Didn't really read this closely the first time, but now I have I can't let it slip by...
A closed box woofer has a mechanical mass and compliance resonance that is equivalent to the self resonance of an LC high pass filter loaded by R.
No matter what the loaded Q of an LC high pass filter is, no non-linear distortion products will be produced, although linear distortion of amplitude and phase will of course result.
Any distortion products from the speaker must therefore come from other non-linear behaviour of the speaker, (of which there are no shortage of causes) not from it's resonance.
I've never come across any texts that claim that a damped resonance can generate harmonics, and it doesn't make the slightest sense so it's a pretty extraordinary claim, which needs extraordinary proof to back up.
Why try to invent new causes of distortion in a loudspeaker when there are already so many real ones ?
Besides, Q only exists in the context of a resonance, so talking about raising the Q at an arbitrary frequency doesn't make sense.
If your woofer resonance is at 50Hz, how exactly would you raise the "Q" at 80Hz with your special amplifier ?
I presume what you're really talking about is playing with the damping factor at different frequencies, but again, to what end ? A standard voltage source amplifier already has maximum damping factor, any increase in output impedance is just going to increase the overall Q - which according to you causes more harmonics.
Passive networks can affect the damping factor at different frequencies by the way, you might want to check the following article, specifically the paragraph of text above figure 2.4 which is discussing the "look-back impedance" of passive series crossovers versus passive parallel crossovers:
Series vs. Parallel Crossover Networks
The "skirt" of a resonance does not have a Q of it's own, the presence of the skirt and it's shape defines the Q of the resonance.
Now apply boost to the signal going into an LCR high pass filter with the same Q and resonant frequency as the woofer and see if any more distortion is produced. Nope ?
Let me suggest one possible reason for increased distortion when boosting at or below mechanical resonance of the driver.
Well above the resonant frequency the driver is mass controlled. The excursion in response to a given force is limited by the inertia of the mass itself. The acceleration due to inertia is extremely "linear", in fact it's very close to ideal, as it by far dominates the restoring force compared to the suspension compliance.
Well above resonance only the linearity of the motor will have any significant effect on distortion right up until you reach the point where the suspension is stretched near it's limit.
Well below resonance the driver is compliance controlled. Any non-linearity in the compliance of the suspension with be directly reflected as non-linear distortion in the output, as typical suspensions are rather non-linear, actually getting softer with increasing excursion, and not even in a linear fashion at that.
At resonance the restoring force of compliance and inertia are equal.
Any time you extend the low frequency response of a driver well below its mechanical resonance with EQ you're going to see a lot greater distortion because you're operating the driver well into it's compliance controlled range, compared to if you just had a low resonance frequency to begin with.
How exactly is a loudspeaker an oscillator ? Does it have an over unity gain ?
A closed box woofer has a mechanical mass and compliance resonance that is equivalent to the self resonance of an LC high pass filter loaded by R.
No matter what the loaded Q of an LC high pass filter is, no non-linear distortion products will be produced, although linear distortion of amplitude and phase will of course result.
Any distortion products from the speaker must therefore come from other non-linear behaviour of the speaker, (of which there are no shortage of causes) not from it's resonance.
I've never come across any texts that claim that a damped resonance can generate harmonics, and it doesn't make the slightest sense so it's a pretty extraordinary claim, which needs extraordinary proof to back up.
Why try to invent new causes of distortion in a loudspeaker when there are already so many real ones ?
Obviously. The speaker is a high pass filter after all, with a specific Q value...
Why would you want to do this in the first place ?
Besides, Q only exists in the context of a resonance, so talking about raising the Q at an arbitrary frequency doesn't make sense.
If your woofer resonance is at 50Hz, how exactly would you raise the "Q" at 80Hz with your special amplifier ?
I presume what you're really talking about is playing with the damping factor at different frequencies, but again, to what end ? A standard voltage source amplifier already has maximum damping factor, any increase in output impedance is just going to increase the overall Q - which according to you causes more harmonics.
Passive networks can affect the damping factor at different frequencies by the way, you might want to check the following article, specifically the paragraph of text above figure 2.4 which is discussing the "look-back impedance" of passive series crossovers versus passive parallel crossovers:
Series vs. Parallel Crossover Networks
Gobbledegook..."damping all frequencies except the band in question" ??? I can't even fathom what you're trying to suggest here.
Again - unless you know something about Q I don't, this doesn't make the slightest sense. A resonance occurs at one single frequency, and that resonance has a Q factor. At other nearby frequencies there is no resonance, and therefore no Q.
The "skirt" of a resonance does not have a Q of it's own, the presence of the skirt and it's shape defines the Q of the resonance.
So you measure more distortion near resonance when boost is applied, so it must somehow be because resonance causes non-linear distortion ? That's a huge leap to make.
Now apply boost to the signal going into an LCR high pass filter with the same Q and resonant frequency as the woofer and see if any more distortion is produced. Nope ?
Let me suggest one possible reason for increased distortion when boosting at or below mechanical resonance of the driver.
Well above the resonant frequency the driver is mass controlled. The excursion in response to a given force is limited by the inertia of the mass itself. The acceleration due to inertia is extremely "linear", in fact it's very close to ideal, as it by far dominates the restoring force compared to the suspension compliance.
Well above resonance only the linearity of the motor will have any significant effect on distortion right up until you reach the point where the suspension is stretched near it's limit.
Well below resonance the driver is compliance controlled. Any non-linearity in the compliance of the suspension with be directly reflected as non-linear distortion in the output, as typical suspensions are rather non-linear, actually getting softer with increasing excursion, and not even in a linear fashion at that.
At resonance the restoring force of compliance and inertia are equal.
Any time you extend the low frequency response of a driver well below its mechanical resonance with EQ you're going to see a lot greater distortion because you're operating the driver well into it's compliance controlled range, compared to if you just had a low resonance frequency to begin with.
I think it's you that needs to provide something to back up the idea that damped resonances can by themselves produce harmonic distortion, rather than the resonance just affecting the pre-existing non-linear behaviours of a real driver.
One that is poorly damped generates a higher than ideal level of non linear distortion (harmonics). This is very basic stuff. But then again, we're on DIY here - a place where plastic cork makers and home made loudspeaker geeks like to congregate and puff their chests out.
The data collected is very easy to duplicate.
Fortunately, these (former) cork makers and loudspeaker geeks know basic physics (and, for that matter, grammar and sentence construction). They do their best to teach others, and many benefit. Some cannot. Tant pis.
But however you would care to close your eyes and pretend, increased displacement in any non-Hooke's Law oscillator causes increased distortion. Constant displacement does not. This is unremarkable, and it's doubtful that you're going to inspire someone to bother to take the time to demonstrate commonplace knowledge to you if you're not willing to learn the basic physics and the proper way to use the powerful tools at the loudspeaker builder's disposal so that you can derive this trivial result on your own.
Your pure conjecture that an increased displacement was the sole reason for a marked increase in distortion is clearly disproven by the data which you have repeatedly criticized without any scientific basis whatsoever. Like I said. Conduct the simple experiment. I have several active speaker systems at my disposal. I'm sure amidst the piles of corks in your presence, you could find an active speaker system that you've constructed to actually disprove what I've been asserting. Anything other than raw data is pure conjecture, pure handwaiving, and pure rubbish.
Where have I misquoted you ? To misquote I would have to leave out some key piece of text in my quote, but I quoted and responded to everything.
Misunderstood you ? Yes possibly, as some of what you said makes no sense it's hard to be certain what exactly you were trying to get across in some places, so I can only respond to what I believe you're trying to say.
As for rambling, I responded to each key point you tried to make, of which there were many. If I left anything out I would be accused of taking you out of context or misquoting you
I could have just made a snarky comment like "you're talking a load of nonsense" but that doesn't really do anyone any favours does it ? Instead I chose to try and discuss it point by point in a civilised fashion, if for no other reason than to try and get a better idea of what it is exactly you're trying to get across.
The reason why I brought up the fact that a speaker is not an over unity oscillator is that any self sustaining oscillator with a gain over unity must by definition include an amplifier of some sort. Such an amplifier will inevitably introduce it's own non-linearities.
In the case of an RLC filter/resonator with ideal components there is no non-linearity. Add an amplifier to make it self sustaining and inevitably there will be some distortion introduced. So what ?
You keep stating "One [oscillator] that is poorly damped generates a higher than ideal level of non linear distortion (harmonics)." as a self evident fact over and over, yet you provide no evidence to back up this remarkable claim. Show even one reference text or article that makes this claim. I think this is the number one point of dispute everyone is having with you.
In fact in a real world electronic LC oscillator where the gain stage has non-linear distortion the opposite is true - a higher Q ("poorly damped") resonator usually results in less harmonic distortion, because the increased selectivity of the high Q resonator provides increased suppression of the harmonic frequencies in the feedback loop.
None of this is directly relevant to a speaker though - it doesn't have a gain stage, nor feedback. It's non-linearities lie elsewhere - motor non-linearity with displacement, and suspension non-linearity with both displacement and time. (Memory effects in the material)
In your previous post you were talking about boosting the speakers responses at resonance:
Now you're talking about boosting at the 3rd or 4th harmonic. So which is it ?fntn said:
In any case, your measurements aren't being questioned, only your conclusions that "poorly damped" resonances (of any sort) are inherently a non-linear effect that can create harmonics in and of themselves, something which no text book would agree to.
Resonances don't create harmonics, however in a complex non-linear device like a speaker, the linear changes in response due to the mechanical resonance can modulate and alter the inherent non-linear properties of the driver in interesting and non-obvious ways.
Let me throw another fly into your ointment. You speak about the resonant frequency of a speaker as if it's a constant, unfortunately this is not true with any real speaker due to speaker suspensions deviating quite substantially from ideal Hookes law springs.
Any time a spring in a mass/spring resonator deviates even slightly from an ideal hookes law spring, the resonant frequency becomes dependant on amplitude. This was discussed quite extensively in another thread which cumulated in me measuring the free air resonant frequency (Fs) of two drivers across a wide range of drive levels and plotting the results. See the following graphs in post #28:
http://www.diyaudio.com/forums/multi-way/182688-help-understanding-physics-vas.html#post2462768
You'll notice that not only does the resonant frequency change substantially with level, but that it decreases with increased drive level.
Since Mms must remain the same a decreased Fs means the compliance must be increasing - becoming softer as excursion increases, at least up until the point where the suspension reaches its maximum extension. A somewhat counter-intuitive result on the face of it.
The difference in Fs between small and large signals of one of the drivers was from 48Hz down to 34.5Hz, which is a substantial change in Cms. You'll also notice that on the same driver the slope of the line was highly irregular, which would lead to unusual results if you were making measurements near "resonance" at different drive levels, since the resonance itself depends on drive.
As well as real-time variations in compliance with excursion most drivers also have a "memory effect" in their compliance, again discussed in that thread, whereby a large excursion causes a temporary (on the order of up to 10 seconds) increase in compliance even for low drive levels, which gradually returns to normal.
Although the exact cause of this wasn't conclusively agreed on in the discussion the effect is very real and can be measured with a real-time impedance curve measurement system - such as the noise mode in LIMP. (ARTA) Measure at a very low drive level, stretch the suspension of the driver by hand, let go, and watch the impedance curve (and resonant frequency) morph back to it's small signal response before your eyes...
All of which is to say that the non-linear behaviours of a driver are very complex and are not the simple "bent transfer function" of a simple electronic circuit with an easily quantifiable non-linear distortion coefficient.
I wouldn't be at all surprised if the anomalous changes in distortion you're measuring are a result of the unusual non-hookes law characteristic of real driver suspensions, coupled with motor non-linearities.
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You are so far over your head here, it's embarrassing. Clearly, you have no idea how to distinguish between physical Q and Q in the frequency domain. The element that you completely ignore is the impact on physical q that the active system's amplification at a specified frequency has on a loudspeaker - particularly one operating at or near its fundamental resonance.
Clearly, you have a lot of reading to do. Here would be a good place to start.
Damping ratio - Wikipedia, the free encyclopedia
In particular, the section for the derivation of the damping ratio.
Loudspeaker physical Q varies dramatically from one end of its operating spectrum to the other. The frequency domain Q is an amalgamation of the multitude of physical q's . Neither value has a dimension associated with it. Both are dimensionless. But they are not equivalent. Importantly in this particular situation, the ratio of energy stored to energy dissipated per cycle at a given frequency (physical q) can be substantially increased with the use of an equalizer and amplifier. The resulting physical Q is the product of the equalizer/amp's Q and the loudspeaker's natural physical Q at any given frequency. Adding a spike of energy at a particular frequency while leaving adjacent frequencies alone can severely reduce the damping at that frequency and the natural harmonics of that frequency. This has a particularly unsettling effect when the frequency at which energy is applied is within the driver's resonance band - an area where the ratio of energy stored versus energy dissipated is quite high. If you had a professional background in this area, this should be obvious to you. If you approach this as a hobby, I could understand why you might be confused. But that does not give you the right to be rude or condescending to someone with a different perspective. People who have different perspectives should be treated with respect, especially if you have an inkling in your brain that you might not have all the answers.
fntn,
When engaging in the deep online fora like DIYAudio there are three high probabilities that wise posters will acknowledge to guide their dialog on a particular topic:
1. There are participants with more raw intelligence than me.
2. There are participants with more facts (data) in hand than me.
3. There are participants with deeper insight into the data than me.
When you make assertions that run counter to accepted technical principles you should expect your assertions to be challenged and you should be willing to patiently understand the details of the challenge and be able to repond with information relevant to the challenge. If you are doing that effectively other participants who fall into the one or more of three aforementioned groups will take notice and will begin to see the wisdom of your arguments. When that does not happen you should assume one or both of the following are true:
A. You are interacting with other participants in a manner that interferes with their seeing the wisdom in your assertions.
B. There is no wisdom in your assertions.
I claim no special deep expertise into this particular topic beyond the general insight that any skilled engineer would possess.
When engaging in the deep online fora like DIYAudio there are three high probabilities that wise posters will acknowledge to guide their dialog on a particular topic:
1. There are participants with more raw intelligence than me.
2. There are participants with more facts (data) in hand than me.
3. There are participants with deeper insight into the data than me.
When you make assertions that run counter to accepted technical principles you should expect your assertions to be challenged and you should be willing to patiently understand the details of the challenge and be able to repond with information relevant to the challenge. If you are doing that effectively other participants who fall into the one or more of three aforementioned groups will take notice and will begin to see the wisdom of your arguments. When that does not happen you should assume one or both of the following are true:
A. You are interacting with other participants in a manner that interferes with their seeing the wisdom in your assertions.
B. There is no wisdom in your assertions.
I claim no special deep expertise into this particular topic beyond the general insight that any skilled engineer would possess.
fntn, if what you were saying is true, then surely the distortion plots for all loudspeakers would show large peaks in the harmonic spectra @ multiples of the system resonance?
Or have I missed something? Which is entirely possible as it would seem that the majority of the people posting in this thread have at least 2 and 3 over me in kevinahcc20's previous post.
Or have I missed something? Which is entirely possible as it would seem that the majority of the people posting in this thread have at least 2 and 3 over me in kevinahcc20's previous post.
less noise in the class
I'm sure he will use time to be back with a a lot of watertight plots that both prove his ideas regarding distortion related to resonance plus his skills in documenting and performing appropriate measurements - possibly even *in his own thread*..
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This is a little bit asking to bring back the fish form bouillabaisse...
To clean up a FR plot best is to use one of the hardware or software tools cheaply available now.
http://www.diyaudio.com/forums/multi-way/100392-beyond-ariel-115.html#post1837992
If the response is flattend SL's measurements would show the remaining "stored energy" of the HP filter.
Thats the core of all statments regarding SL's term - nothing he revealed - but a lot of fuss around it and also a lot of fogging technical meanings.
Michael
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I'm actually saying a little bit more than that - I'm focusing to the point SL tried to make but gorgeous missed it - leaving scorched earth with respect to understanding of "energy storage" in speakers ...
Michael
The term "stored energy" - as most audio folks (he himself included) *think* they understand the issue tagged with it - certainly is heavily linked to SL's presentation that he actually put up to support his product (and how clever he selected the midrange speaker
).If you are uncertain what my point regarding the current thread is, may I possibly suggest to re-read the first posts to grasp the point and come back afterwards with more specific questions or statements ?
Michael
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No Jan, I actually I didn't - and actually - I don't see the point to do ?
I mean, he has clearly expressed his point of view and I've mine.
Besides, I guess he might already be aware of that thread - having his reasons not to enter the stage.
Without any irony : I can understand that.
It isn't that he would not have my warm feelings for what he has done for audio *in general* - so, as the person, no problem, but what he did regarding "stored energy" is simply "B++S with impact" ! - sorry Siegfried.
Well – sometimes even the most obvious has to be stated !
No big deal .
Michael
I mean, he has clearly expressed his point of view and I've mine.
Besides, I guess he might already be aware of that thread - having his reasons not to enter the stage.
Without any irony : I can understand that.
It isn't that he would not have my warm feelings for what he has done for audio *in general* - so, as the person, no problem, but what he did regarding "stored energy" is simply "B++S with impact" ! - sorry Siegfried.
Well – sometimes even the most obvious has to be stated !
No big deal .
Michael
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No Jan, I actually I didn't - and actually - I don't see the point to do ?
I mean, he has clearly expressed his point of view and I've mine.
Besides, I guess he might already be aware of that thread - having his reasons not to enter the stage.
Without any irony : I can understand that.
It isn't that he would not have my warm feelings for what he has done for audio *in general* - so, as the person, no problem, but what he did regarding "stored energy" is simply "B++S with impact" ! - sorry Siegfried.
Well – sometimes even the most obvious has to be stated !
No big deal .
Michael
The problem is that it's your word against his, and it would be very gentleman-like to take it up with him first.
There must be many who have the same views as Siegfried.
A dialogue might even clear the whole thing up.
The way you discuss it here seems to go nowhere.
But hey, it's your time
jan didden
The term "stored energy" - as most audio folks (he himself included) *think* they understand the issue tagged with it - certainly is heavily linked to SL's presentation that he actually put up to support his product (and how clever he selected the midrange speaker
If you are uncertain what my point regarding the current thread is, may I possibly suggest to re-read the first posts to grasp the point and come back afterwards with more specific questions or statements ?
Michael
OK...I reviewed your 1st 10 posts and also reviewed SL's section on "Investigation of energy storage". The differences between your exposition and SL's seems to me to be almost entirely matters of semantics and perspective rather than fundamental differences in understanding that lead to different outcomes.
I find it telling that SL says in his introduction, "In the following I describe what I see as frontiers, if not in yours, then at least in my understanding of what matters for accurate sound reproduction." So while you insist that your perspective and semantics are superior (must be so if his is bunk in need of debunking), SL allows that different observers can have legitimately different ways of understanding and visualizing physical phenomena. He closes that introduction with, "I would hope that the exposé stimulates a few readers to research a subject further and share their insights." so Jan's thought are spot-on!
I will concede that energy storage as the operative term can confuse because the normal function of a speaker over each cycle is all about energy management and exchange, whereas in this context the energy stored is returned over many cycles, so understanding of that distinction is needed. BTW your snarky midrange comment above aside the plots you excerpted from SL's site were of a metal dome tweeter. He did compare the midranges from Orion and Phoenix in a separate section.
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