_part 1_Klippel_Werner.pdf
On page 8 the following can be found;
As well as the case for a multi-tone signal;
Searching a bit more, we can find some more clues in the by now famous document;
"Loudspeaker Nonlinearities – Causes, Parameters, Symptoms" by Klippel
https://www.klippel.de/fileadmin/klippel/Files/Know_How/Literature/Papers/Loudspeaker Nonlinearities_Causes,Parameters,Symptoms_06.pdf
(people should know that thing by heart by now ! )
Although this document doesn't give much direct proof of things, it at least gives us a nice summary.
On page 36 the following table can be found;
So this basically proves my suspicion, that the impact of a non-linear compliance is very limited.
Not only that, but the symptoms of it only result in HD products and no IMD products.
But that leaves a question open.
Many of us look and compare those wonderful LSI Kms(x) and BL(x) graphs.
Using either 10% distortion or 20% distortion limits as guidelines.
However, that is clearly not the entire story I think?
Because it's obvious from everything above that a drop in BL is FAR more significant then just a drop in compliance?
In that case we are not just talking about HD distortion, but IMD as well as change of the actual system response.
The last one is I think maybe even the most audible of all of these things!
We are talking 3dB difference here as well as changing the Q of the system drastically!
The compliance is only responsible for some HD distortion below, near and around Fs.
At the same time, from the field of psycho-acoustics we know that the distortion threshold is much higher at those lower frequencies.
(btw, I am NOT talking about IMD products FROM those lower frequencies, that's a different thing!)
This would suggest that we can't just conclude that the 20% distortion limit of compliance is as important as the same distortion level of BL?
Which brings me to the second subject;
If we practically remove any excursion, I think we are basically only left with HD distortion products?
Or in more simple words, just the THD graph we can measure.
Again for simplicity, we keep Le(i) and all other non-excursion issues out of this, because those still exist.
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Yes I know, I thought I put it in there.
Yes, in theory I agree with this.
I only question its practical significance.
So I would love to see actual data on that.
This was also written above btw.
Up till then it's just a hypothesis for me, falling in the same realm as amplifiers or other things in the chain that "need" the lowest amount of distortion.
Which on itself doesn't hold much scientific foundation and only follows the idea of; less = more better.
Without actual data, there is no way of knowing how significant it will be.
I have done my own error analysis on it, maybe will share that soon when it's nice an tidy, but the numbers don't look mind blowing.
Anyway, I consider that point off-topic for now
agree about Kms(x) not playing a big role in IMD compared to eg Bl modulation. See also https://purifi-audio.com/blog/tech-...o-whats-the-point-of-low-distortion-drivers-4