ucla88 said:
What you state "And if you correct for the FR curve exactly to flat, you have equalized the energy storage away" is true only if the systems under consideration are linear, time-invariant systems (LTIS), and minimum phase systems.
I was generous previously in saying that they are LTIS, since for soft well behaved non-linearities we learn that this analysis is valid for the small signal case where the purturbations about an operating point are small. Driver non-linearity may be soft as far as the driver motor goes, however non-linear distortion due to breakup is there even for small purturbations, and so they do not fit the model as well as basic electronic circuits. Applying this theory is a small signal approximation assuming a linear system, which drivers are not for the large signal case where the non-linearities are much stronger and the approximation is even worse.
Drivers also do not fit the time invariant criterion very well due to voice coil heating and inductance modulation. This depends on the driver obviously, ones with good heat capacity in the voice coil and reduced VC inductance are a better fit.
Exactly how good the theoretical approximations fit depend on the drivers involved, the drive level and many factors. Those making wishful thinking based, theoretical blanket statements need to open their eyes to these considerations. The theory is a small signal approximation, a good engineer comes to understand when the approximation is good enough or at least provides some useful information, but knows that it is only an approximation. But to say that two equalized speakers are then exactly the same is more wishful thinking for the case of speaker drivers. This claim is more valid for electronic circuits, which are a better fit for the theory being more linear.
If I have chosen a driver that has some energy storage issues, I like to see if there is an acoustical solution to bring them under control and reduce/eliminate the energy storage.
Pete B.
PB2 said:
Hi Pete,
While you're comments are correct, I'm not sure they are all that germane.
A loudspeaker unit, though not necessarily a multiway system is minimum phase.
As far as linear time invariance, this applies to the entire set of transforms. So you can't use a CSD to look as this as well, since the CSD also requires LTI.
Also, you're confusing some real world, nonlinearities with linear distortion. heating and inductance modulation mostly cause nonlinear distortion, though there may very well be some linear distortion with, say vc heating. Clearly, as I spend an enormous time documenting on my site, drivers with the same FR do not have the same nonlinear distortion. They do, to a high degree, have the same linear distortion. And a CSD will by no means clarify any subtle energy storage issues inherently better than an FR curve.
Then how would we know if the claim is true or not? That wouldn't make any sense.
This is very true. I am actually impressed that you knew that. Maybe you should keep that in mind when looking at the response curves.
Yes, this is true, but most manufacturers provide them that way and when looking at factory specs that is all you have to go on.
No worries though. I'll oblige you on this one.
Nice request Dave for all that additional information. Maybe I should just send you an impulse file so you can print out your own CSD to look at prior to your read on the curves.
Come on Dave, the claim is that you can see it all from the response curve.
See below. Responses with no smoothing.
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These are pretty easy by the way. Let's see how this goes. I may through in some more (far field) measurements that are real dozes.
Let's not forget my two questions:
1) In each graph what area has the greatest amount of stored energy?
2) Of the three graphs which woofer as the greatest amount of stored energy and where?
5th Element you hit the nail on the head in some of that post.
You can equalize away some stored energy by attenuating areas that ring, or area that have an excess of stored energy. However if you hit the driver hard enough to make it move 3mm (just an example) it will have the same inertia and stored energy regardless of the components that were in line with it.
ucla88 said:
Yes, of course the CSD is subject to the same issues, however this is not the point that I'm making. Actually, it seems that you are missing my point here when you make this statement: "Also, you're confusing some real world, nonlinearities with linear distortion" I am not confusing them, rather I'm pointing them out since the linear model is based on the assumption that the system is linear when in reality it is not. The linear model is an approximation that is less good when a system is in reality non-linear.
My point is not to argue the value of the CSD, rather the claim that an equalized metal cone driver with significant breakup is as good as a softer cone driver with fewer breakup issues.
I have seen your work, it is good and I thank you for providing it on the net.
Pete B.
Hi Pete,
Well,
I really don't mean to imply that "if it has the same FR, it should sound identical." That's a much more complex subject. I agree that often, certain drivers have a characteristic sound apart from their FR curve. The exact nature of this is not always clear. Whether it's linear distortion, nonlinear, or implimentation issues...
In defense of metal cones though-
While I've heard a lot of crummy metal systems, well engineered ones don't seem to have that "metal sound." SL's orion for example. I never got the feeling it had any "metal sound" --harseness or smear. (I use those terms loosely...)
My point in all this is to try to hammer home the point that the CSD does not show some special independent "energy storage property." whose essence, at least mathematically, isn't buried in the FR curve.
I mean, look at the curves Danny just reposted. With slightly higher resolution to the FR curve, the analysis is a little different. So the error was poor resolution measurements to begin with. (and in fact, more measurements would be needed of the drivers Danny posted in order to truely evaluate the drivers.) Those deep nulls, if real and not nearfield artifact, would not be practically equalizable and there would be residual energy storage.
Well,
I really don't mean to imply that "if it has the same FR, it should sound identical." That's a much more complex subject. I agree that often, certain drivers have a characteristic sound apart from their FR curve. The exact nature of this is not always clear. Whether it's linear distortion, nonlinear, or implimentation issues...
In defense of metal cones though-
While I've heard a lot of crummy metal systems, well engineered ones don't seem to have that "metal sound." SL's orion for example. I never got the feeling it had any "metal sound" --harseness or smear. (I use those terms loosely...)
My point in all this is to try to hammer home the point that the CSD does not show some special independent "energy storage property." whose essence, at least mathematically, isn't buried in the FR curve.
I mean, look at the curves Danny just reposted. With slightly higher resolution to the FR curve, the analysis is a little different. So the error was poor resolution measurements to begin with. (and in fact, more measurements would be needed of the drivers Danny posted in order to truely evaluate the drivers.) Those deep nulls, if real and not nearfield artifact, would not be practically equalizable and there would be residual energy storage.
Describe the conditions and define your term
I don't need the impulse file. I could use the SPLTracer to create an SPL file, generate the minimum-phase, then create an impulse from it from which I could then generate a CSD, based on the available SPL data. I don't want that.
If one could rely on those curve. State the conditions, you still haven't done that. Frankly, given your previously bad 12ms graph, I want to know the precise conditions of the measurements, especially given the first and third curve. That should be simple enough for you to do. If I had to comment on them now, I'd say that the measurements of those two were compromised. Specify the condtiions
Define "greatest amount". No matter what I think it is, you'll likely call it something else, so we likely won't agree on that, either. One can't respond without knowing this. You've apparently got some unit of measure for this. In addition, anything below 1K will not have accurate enough data given the limited low end extension due to the 4ms window used.
This is where your misunderstanding comes in, I'm really surprised that you don't recognize it. Maybe I should no longer be. As 5th element said:
What matters here is that the crossover, properly designed, will attenuate the signal so that when coupled with the transfer function of the driver, including the FR non-linearities at the tested level, will have a combined transfer that can totally eliminate the ringing at the test levels used. The signal thus supplied is precisely that signal required to achieve the desired output. This includes the driver's resonances and transfer function. It's not a damn bit different than tapering the signal for a highpass or a lowpass. I hope you can grasp that concept. If you don't, explain how a crossover does work.
Let me ask, what do you think is happening in the area of the Fs of the driver in a box for a woofer or a mid using the box as highpass? The driver has a HUGE resonance there. The design takes that into account to yield a design highpass. In a midrange, there may also be a crossover that takes that into account to deliver the desired combined transfer function. It is absolutely no different for any other area of equalization. Or do you think that the driver Fs resonance somehow does not follow the same physics of resonance?
Motor non-linear distortion, as I pointed out earlier, is certainly a consideration in a driver, but that's a totally separate issue WRT linear distortion.
And I really suspect contaminated or compromised measurements, in part or in whole. All three must be the same, valid and the conditions known. Otherwise it's an exercise in futility.
In the end, the CSD does nothing to provide any information needed to design. The FR shows the influence of the resonances. There is nothing in it useful towards designing a proper crossover. It's essentially useless for design. The FR has all that's needed.
Dave
Danny said:
I don't need the impulse file. I could use the SPLTracer to create an SPL file, generate the minimum-phase, then create an impulse from it from which I could then generate a CSD, based on the available SPL data. I don't want that.
If one could rely on those curve. State the conditions, you still haven't done that. Frankly, given your previously bad 12ms graph, I want to know the precise conditions of the measurements, especially given the first and third curve. That should be simple enough for you to do. If I had to comment on them now, I'd say that the measurements of those two were compromised. Specify the condtiions
Define "greatest amount". No matter what I think it is, you'll likely call it something else, so we likely won't agree on that, either. One can't respond without knowing this. You've apparently got some unit of measure for this. In addition, anything below 1K will not have accurate enough data given the limited low end extension due to the 4ms window used.
This is where your misunderstanding comes in, I'm really surprised that you don't recognize it. Maybe I should no longer be. As 5th element said:
What matters here is that the crossover, properly designed, will attenuate the signal so that when coupled with the transfer function of the driver, including the FR non-linearities at the tested level, will have a combined transfer that can totally eliminate the ringing at the test levels used. The signal thus supplied is precisely that signal required to achieve the desired output. This includes the driver's resonances and transfer function. It's not a damn bit different than tapering the signal for a highpass or a lowpass. I hope you can grasp that concept. If you don't, explain how a crossover does work.
Let me ask, what do you think is happening in the area of the Fs of the driver in a box for a woofer or a mid using the box as highpass? The driver has a HUGE resonance there. The design takes that into account to yield a design highpass. In a midrange, there may also be a crossover that takes that into account to deliver the desired combined transfer function. It is absolutely no different for any other area of equalization. Or do you think that the driver Fs resonance somehow does not follow the same physics of resonance?
Motor non-linear distortion, as I pointed out earlier, is certainly a consideration in a driver, but that's a totally separate issue WRT linear distortion.
And I really suspect contaminated or compromised measurements, in part or in whole. All three must be the same, valid and the conditions known. Otherwise it's an exercise in futility.
In the end, the CSD does nothing to provide any information needed to design. The FR shows the influence of the resonances. There is nothing in it useful towards designing a proper crossover. It's essentially useless for design. The FR has all that's needed.
Dave
There's little agreement as to which is best
Yes, the question is the degree to which a driver exhibits nonlinear distortion. The motor is probably the biggest contributor, so the diaphragm material (since all types are subject to it) becomes less of an issue except for the amplification of the nonlinear distortion due to the diaphragm FR nonlinearities. This does make a peaky hard diaphragm a more difficult example, but then a softer diaphragm has its own, different set of tradeoffs.
To go beyond small signal testing, mostly what gets discussed, a softer material usually has more even order linear distortion vs. a hard material, up until breakup, of course. For large signal testing, it is likely that a softer material will be less linear with signal level than a hard material. Hard materials are generally more "pistonic" in their useful bandpass. The challenge with hard ones is to select it appropriately for the target response so that there can be sufficient equalization to achieve that target. I'm doing it now with an older Seas W17EX 6.5" driver. Not an easy task, but it's coming out better than I anticipated.
The hard cone can indeed be equalized with a crossover to be just as linear, if not more so, than a softer one well into the stop band. The softer ones generally exhibit far more small deviations from linearity even in their bandpass that are almost never equalized. I know, that's almost exclusively what I prefer in my own systems. This may be where the even order distortion is involved. The soft material FR deviations from linearity that are also signal level dependent are likely to show up as additional linear distortion vs. the hard cone, within the desired passband, of course. Outside of that, the hard cone response can be controlled to be as good as a soft one with the right design, but it's more limited in range of use. That doesn't disqualify it at all. The skill (or lack thereof) of the designer is key.
This is where I'm still almost back on the fence. I like doped paper cones. They seem to sound better most of the time, at least those with which I've worked. The Accuton made me question this. Maybe it's the even order distortion in softer materials that is euphonic (as are tubes) and is what I like in them, I don't know for sure. However, I've heard some exceptional systems using hard cone drivers that I could probably just as easily live with. Each material has its own tradeoffs, but some can be mitigated in one driver or the other to be equal to the other in certain ways, never all of course.
Equalize a large peak in a hard cone and it will disappear as a decay ridge in the CSD. I don't need to look at a measurement to know this, I've seen it more than enough times in the past. The CSD just doesn't tell me anything about the driver that I can't get from the FR. I could design a system and never look at the CSD (pretty much always the case now) or study the CSD carefully for a driver and the crossover impact would zero. A good designer has no need of the CSD.
At high signal levels, the hard material is likely to remain pistonic through a larger range of driver levels for a properly designed bandpass than will a soft material. Distortion will probably increase more with drive level in the softer material when viewed as a delta of the distortion. The only way to know would be to do the distortion tests. The CSD is certainly not going to tell you anything in this regard. But since I seldom ever push my system so hard as to make that an issue, I expect that I'll continue to prefer my favorite doped paper midrange (12m/4631).
Dave
PB2 said:
Yes, the question is the degree to which a driver exhibits nonlinear distortion. The motor is probably the biggest contributor, so the diaphragm material (since all types are subject to it) becomes less of an issue except for the amplification of the nonlinear distortion due to the diaphragm FR nonlinearities. This does make a peaky hard diaphragm a more difficult example, but then a softer diaphragm has its own, different set of tradeoffs.
To go beyond small signal testing, mostly what gets discussed, a softer material usually has more even order linear distortion vs. a hard material, up until breakup, of course. For large signal testing, it is likely that a softer material will be less linear with signal level than a hard material. Hard materials are generally more "pistonic" in their useful bandpass. The challenge with hard ones is to select it appropriately for the target response so that there can be sufficient equalization to achieve that target. I'm doing it now with an older Seas W17EX 6.5" driver. Not an easy task, but it's coming out better than I anticipated.
The hard cone can indeed be equalized with a crossover to be just as linear, if not more so, than a softer one well into the stop band. The softer ones generally exhibit far more small deviations from linearity even in their bandpass that are almost never equalized. I know, that's almost exclusively what I prefer in my own systems. This may be where the even order distortion is involved. The soft material FR deviations from linearity that are also signal level dependent are likely to show up as additional linear distortion vs. the hard cone, within the desired passband, of course. Outside of that, the hard cone response can be controlled to be as good as a soft one with the right design, but it's more limited in range of use. That doesn't disqualify it at all. The skill (or lack thereof) of the designer is key.
This is where I'm still almost back on the fence. I like doped paper cones. They seem to sound better most of the time, at least those with which I've worked. The Accuton made me question this. Maybe it's the even order distortion in softer materials that is euphonic (as are tubes) and is what I like in them, I don't know for sure. However, I've heard some exceptional systems using hard cone drivers that I could probably just as easily live with. Each material has its own tradeoffs, but some can be mitigated in one driver or the other to be equal to the other in certain ways, never all of course.
Equalize a large peak in a hard cone and it will disappear as a decay ridge in the CSD. I don't need to look at a measurement to know this, I've seen it more than enough times in the past. The CSD just doesn't tell me anything about the driver that I can't get from the FR. I could design a system and never look at the CSD (pretty much always the case now) or study the CSD carefully for a driver and the crossover impact would zero. A good designer has no need of the CSD.
At high signal levels, the hard material is likely to remain pistonic through a larger range of driver levels for a properly designed bandpass than will a soft material. Distortion will probably increase more with drive level in the softer material when viewed as a delta of the distortion. The only way to know would be to do the distortion tests. The CSD is certainly not going to tell you anything in this regard. But since I seldom ever push my system so hard as to make that an issue, I expect that I'll continue to prefer my favorite doped paper midrange (12m/4631).
Dave
Alright, I still don't think the original posters point has been addressed at all - why is the CSD for the L18 so much worse than that of the P18?
And if you're going to tell me that CSD's and burst decay measurements don't matter because all you have to do is equalize the FR, then give real world examples that show your point ... not theoretical ones.
I've had this discussion before with Danny and others in the past, and from my experience there's more direct correlation between the sound of a speaker and it's energy stoarge than any other measurement - even frequency response. I've measured commercial products before from Dynaudio Evidence series, Revel, and Von Schweikert that sound great but don't measure anywhere near flat - and further measurements show good to great measurement of energy storage. And when I listen to my RS180/RS28A MTM that has a flat FR with low distortion across the board but sounds like crap, all I can reason the culprit can be is energy storage.
And if you're going to tell me that CSD's and burst decay measurements don't matter because all you have to do is equalize the FR, then give real world examples that show your point ... not theoretical ones.
I've had this discussion before with Danny and others in the past, and from my experience there's more direct correlation between the sound of a speaker and it's energy stoarge than any other measurement - even frequency response. I've measured commercial products before from Dynaudio Evidence series, Revel, and Von Schweikert that sound great but don't measure anywhere near flat - and further measurements show good to great measurement of energy storage. And when I listen to my RS180/RS28A MTM that has a flat FR with low distortion across the board but sounds like crap, all I can reason the culprit can be is energy storage.
TurboFC3S said:
Because it is frequency response plot is not as smooth as frequency response plot of PL18. At its frequency response it's dip at 1Khz is not as smooth as the dip of PL18 at 900Hz. It also has peak/knee at 700Hz. Another knee at 2Khz, P18 has one knee at 1.8Khz, but it is still smoother. The dip of L18 at 3.1Khz has a very sudden turn, it will ring there, and so at 4Khz as well. In comparison, P18 has a smaller peak at 2.7Khz, and a relatively smoother dip at 3Khz, but its peak at 3.5Khz is sharp with sudden bends, it will ring there also. After that peak, P18 rolls of very smoothly till amplitude dimishes to low level. L18 on the other hand as frequency rises has zigy zig zag frequency response which means ringy ding ding
And conventional drivers by great majority are safe to be considered minimum phase and LTI in the context of measurements taken for FR, impulse response, burst tone etc. Try this if you don't believe me, take a driver and record its impulse response. Then apply it a burst tone, and record its burst tone response. Then generate the same burst tone in computer, convolve it with the driver's impulse response, and plot this simulated response together with the recorded burst response, compare the two. And moreover, take the FR of the tone burst, and generate a simulated FR of tone burst using the impulse response measurement at the same point. Again plot these to FR and compare. They will with the exception of calculation artifacts will be same. Been there done that.
One well known exception is whizzer cone drivers, they can exhibit nonminimum phase behaviour, and that is because they are like two drivers with very different FR, whose output then gets summed.
In summary, drivers are safe to consider minimum phase, then there is a direct relationship between their frequency response amplitude plot and CSD, or any other so called energy storage measurements. If there is an "energy storage" in a minimum phase device, it will show as a non flat, peak, dip, bend etc in its FR amplitude plot somewhere.
CSD is visually good to show resonances with its ridges. It is like looking at same data from a different view, it can be useful, and it can also be used to deceit as well.
A CSD will show the "energy storage" of a non-minimum phase system with a flat or very smooth amplitude very openly, like the CSD of an all pass sum filter. But that can be seen if we look at the phase response also in that case.
Then there is the off axis response of the drivers, which makes things more complex when it comes to compare which driver is better, drivers output are 3-D, the FR, CSD, tone burst are only for a single point in space, and there is the nonlinearity aspects of drivers to compare, and then how the phychoacoustics play into what we hear as "better" etc. etc. etc. etc.....
Re: There's little agreement as to which is best
I'm not making any claims about the sound of any drivers or systems, as this was not my point, it requires too many controls to be valid, and there are also psychoacoustic considerations. I was addressing some sweeping claims made about the theory involved in EQing a metal driver to work as well as a soft cone driver. I also do not make any sweeping claims about driver cone materials, I prefer to treat drivers on a case by case basis.
Let me repeat, I have no particular favor for CSD plots. I do find that they tend to magnify FR issues and I find them useful in that regard.
I'm seeing a lot of speculation from you and I would not agree with many of the points you're trying to make here. Let me just comment on a few, and let's keep in mind that this thread was a comparision of the L18 and P18.
The L18 has 7 peaks in the amplitude response below 20 kHz, and agreed if the driver was a LTIS and minimum phase then notching all 7 and EQing the response to match another driver would result in identical small signal performance. Are you really going to notch all 7 peaks? I think not. Is it practical? I think not. Will one notch work "good enough" in a practical real system, perhaps, but this was not the claim made in this thread.
Second, and I think you miss this point, metal cone drivers do not meet the requirement for a soft non-linearity for the theory that some here are claiming applies, which means it is not valid even for the small signal case. It certainly does not apply to the medium-large signal case.
There is non-linear distortion associated with the peaks that you claim can be EQ out, and therefore theory that relies on a LTIS does not apply. Let me take a simpler case and quote from one of andy_c's posts (from: http://www.diyaudio.com/forums/showthread.php?postid=545712#post545712): "given two memoryless nonlinearities f(x) and g(x) in cascade that don't interact with each other, the combined nonlinearity is g(f(x))" .... "But nonlinear input-output descriptions of cascaded networks do not commute."
This means that given two non-linear transfer functions, you cannot even change the order of the functions let alone use one linear function to EQ a non-linear one.
g(f(x)) is not equal to f(g(x)) for the non-linear case.
This is a fundamental property of non-linear systems.
I would agree that the claim is a fairly good approximation for drivers with soft non-linearities.
Further, it is obvious that the P18 has better distortion performance than the L18 at both low and high frequencies. It looks as if they improved the motor but I cannot be sure not having done the tests myself.
Pete B.
dlr said:
I'm not making any claims about the sound of any drivers or systems, as this was not my point, it requires too many controls to be valid, and there are also psychoacoustic considerations. I was addressing some sweeping claims made about the theory involved in EQing a metal driver to work as well as a soft cone driver. I also do not make any sweeping claims about driver cone materials, I prefer to treat drivers on a case by case basis.
Let me repeat, I have no particular favor for CSD plots. I do find that they tend to magnify FR issues and I find them useful in that regard.
I'm seeing a lot of speculation from you and I would not agree with many of the points you're trying to make here. Let me just comment on a few, and let's keep in mind that this thread was a comparision of the L18 and P18.
The L18 has 7 peaks in the amplitude response below 20 kHz, and agreed if the driver was a LTIS and minimum phase then notching all 7 and EQing the response to match another driver would result in identical small signal performance. Are you really going to notch all 7 peaks? I think not. Is it practical? I think not. Will one notch work "good enough" in a practical real system, perhaps, but this was not the claim made in this thread.
Second, and I think you miss this point, metal cone drivers do not meet the requirement for a soft non-linearity for the theory that some here are claiming applies, which means it is not valid even for the small signal case. It certainly does not apply to the medium-large signal case.
There is non-linear distortion associated with the peaks that you claim can be EQ out, and therefore theory that relies on a LTIS does not apply. Let me take a simpler case and quote from one of andy_c's posts (from: http://www.diyaudio.com/forums/showthread.php?postid=545712#post545712): "given two memoryless nonlinearities f(x) and g(x) in cascade that don't interact with each other, the combined nonlinearity is g(f(x))" .... "But nonlinear input-output descriptions of cascaded networks do not commute."
This means that given two non-linear transfer functions, you cannot even change the order of the functions let alone use one linear function to EQ a non-linear one.
g(f(x)) is not equal to f(g(x)) for the non-linear case.
This is a fundamental property of non-linear systems.
I would agree that the claim is a fairly good approximation for drivers with soft non-linearities.
Further, it is obvious that the P18 has better distortion performance than the L18 at both low and high frequencies. It looks as if they improved the motor but I cannot be sure not having done the tests myself.
Pete B.
quote,
There is non-linear distortion associated with the peaks that you claim can be EQ out, and therefore theory that relies on a LTIS does not apply. Let me take a simpler case and quote from one of andy_c's posts (from: http://www.diyaudio.com/forums/show...5712#post545712): "given two memoryless nonlinearities f(x) and g(x) in cascade that don't interact with each other, the combined nonlinearity is g(f(x))" .... "But nonlinear input-output descriptions of cascaded networks do not commute."
This means that given two non-linear transfer functions, you cannot even change the order of the functions let alone use one linear function to EQ a non-linear one.
g(f(x)) is not equal to f(g(x)) for the non-linear case.
This is a fundamental property of non-linear systems
Pete,
you're again confusing linear and nonlinear distortion. The peak in the L18's metal cone represents linear distortion and can be eq'd as it is a linear phenomena.
There is nonlinear distortion associated with the peak, but it's not from the peak per say.
The increase in nonlinear distortion occurs as follows-
Say that a motor has high 3rd order nonlinear distortion products. A driving signal at 2.3k will have an actual 3rd order peak at 7k. Well, what do you know, that's exciting the bell resonance at 7k of the L18. So the distortion product is magnified significantly.
Or, to put it another way, the nonlinear distortion product is magnified by a linear distortion.
Equalizing the bell resonance will eliminate the linear distortion associated with the 7k peak, but it will not reduce the magnitude of distortion. You cannot notch out this extra distortion because it is generated in the motor and amplified by the cone. putting a notch at 7k won't lower the 2.3k driving force that caused the distortion in the first place.
So the moral of the story is that, to avoid significant distortion, you have to look at the nonlinear distortion products and the peak, and carefully choose your cross point.
For example, in the L18, a 2.5k cross would be a poor choice, no matter how steep the xover because of this.
And, none of this shows in a CSD. Or, an FR curve.
There is non-linear distortion associated with the peaks that you claim can be EQ out, and therefore theory that relies on a LTIS does not apply. Let me take a simpler case and quote from one of andy_c's posts (from: http://www.diyaudio.com/forums/show...5712#post545712): "given two memoryless nonlinearities f(x) and g(x) in cascade that don't interact with each other, the combined nonlinearity is g(f(x))" .... "But nonlinear input-output descriptions of cascaded networks do not commute."
This means that given two non-linear transfer functions, you cannot even change the order of the functions let alone use one linear function to EQ a non-linear one.
g(f(x)) is not equal to f(g(x)) for the non-linear case.
This is a fundamental property of non-linear systems
Pete,
you're again confusing linear and nonlinear distortion. The peak in the L18's metal cone represents linear distortion and can be eq'd as it is a linear phenomena.
There is nonlinear distortion associated with the peak, but it's not from the peak per say.
The increase in nonlinear distortion occurs as follows-
Say that a motor has high 3rd order nonlinear distortion products. A driving signal at 2.3k will have an actual 3rd order peak at 7k. Well, what do you know, that's exciting the bell resonance at 7k of the L18. So the distortion product is magnified significantly.
Or, to put it another way, the nonlinear distortion product is magnified by a linear distortion.
Equalizing the bell resonance will eliminate the linear distortion associated with the 7k peak, but it will not reduce the magnitude of distortion. You cannot notch out this extra distortion because it is generated in the motor and amplified by the cone. putting a notch at 7k won't lower the 2.3k driving force that caused the distortion in the first place.
So the moral of the story is that, to avoid significant distortion, you have to look at the nonlinear distortion products and the peak, and carefully choose your cross point.
For example, in the L18, a 2.5k cross would be a poor choice, no matter how steep the xover because of this.
And, none of this shows in a CSD. Or, an FR curve.
Re: Re: There's little agreement as to which is best
Actually metal cone drivers tend to be more linear (before the amplification effect of their response peak startes) than soft versions, based on some the Seas excel drivers factory measurements which is on their archieve section of their website. They used to have paper, glass fiber and metal versions of some of their Excel drivers, using same motor. You are assuming just because the cone is metal and rings it must be a distortion generator, and based on what?
If what you say is true, then we shouldn't even attemp to take FR measurements of metal cone drivers, because say we use a sine sweep to take the FR measurement. How do we get the FR? We need to take FFT of the sweep and FFT of the measured response, then divide them to arrive at the FR. And since FFT is a linear operation and the division of the two FR to arrive at the final assumes the system is linear, it means the FR we measured is useless, since the metal cone drivers are so badlly nonlinear. So may be they don't have those breakup peaks that show up in their FR plots? And the CSD is worse, it is repeated FFT of the impulse response, lots of operations that assume a linear system. And the impulse response that the CSD is being calculated from is the result of couple of linear operations that assume a linear system also. Note the measurement systems don't use an impulse as input, they use a sine sweep, or MLS or some other signal. Therefor to arrive at impulse response they have to do some operations and at the end an inverse FFT, which all are done at the assumption that the system is linear.... What is the FR of a nonlinear system anyways? How do you define it?
Instead of looking at nonlinearity as objection to correcting the FR (and therefore time response since they are minimumphase safe enough), I would look at what goes on at off axis. If you correct on axis, how the off axis response becomes, and that effectst the sound heard.....
PB2 said:
Actually metal cone drivers tend to be more linear (before the amplification effect of their response peak startes) than soft versions, based on some the Seas excel drivers factory measurements which is on their archieve section of their website. They used to have paper, glass fiber and metal versions of some of their Excel drivers, using same motor. You are assuming just because the cone is metal and rings it must be a distortion generator, and based on what?
If what you say is true, then we shouldn't even attemp to take FR measurements of metal cone drivers, because say we use a sine sweep to take the FR measurement. How do we get the FR? We need to take FFT of the sweep and FFT of the measured response, then divide them to arrive at the FR. And since FFT is a linear operation and the division of the two FR to arrive at the final assumes the system is linear, it means the FR we measured is useless, since the metal cone drivers are so badlly nonlinear. So may be they don't have those breakup peaks that show up in their FR plots?
And the CSD is worse, it is repeated FFT of the impulse response, lots of operations that assume a linear system. And the impulse response that the CSD is being calculated from is the result of couple of linear operations that assume a linear system also. Note the measurement systems don't use an impulse as input, they use a sine sweep, or MLS or some other signal. Therefor to arrive at impulse response they have to do some operations and at the end an inverse FFT, which all are done at the assumption that the system is linear.... What is the FR of a nonlinear system anyways? How do you define it?Instead of looking at nonlinearity as objection to correcting the FR (and therefore time response since they are minimumphase safe enough), I would look at what goes on at off axis. If you correct on axis, how the off axis response becomes, and that effectst the sound heard.....
ucla88 said:
I think you are the one confused, you seem to think you can just dismiss the non-linear aspects of the system and say we're just going to look at the linear case, then you apply a theorem that requires a linear system which is not the case in reality.
The source of the distortion does not matter, if it is the driver motor fine, as soon as there is a significant non-linearity in the system it matters where you put frequency response correction, and therefore notching ahead of the non-linear motor does not work, just as you have concluded on your own. I knew that, it is the point I've been making and you seem to *think* I don't get. I get it, it is what I've been trying to explain to you. More clearly, you claim that the motor is non-linear, the metal cone simply introduces a frequency response factor that "amplifies" certain harmonics, my point exactly is that a filter in front of the motor that equalizes the FR to match another driver will not match or reduce the distortion. The distortion amplification is still there, that has been one of my points all along.
Your own statement "For example, in the L18, a 2.5k cross would be a poor choice, no matter how steep the xover because of this." contradicts the previous statements that as long as you EQ the performance is the same. Now your saying as long as you EQ and do not use the driver above 2.5 K, well now that is a different claim.
OK, I'm going to bow out of this now, I certainly understand this, and it seems you do now also. I'm getting tired of you jumping to the conclusion that I don't get it, I'm professionally trained in this area thank you.
Pete B.
One possible answer: Curve fitting.
In order to obtain smooth-looking curves from discrete data points, the software has to use some form of curve fitting to fill in the the gaps. The L18 response has a sharp discontinuity around 6kHz, and this could cause a high-order polynomial "best fit" curve to contain a lot of ringing above and below that frequency.
Another possibility: a DC offset before the start of the impulse, or after it finishes
This is a type of glitch in the algorithm, creating similar problems to using a square window instead of a Hanning/or other window. A long sampling period after and before the impulse is important, because you can never really be sure what DC level is used in the calculations.
Just a couple of ideas
Cheers,
Re: Re: There's little agreement as to which is best
My comments never related to those drivers, I responded to specific erroneous statements that are proveaby false. I will be posting at my site, after I have time to finish the work, empirical proof that hard cone resonance peaks can indeed be absolutely controlled. Would one do that with all of them? No. Could that be done? Yes. Is that practical? No, not without DSP. But the fact that they can be is the topic of the discussion here. I will also do small signal and large signal measurements, though I don't plan on doing any compression tests requiring significant voice coil heating.
I have also, for many, many years, used CALSOD to recreate with fine detail every single tiny peak in a measurement up to 20KHz, even in large drivers, and have that mode used to generate the Hilbert-Bode phase. The phase thus generated matches precisely the measured phase. Raw drivers, with rare exception, are minimum-phase devices. They can be modified with a crossover that has a minimum-phase transfer response that can and will result in a minimum-phase driver response for the correction of non-linearities. Were that not so, CAD software for speaker design would not work.
Coincidentally, I was recently reading for the first time an AES article on CALSOD presented by the designer that included reference to the minimum-phase nature of raw drivers. To quote:
See "Simulation and Optimization of Multiway Loudspeaker System Using a Person Computer", by Witold Waldman, Audio Engineering Society, September 1988. I'll leave it to you to research in more detail if you care. As for me, I know that they are minimum-phase devices. That's no speculation on my part. I have gone well beyond the "working range" and modeled raw driver FR up to 22KHz in fine detail. They are still minimum-phase. CALSOD uses minimum-phase elements as the fundamental building block for creating a CAD model of FR response from which the H-B phase is generated. There is never any disagreement between measured and modeled phase up to the limit. It is a time consuming task, but I have done that on several occasions over the years.
No, I think not as well. But handling that is part of the art of speaker design.
That was just not what was at issue. What was at issue was whether or not it was even possible. That should no longer be at issue. I will be following up over the next few days, over the weekend I hope, with a post of some initial measurements that directly support my points. I've been listening to a set of speakers with a peaky driver for a few weeks now, but I'm continually refining the crossover. Fortunately, I have SoundEasy and can use it's Digital Filter mode and not have to construct a physical crossover, though I will once I've finalized it.
Can't disagree in large part. All drivers have breakup, thus all drivers are compromises in the bandpass and the stopband, soft as well as hard.
One notch very well might, it's case dependent. But the claim was related to possibility, not practicality. Even so, the posting of a crossover for the said peaky driver is "good enough" in the stop band. You may be surprised at just how insignificant the higher mode resonances will be. I'll even post CSD graphs!!!!!
Here I believe it is you who may be using conjecture and are in error. It is valid for the FR linear system characteristic. Even so, as I pointed out, ALL drivers have non-LTI characteristics. I'm puzzled as to why you have formed this opinion. Years of AES papers, the least of which is the one quoted, contradict that, I believe. The typical driver is a minimum-phase device. The motor non-linearity is an issue, but it's primarily the motor, not the diaphragm material, that is the culprit. That exists in all motors. It is easily demonstrated in the distortion measurements, by far the best way to analyze a driver for this influence. But that does not alter the linear response characteristics that are LTI. The linear distortion of the diaphragm does influence the amplification of the nonlinear motor influences, yes, but the linear FR is fully minimum-phase. We do need to be more precise if this level of detail is to be debated.
This is probably the misunderstanding between us. I do not claim that nonlinear distortion can be equalized, never have, never will. I do claim that the FR nonlinearities that are linear functions can be equalized and I will be providing fully documented emprical proof when I finish the crossover and can write up the page to post at my site. I had planned on this only for presenting a possible crossover redesign for a system that I recently purchased, but it will serve this purpose well in addition.
Now are any drivers absolutely LTI? No, none are. Are they reasonably so? Yes. Of course one of the factors between drivers is, indirectly, how close to LTI are they? The better drivers have better heat dissipation thus lower compression thus are closer to LTI. Drivers with better motors likely have copper clad voice coil gaps that mitigate dynamic gap Bl modulation (if I've got the term correct), that helps to making it LTI. But in most cases, practically all, the design issues related to this are generally not associated with the breakup and driver FR nonlinearities, it is the low level T/S parameters that used in the box design, though it will affect the driver across the board to one extent or another and choosing the driver for the target that best fits, including distortion considerations when that data is available. Also, not many folks have access to a Klippel system or similar to assist with a higher signal level design. Certainly most who may read this do not, I believe. But the T/S parameters, though they can be highly affected by heat compression, still are used and still are fairly reliable for system design.
I believe that for practical purposes, all typical drivers a reasonably "soft" as you say. Certainly so for the FR linear characteristics. CAD models would break down for drivers that don't exhibit this, but in fact, essentially all drivers can be modeled for FR very accurately due to their minimum-phase nature.
I'm sure that zaph would be much better at addressing this than I.
Just as I was about to post I saw Feyz' post, but I'm not going to edit mine. If you has data correcting anything in mine, I thank him for posting.
Dave
[/QUOTE]
PB2 said:
My comments never related to those drivers, I responded to specific erroneous statements that are proveaby false. I will be posting at my site, after I have time to finish the work, empirical proof that hard cone resonance peaks can indeed be absolutely controlled. Would one do that with all of them? No. Could that be done? Yes. Is that practical? No, not without DSP. But the fact that they can be is the topic of the discussion here. I will also do small signal and large signal measurements, though I don't plan on doing any compression tests requiring significant voice coil heating.
I have also, for many, many years, used CALSOD to recreate with fine detail every single tiny peak in a measurement up to 20KHz, even in large drivers, and have that mode used to generate the Hilbert-Bode phase. The phase thus generated matches precisely the measured phase. Raw drivers, with rare exception, are minimum-phase devices. They can be modified with a crossover that has a minimum-phase transfer response that can and will result in a minimum-phase driver response for the correction of non-linearities. Were that not so, CAD software for speaker design would not work.
Coincidentally, I was recently reading for the first time an AES article on CALSOD presented by the designer that included reference to the minimum-phase nature of raw drivers. To quote:
See "Simulation and Optimization of Multiway Loudspeaker System Using a Person Computer", by Witold Waldman, Audio Engineering Society, September 1988. I'll leave it to you to research in more detail if you care. As for me, I know that they are minimum-phase devices. That's no speculation on my part. I have gone well beyond the "working range" and modeled raw driver FR up to 22KHz in fine detail. They are still minimum-phase. CALSOD uses minimum-phase elements as the fundamental building block for creating a CAD model of FR response from which the H-B phase is generated. There is never any disagreement between measured and modeled phase up to the limit. It is a time consuming task, but I have done that on several occasions over the years.
No, I think not as well. But handling that is part of the art of speaker design.
That was just not what was at issue. What was at issue was whether or not it was even possible. That should no longer be at issue. I will be following up over the next few days, over the weekend I hope, with a post of some initial measurements that directly support my points. I've been listening to a set of speakers with a peaky driver for a few weeks now, but I'm continually refining the crossover. Fortunately, I have SoundEasy and can use it's Digital Filter mode and not have to construct a physical crossover, though I will once I've finalized it.
Can't disagree in large part. All drivers have breakup, thus all drivers are compromises in the bandpass and the stopband, soft as well as hard.
One notch very well might, it's case dependent. But the claim was related to possibility, not practicality. Even so, the posting of a crossover for the said peaky driver is "good enough" in the stop band. You may be surprised at just how insignificant the higher mode resonances will be. I'll even post CSD graphs!!!!!
Here I believe it is you who may be using conjecture and are in error. It is valid for the FR linear system characteristic. Even so, as I pointed out, ALL drivers have non-LTI characteristics. I'm puzzled as to why you have formed this opinion. Years of AES papers, the least of which is the one quoted, contradict that, I believe. The typical driver is a minimum-phase device. The motor non-linearity is an issue, but it's primarily the motor, not the diaphragm material, that is the culprit. That exists in all motors. It is easily demonstrated in the distortion measurements, by far the best way to analyze a driver for this influence. But that does not alter the linear response characteristics that are LTI. The linear distortion of the diaphragm does influence the amplification of the nonlinear motor influences, yes, but the linear FR is fully minimum-phase. We do need to be more precise if this level of detail is to be debated.
This is probably the misunderstanding between us. I do not claim that nonlinear distortion can be equalized, never have, never will. I do claim that the FR nonlinearities that are linear functions can be equalized and I will be providing fully documented emprical proof when I finish the crossover and can write up the page to post at my site. I had planned on this only for presenting a possible crossover redesign for a system that I recently purchased, but it will serve this purpose well in addition.
Now are any drivers absolutely LTI? No, none are. Are they reasonably so? Yes. Of course one of the factors between drivers is, indirectly, how close to LTI are they? The better drivers have better heat dissipation thus lower compression thus are closer to LTI. Drivers with better motors likely have copper clad voice coil gaps that mitigate dynamic gap Bl modulation (if I've got the term correct), that helps to making it LTI. But in most cases, practically all, the design issues related to this are generally not associated with the breakup and driver FR nonlinearities, it is the low level T/S parameters that used in the box design, though it will affect the driver across the board to one extent or another and choosing the driver for the target that best fits, including distortion considerations when that data is available. Also, not many folks have access to a Klippel system or similar to assist with a higher signal level design. Certainly most who may read this do not, I believe. But the T/S parameters, though they can be highly affected by heat compression, still are used and still are fairly reliable for system design.
I believe that for practical purposes, all typical drivers a reasonably "soft" as you say. Certainly so for the FR linear characteristics. CAD models would break down for drivers that don't exhibit this, but in fact, essentially all drivers can be modeled for FR very accurately due to their minimum-phase nature.
I'm sure that zaph would be much better at addressing this than I.
Just as I was about to post I saw Feyz' post, but I'm not going to edit mine. If you has data correcting anything in mine, I thank him for posting.
Dave
[/QUOTE]
Re: Re: Re: There's little agreement as to which is best
Let me put this in simple terms, let's take the very low frequency example where most drivers will be easily driven to high levels of distortion. Let's say we wanted to know the frequency response of a closed box woofer from 5 Hz to 100 Hz using pure tones, a nearfield mic and an RMS meter. Many systems driven at 5 Hz will produce over 100 % THD even at moderate levels, yes there is more level in the harmonics than the fundamental and if we measure the output with a meter we will obviously read the fundamental + THD and get a false reading. The solution is to do a filtered measurement, or one using a spectrum analyzer and obviously just take the level of the fundamental. This example was given when I studied audio engineering as an undergraduate.
Measurements in the presence of high levels of distortion are complex, more complex than with well behaved systems. Distortion will introduce an error into a frequency response measurement that assumes a linear system and does not provide filtering. Isn't this obvious?
I'm getting busy with some real work, so I'll bow out of this one also.
Pete B.
Feyz said:
Actually metal cone drivers tend to be more linear (before the amplification effect of their response peak startes) than soft versions, based on some the Seas excel drivers factory measurements which is on their archieve section of their website. They used to have paper, glass fiber and metal versions of some of their Excel drivers, using same motor. You are assuming just because the cone is metal and rings it must be a distortion generator, and based on what?
If what you say is true, then we shouldn't even attemp to take FR measurements of metal cone drivers, because say we use a sine sweep to take the FR measurement. How do we get the FR? We need to take FFT of the sweep and FFT of the measured response, then divide them to arrive at the FR. And since FFT is a linear operation and the division of the two FR to arrive at the final assumes the system is linear, it means the FR we measured is useless, since the metal cone drivers are so badlly nonlinear. So may be they don't have those breakup peaks that show up in their FR plots?
Instead of looking at nonlinearity as objection to correcting the FR (and therefore time response since they are minimumphase safe enough), I would look at what goes on at off axis. If you correct on axis, how the off axis response becomes, and that effectst the sound heard.....
Let me put this in simple terms, let's take the very low frequency example where most drivers will be easily driven to high levels of distortion. Let's say we wanted to know the frequency response of a closed box woofer from 5 Hz to 100 Hz using pure tones, a nearfield mic and an RMS meter. Many systems driven at 5 Hz will produce over 100 % THD even at moderate levels, yes there is more level in the harmonics than the fundamental and if we measure the output with a meter we will obviously read the fundamental + THD and get a false reading. The solution is to do a filtered measurement, or one using a spectrum analyzer and obviously just take the level of the fundamental. This example was given when I studied audio engineering as an undergraduate.
Measurements in the presence of high levels of distortion are complex, more complex than with well behaved systems. Distortion will introduce an error into a frequency response measurement that assumes a linear system and does not provide filtering. Isn't this obvious?
I'm getting busy with some real work, so I'll bow out of this one also.
Pete B.
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