There is no "resolution" problem as such - the limiting factor in that particular test set up was primarily a result of using L-Pad's on the line inputs - throwing away at least 20dB of potential SNR right there.
I wasn't able to get enough drive directly from the sound card to get the maximum excursion I required for that test (half Xmax) so I was forced to use an amplifier, and as soon as I do that I need to protect the line inputs from over-drive, therefore a significant attenuator is required.
On the small driver, the 0dB point was actually 2.3v, almost exactly the sound card full scale line in sensitivity, however that is before the 33 ohm series resistor. Because the driver impedance was so high at resonance the attenuation of the 33 ohm resistor would have only been about 2dB there, but at the skirts of the resonance where the impedance is much lower there would be ~12dB of attenuation.
I actually measured down to -60dB but discarded that reading as the impedance plot showed visible noise.
At -60dB the line input signal level at the skirts of the impedance curve would be -60-20-12 = -92dB relative to full scale, very close to the maximum theoretical possible SNR of 96dB of the sound card. (I took the measurements in 48Khz/16bit mode, in hindsight I should have used 96Khz / 24bit mode, which gives about an extra 10dB of usable SNR)
There is also no doubt some introduced noise and hum from the power amplifier in this test, which won't help either.
Now, if I had gone back to my prior test set up of the 33 ohm resistor driven directly from the sound card line out, and the line inputs directly connected to the 33 ohm resistor, I would have immediately been able to measure 20dB lower without noise problems, however I didn't think it was appropriate for me to do so in the middle of the test - plotting some of the higher level values via a power amp and two L-Pad's, and the lower levels directly without amp or L-Pad, so I decided to keep the test set up consistent within the entire graph and only go as low as I could without getting noisy results.
What I may do at some point is re-run the test with the direct connection method, omitting the very high excursion measurements to focus more on what's happening at the very low levels.
However even then another problem at such low levels is microphony of the driver. I'm near a main road so even with windows closed there is sometimes some low level vehicle noise/rumble, I also have building demolition going on in the other direction only ~150 metres away, and the computer itself is physically quite noisy. All these small vibrations are picked up by the speaker and can influence the results at such small levels.
Again, I'd rather discard those low level readings that I think are being influenced by pick-up of vibrations.
I did do many of the measurements more than once and in all cases got the same value of Fs to 0.1Hz. Although the lowest signal I could go down to accurately was slightly limited by the L-Pad and amplifier combination, I don't think there was any problem with repeatability of the measurements, they were much more consistent than I expected in fact.
With due respect, I've been measuring T/S parameters manually for about 10 years now. Variable sine wave oscillator, high value series resistor, volt meter, and calculating all the T/S parameters by hand (well, calculator and paper
) so I think I have a pretty good grasp of how measure them, what makes sense, and what doesn't.LIMP is the first software aided T/S measuring program I've tried that I get consistently excellent results with, that agree with manually measured and calculated results very well, (a few other programs are poor indeed) in fact it is probably more accurate and less error prone as it analyses the shape of the entire impedance and phase curves rather than just looking at the resonance frequency and two skirt values as most manual calculations do. I get much closer results taking multiple measurements with LIMP than I do taking multiple measurements manually, and don't have to worry about making errors in manual calculations.
While I appreciate everyone pointing out potential measurement flaws and how to remedy them, (that's what a discussion about something like this is all about) I think that the possibilities for error have been pretty well covered by now, at least to my satisfaction.
I'm yet to see anyone else in the discussion taking measurements at different signal levels (or who has done so in the past) to prove or disprove my findings. LIMP is a free download, why not just try it and see what results you get on some of your own drivers ? Back up those measurements with manually taken measurements at the same drive levels if you like, but I think you'll find LIMP pretty bullet proof.
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You should be using a low impedance amp to perform T/S parameter tests. I'm not familiar with any "1/2 Xmax" T/S parameter test. The entire thrust of the Theile Small small signal model is to provide a reliable benchmark means of comparing drivers when they are behaving as intended - in a relatively linear fashion. This is why the stipulation for T/S testing is roughly between .7v and 1v applied signal. If you've been conducting T/S tests for ten years, it's about time you learned more about their origins and why they were devised in the first place. When you modify them at will to serve your own individual purposes you get uniquely individual results.
For some current research on T/S parameters (and references to more) it is worth reading Thorborg, Tinggaard, Agerkvist & Futtrup, "Frequency Dependence of Damping and Compliance in Loudspeaker Suspensions" J. Audio Eng. Soc., vol. 58, pp. 472-486 (June 2010). I used their FDD model in REW's Thiele-Small analysis module, I've included some info on the model in the help file.
Hmm,
It seems almost as if you're skimmed the last few posts and jumped into the fray thus completely missing the point of the discussion and the associated measurements.
For the high level tests that resulted in the drive vs Fs graphs I was using a normal stereo amplifier which has a <0.2 ohm output impedance.
Not that it matters though, as a series resistor is still required to measure the impedance, (how would you measure it if the driver was connected directly ??) and the dual channel measurement approach which LIMP uses measures both sides of the resistor and is able to determine the voltage drop across the resistor, (therefore the current through the resistor and speaker) and the voltage across the speaker. (And from those two can directly derive the impedance and phase response of the speaker)
With this measurement technique you don't require a low impedance amplifier to feed the resistor either - because it's a differential measurement any "droop" in the signal level going into the resistor due to amplifier / sound card output impedance (even frequency dependent droop) is cancelled out, because only the relative phase and amplitude of the voltage across the resistor and speaker matter - that relationship is only determined by the impedance of the series resistor and the speaker.
The 35 ohm output of the Audigy 2 ZS is able to drive the 33 ohm resistor + speaker with low distortion and noise, and at sufficient level, so there is no problem. (Many sound cards have much higher impedance of a few hundred ohms though, and can't do so without an external amplifier, so it's important to actually verify the sound cards output impedance and it's distortion under load)
The more traditional approach of using a very high series resistor to approximate a current source and then just measuring the voltage across the speaker (the method typically used in manual measurements) also doesn't require a low impedance amplifier, for obvious reasons. This method also introduces measurement errors due to the resistor not being a true constant current source, on the order of 5% or so for 1K ohm.
Nowhere did I say I was trying to measure T/S parameters at 1/2 Xmax. What you apparently skimmed over was that in an effort to find where the threshold between "large signal" and "small signal" actually is for a given driver, (instead of just guessing or assuming, which is what many people seem to be doing) and having noticed that Fs and other related parameters can vary considerably at different test levels, I devised a test to plot Fs (not full T/S parameters) vs drive level to see what the characteristic curve was.
I selected 1/2 Xmax as the largest signal to test purely on an empirical basis - I wanted something that would be considered to be well within the "large signal" portion of the drivers range, but still comfortably within Xmax so that gross non linearity of the motor and/or suspension wouldn't be an issue.
Another reason is that although the Visaton driver is a big rugged woofer that can take a lot of abuse (and has an Xlim of more than twice Xmax) the Coral one is a smaller, very old, damageable and nearly irreplaceable driver whose exact Xmax is unknown. I saw no reason to risk damaging it by subjecting it to prolonged high amplitude low frequency tones without a cabinet just for the purpose of this test.
Usually at a level where cone movement is just visible, and certainly no more than about 0.5 - 1v.
The problem with your suggestion of "between .7v and 1v" is that no matter who has stipulated it it's just a rule of thumb, with probably not a lot of science behind it. For very sensitive drivers 1v is a lot of excursion, so it's debatable whether that constitutes a small signal condition.
As head_unit pointed out earlier in the thread, the whole T/S model is only a convenient approximation in the first place.
One of the assumptions/approximations in the model itself is that the parameters are relatively stable once you're significantly below the excursion limits of the driver, eg the concept of a reproducible "small signal" response. (I had taken this on faith but in light of these measurements this appears to be a very dubious assumption in the case of compliance)
However what doesn't seem well defined is exactly what a small signal is, which is obviously going to vary from one driver type to another.
If you take small signal to be that below which the change in parameters is less than a few percent, then the measurements I've taken on two drivers so far show that to get a true small signal response you may be talking about a very small signal for some drivers, on the order of a few 10's of millivolts, and that 0.7 to 1v is in fact well into "large signal" territory.
Because of this, drive level can't be ignored when trying to achieve reproducible measurements, so rules of thumb like "0.7 to 1v" are useless, the small signal threshold of a particular driver needs to be investigated before taking its T/S measurements.
The second related issue I'm discussing is of how much relevance these T/S measurements then have if, on some drivers, there is such a huge change between true small signal measurements, and those that occur at modest excursions where audible bass is being produced.
On a driver like the Visaton the change although significant is small enough that you could happily model the small signal response and get a useful large signal prediction - it would be a bit out, but not grossly so.
On the Coral driver, and maybe many others, the characteristics of the suspension are just such that it changes a lot with excursion, so modelling the likely bass response based on the small signal results is going to be so far out of whack that the approximation provided by the T/S model is verging on useless.
What to do in that case though ? I'm not sure, because for that particular driver the change in Fs with excursion is on a downwards slope for almost the entire dynamic range, so there is no one correct place to measure it.
People taking measurements at different test signal levels on this slope will be getting different results even if there are no other inaccuracies in their measurement system. Doesn't seem like a good idea to be in blissful ignorance of this fact...
It seems almost as if you're skimmed the last few posts and jumped into the fray thus completely missing the point of the discussion and the associated measurements.
Using what test methodology ? There is more than one way to measure impedance....
For the high level tests that resulted in the drive vs Fs graphs I was using a normal stereo amplifier which has a <0.2 ohm output impedance.
Not that it matters though, as a series resistor is still required to measure the impedance, (how would you measure it if the driver was connected directly ??) and the dual channel measurement approach which LIMP uses measures both sides of the resistor and is able to determine the voltage drop across the resistor, (therefore the current through the resistor and speaker) and the voltage across the speaker. (And from those two can directly derive the impedance and phase response of the speaker)
With this measurement technique you don't require a low impedance amplifier to feed the resistor either - because it's a differential measurement any "droop" in the signal level going into the resistor due to amplifier / sound card output impedance (even frequency dependent droop) is cancelled out, because only the relative phase and amplitude of the voltage across the resistor and speaker matter - that relationship is only determined by the impedance of the series resistor and the speaker.
The 35 ohm output of the Audigy 2 ZS is able to drive the 33 ohm resistor + speaker with low distortion and noise, and at sufficient level, so there is no problem. (Many sound cards have much higher impedance of a few hundred ohms though, and can't do so without an external amplifier, so it's important to actually verify the sound cards output impedance and it's distortion under load)
The more traditional approach of using a very high series resistor to approximate a current source and then just measuring the voltage across the speaker (the method typically used in manual measurements) also doesn't require a low impedance amplifier, for obvious reasons. This method also introduces measurement errors due to the resistor not being a true constant current source, on the order of 5% or so for 1K ohm.
I'm not surprised, since there isn't such a thing.
Nowhere did I say I was trying to measure T/S parameters at 1/2 Xmax. What you apparently skimmed over was that in an effort to find where the threshold between "large signal" and "small signal" actually is for a given driver, (instead of just guessing or assuming, which is what many people seem to be doing) and having noticed that Fs and other related parameters can vary considerably at different test levels, I devised a test to plot Fs (not full T/S parameters) vs drive level to see what the characteristic curve was.I selected 1/2 Xmax as the largest signal to test purely on an empirical basis - I wanted something that would be considered to be well within the "large signal" portion of the drivers range, but still comfortably within Xmax so that gross non linearity of the motor and/or suspension wouldn't be an issue.
Another reason is that although the Visaton driver is a big rugged woofer that can take a lot of abuse (and has an Xlim of more than twice Xmax) the Coral one is a smaller, very old, damageable and nearly irreplaceable driver whose exact Xmax is unknown. I saw no reason to risk damaging it by subjecting it to prolonged high amplitude low frequency tones without a cabinet just for the purpose of this test.
I'm well aware that the T/S model is a small signal model, and I've always done my measurements at low signal levels, thanks very much.
Usually at a level where cone movement is just visible, and certainly no more than about 0.5 - 1v.The problem with your suggestion of "between .7v and 1v" is that no matter who has stipulated it it's just a rule of thumb, with probably not a lot of science behind it. For very sensitive drivers 1v is a lot of excursion, so it's debatable whether that constitutes a small signal condition.
As head_unit pointed out earlier in the thread, the whole T/S model is only a convenient approximation in the first place.
One of the assumptions/approximations in the model itself is that the parameters are relatively stable once you're significantly below the excursion limits of the driver, eg the concept of a reproducible "small signal" response. (I had taken this on faith but in light of these measurements this appears to be a very dubious assumption in the case of compliance)
However what doesn't seem well defined is exactly what a small signal is, which is obviously going to vary from one driver type to another.
If you take small signal to be that below which the change in parameters is less than a few percent, then the measurements I've taken on two drivers so far show that to get a true small signal response you may be talking about a very small signal for some drivers, on the order of a few 10's of millivolts, and that 0.7 to 1v is in fact well into "large signal" territory.
Because of this, drive level can't be ignored when trying to achieve reproducible measurements, so rules of thumb like "0.7 to 1v" are useless, the small signal threshold of a particular driver needs to be investigated before taking its T/S measurements.
The second related issue I'm discussing is of how much relevance these T/S measurements then have if, on some drivers, there is such a huge change between true small signal measurements, and those that occur at modest excursions where audible bass is being produced.
On a driver like the Visaton the change although significant is small enough that you could happily model the small signal response and get a useful large signal prediction - it would be a bit out, but not grossly so.
On the Coral driver, and maybe many others, the characteristics of the suspension are just such that it changes a lot with excursion, so modelling the likely bass response based on the small signal results is going to be so far out of whack that the approximation provided by the T/S model is verging on useless.
What to do in that case though ? I'm not sure, because for that particular driver the change in Fs with excursion is on a downwards slope for almost the entire dynamic range, so there is no one correct place to measure it.
Uniquely individual results is what I'm trying to avoid by investigating this issue. It seems that the compliance of the suspension (and maybe the loss too to a lesser extent) changes dramatically with excursion, more so on some drivers than others, and that this is happening at lower levels many people assume are "small signal", when in fact they are already on the slope where it is changing with level.When you modify them at will to serve your own individual purposes you get uniquely individual results.
People taking measurements at different test signal levels on this slope will be getting different results even if there are no other inaccuracies in their measurement system. Doesn't seem like a good idea to be in blissful ignorance of this fact...
I suspect there is a lot of science behind that empirical rule.
1Vac applied to a series combination of 1k0+Driver Voice Coil is very different from 1Vac applied to a Driver directly.
Fair point, although as fntn failed to mention any series resistor value with his 0.7 - 1v rule of thumb (and in fact confusingly mentioned a "requirement" to use a low output impedance amplifier) I couldn't make an assumption of the drive level across the actual speaker resulting from his suggestion. Yeah, a lot of people use 1K for that, but not everyone.
If we assume 1v across 1K + the speaker, we're still in rule of thumb no mans land though - in the specific case of the Coral driver the impedance peaks at 150 ohms at resonance with low drive levels (as shown in my graph) which would only give ~17dB attenuation at resonance, which would be roughly at -24dB on my previously posted graph which is referenced to 2.3v. At -24dB it's already well on it's way down the slope, thus the level is above the "small signal" conditions, and inaccurate by that definition.
In the case of the Visaton driver the impedance at resonance is (from memory) about 25 ohms, so the drive at resonance would be ~32dB down, so on my graph referenced to 5.3v about -46dB, which is within the flat small signal region, so in the case of this driver, yes, it is valid.
So it's still a rule of thumb in that it's valid for some (maybe many) drivers, but incorrect for others. Better to measure where the small signal region lies for a given driver and use that, no ?
Whenever I see someone foist heavy handed criticism of the Thiele Small small signal model and how useless it is or how vague or "approximated" it is, inevitably, I revert back to this simple question:
If you feel it is that inadequate, why not invent your own method for establishing driver performance parameters?
It's easy to lob misguided or less than fair criticisms at a particular approach to a problem but much harder to devise a better way. I've heard a lot of criticisms and complaints over the years. Most of them by people who don't have a firm grasp on the fundamental interaction between energy applied, energy stored, energy dissipated as sound, energy dissipated as mechanical loss, and energy dissipated as electrical loss. Non linearity is not limited simply to a description of a portion of the BL curve. There are very good reasons why analysis is confined to an applied force of less than 1V. Most of them are beyond the scope of a discussion with DIY folks.
The Thiele Small small signal approach has been with us for more than 30 years as the "industry standard". This alone should not discourage anyone from creating a newer, better model. But it should give us pause for thought before we relentlessly attack it for its "many faults".
If you feel it is that inadequate, why not invent your own method for establishing driver performance parameters?
It's easy to lob misguided or less than fair criticisms at a particular approach to a problem but much harder to devise a better way. I've heard a lot of criticisms and complaints over the years. Most of them by people who don't have a firm grasp on the fundamental interaction between energy applied, energy stored, energy dissipated as sound, energy dissipated as mechanical loss, and energy dissipated as electrical loss. Non linearity is not limited simply to a description of a portion of the BL curve. There are very good reasons why analysis is confined to an applied force of less than 1V. Most of them are beyond the scope of a discussion with DIY folks.
The Thiele Small small signal approach has been with us for more than 30 years as the "industry standard". This alone should not discourage anyone from creating a newer, better model. But it should give us pause for thought before we relentlessly attack it for its "many faults".
Where did you see that? I've read through the whole thread twice and failed to spot anything of the sort. Since page 2 it has primarily been an interesting discussion of how T/S parameters are affected by excitation level.
First of all, saying that someone isn't allowed to recognise or point out the limitations of a system unless they have a better approach is a silly strawman argument, so I won't even respond to that.
Secondly, I fail to see anywhere I have made a "heavy handed criticism of the Thiele Small small signal model". In fact I'm very much for the T/S approach, and I am grateful to those that developed it, and anything that helps better understand or improve measurement technique of T/S parameters to get more accurate/consistent results I am all for.
However, lets not lose sight of the fact that it is still at the end of the day just a useful approximation to the physical processes that go on in a speaker, that takes into account some but not all of the variables involved. It's not like its a fundamental irrefutable iron law of physics like E=mc^2, and it shouldn't be construed as such.
If anything I would say many DIY'ers expect too much accuracy from T/S models, and are disappointed when measurements and prediction don't align as closely as they were expecting.
Some of the approximations are due to leaving out certain properties to keep the model from being unnecessarily complex, for example the effects of mutual coupling between a port and woofer were left out in their original papers because they found that the error caused by simplifying the model in this way was relatively small in most practical speakers they tested, provided the mouth of the port wasn't too close to the woofer, therefore they made a judgement call to ignore the effects of mutual coupling from the equations. There's nothing wrong with that per se except to point out it is one of many simplifications, and errors from multiple simplifications can stack up in weird corner cases.
Other approximations are due not to simplification of the model, but to having constants which you must know to generate the response, but can't accurately predict for an as-yet unmade box, nor easily measure after the fact. For example Box leakage and losses are an important part of the equations to derive a response but without being able to measure or predict them accurately for a design not previously built you just have to plug in "rule of thumb" values to approximate them, as sim software does. It's not until after the box is built and measured that you can work backwards to find out what those values were, (by adjusting them until the predicted and actual response most closely match) but by then you have measured the box anyway, so it's of academic interest at that point.
I don't seek to attack the T/S model at all, only to work with it, within it's limitations and realise that it is not the be all and end all.
Seems that you're agreeing with me here, or did I miss something ? I'm actually saying that to measure "small signal" parameters of the drivers you need a rather smaller signal than maybe some people expect, and that it's important to quantify what represents a small signal for a given driver, rather than leaving it to chance with rules of thumb.
By the way, although I wouldn't consider myself anything other than a DIY'er when it comes to speakers, there are people on this and other forums who have experience and knowledge that goes far beyond casual DIY level, so it's a bit presumptuous to talk about what is and isn't beyond the scope of participants on discussion forums such as this
If I may, allow me to repeat what I have been able to gather from this conversation, minus the side conversations. I'm new to this so please understand that and if you would,respond back.
OK, what we have here is fs=1/(2pi(MmsCms)1/2). Mms is pretty much constant, so we are observing a delta Cms causing fs to decrease with excursion. Cms = dx/dF where F=spring force.
Ideally we would like to see fs remain constant with excursion, which says that the ratio of excursion to force should always be the same. To me, this means that both the excursion function and the force function need to be linear.
For the 2 speakers presented, that doesn't seem to be the case.
Is this so surprising, really? I'm no mechanical guy, but isn't the speaker designer trying to juggle 2 non-linear functions(surround and spider) in parallel trying for some happy compromise?
OK, what we have here is fs=1/(2pi(MmsCms)1/2). Mms is pretty much constant, so we are observing a delta Cms causing fs to decrease with excursion. Cms = dx/dF where F=spring force.
Ideally we would like to see fs remain constant with excursion, which says that the ratio of excursion to force should always be the same. To me, this means that both the excursion function and the force function need to be linear.
For the 2 speakers presented, that doesn't seem to be the case.
Is this so surprising, really? I'm no mechanical guy, but isn't the speaker designer trying to juggle 2 non-linear functions(surround and spider) in parallel trying for some happy compromise?
This, then, brings us full circle back to an early question, how small is small?
It seems to me that the term "small" is there to reduce heating effects, and other low order effects which, for sake of convenience and ignorance are not included in the generalized formulae which we all seem to take as gospel. ( I am just now learning of these formulae, so therein ly my credentials!)
To my way of thinking at this point in time, as speakers, sound reproduction in general, is an art form, not a purely plug n' chug, I should do my calcs at some constant, low, comfortable level, compare to the level I may listen at, and tweak the tuning to MY pleasure.
I believe that speaker design is asymptotic, certainly get close, but lets not do this:
Imagine what those blows are doing to your hearing.
It seems to me that the term "small" is there to reduce heating effects, and other low order effects which, for sake of convenience and ignorance are not included in the generalized formulae which we all seem to take as gospel. ( I am just now learning of these formulae, so therein ly my credentials!)
To my way of thinking at this point in time, as speakers, sound reproduction in general, is an art form, not a purely plug n' chug, I should do my calcs at some constant, low, comfortable level, compare to the level I may listen at, and tweak the tuning to MY pleasure.
I believe that speaker design is asymptotic, certainly get close, but lets not do this:
Imagine what those blows are doing to your hearing.
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