gedlee said:
The beauty of audio – everything goes
gedlee said:
Yes you are right – SPICE can analyse circuit behaviour along the time line – in fact, transient analysis in SPICE is superior to Mathlab in this respect - I haven't thought about that.
On the other hand you do *not* necessarily need a transient analysis to validate the existence of Thermal Distortion on the level of wave form deformation.
I had hope that you do that – because its the part you are most interested in.
I have shown that – from my thermal model and from measurement – TD on the level of wave form deformation is present at thermal equilibrium as well.
This puts us into a position to look at steady signals to detect this kind of distortion.
Mathlab analysis should be fine to do the prove.
Michael
Michael
I believe that there are basically two time constants, the VC and the motor structure. The motor structure may have several constants, but since they are all so long, they will be seen as one. Its the VC time constant that I believe will determine most things of audible significance. The long term will be secondary in systems that are not pushed to their thermal limits. But the VC time constant will be a factor in every situation.
I believe that there are basically two time constants, the VC and the motor structure. The motor structure may have several constants, but since they are all so long, they will be seen as one. Its the VC time constant that I believe will determine most things of audible significance. The long term will be secondary in systems that are not pushed to their thermal limits. But the VC time constant will be a factor in every situation.
Earl, agree –
Time constant of the VC will dominate audibility, VC constant of motor will be of concern for long term effects – what "power compression" figures are good for, now.
Interesting thing for the ferro fluid Seas:
the "melt down factor" of each of the two thermal time constants is balanced *at one half* – meaning SPL melt down is 0.5 after roughly 5 sec and at its full after roughly 1500 sec.
Another interesting thing to underline is that the SPL melt down shape is really close to the simu, though I'm sure, also for the VC there must be multiple time constants due to different cooling effects / branches.
But – for now – it seems, that my relatively simple model
is close enough to reality that I don't necessarily have to model this non-dominant effects too. (quite a relieve to be honest).
Michael
Time constant of the VC will dominate audibility, VC constant of motor will be of concern for long term effects – what "power compression" figures are good for, now.
Interesting thing for the ferro fluid Seas:
the "melt down factor" of each of the two thermal time constants is balanced *at one half* – meaning SPL melt down is 0.5 after roughly 5 sec and at its full after roughly 1500 sec.
Another interesting thing to underline is that the SPL melt down shape is really close to the simu, though I'm sure, also for the VC there must be multiple time constants due to different cooling effects / branches.
But – for now – it seems, that my relatively simple model
is close enough to reality that I don't necessarily have to model this non-dominant effects too. (quite a relieve to be honest).
Michael
I believe that there will be different time constants for cooling, correct, but only one for heating. This is why I don;t think that heating and cooling will be symmetrical (meaning also not linear). This is a big factor IMO as it will be difficult to get these factors from linear signal processing.
No, Earl – you go wrong here IMO.
Look at this:
Cooling is *always* involved - also at heating (temperature rise above ambient). If it were not, the envelope shape of resistance increase would be linear (not the inverse trumpet) - and also no "thermal time constant" (for heating) could be defined (having linear temperature rise as there is no energy loss bending the curve).
This odd behaviour would only be the case if we would inject constant power into a thermally *absolutely* isolated VC.
There also would be *no* recovery from SPL melt down - as we thermally *absolutely* isolated VC.
Meaning the measurements would look like a "staircase to heaven"
(which they definitely don't look like)
You have to look at the whole system, I don't think you can come to a understanding if you "disconnect parts", like you try.
On the other hand – that all three different branches of heat transfer – radiation, conduction, convection – can be subsumed with no big penalty to a single (or dual) time constant really gave *me* a surprise.
Michael
Look at this:
Cooling is *always* involved - also at heating (temperature rise above ambient). If it were not, the envelope shape of resistance increase would be linear (not the inverse trumpet) - and also no "thermal time constant" (for heating) could be defined (having linear temperature rise as there is no energy loss bending the curve).
This odd behaviour would only be the case if we would inject constant power into a thermally *absolutely* isolated VC.
There also would be *no* recovery from SPL melt down - as we thermally *absolutely* isolated VC.
Meaning the measurements would look like a "staircase to heaven"
(which they definitely don't look like)
You have to look at the whole system, I don't think you can come to a understanding if you "disconnect parts", like you try.
On the other hand – that all three different branches of heat transfer – radiation, conduction, convection – can be subsumed with no big penalty to a single (or dual) time constant really gave *me* a surprise.
Michael
Hi guys
I have been thinking about this issue and have a few thoughts / questions.
Specifically, what mechanism causes a driver’s distortion to change as a function of VC temp alone?
If one said, ok, heat causes the Rdc to change, to approximately double at 230C if I recall, how does this change in R effect or cause a non-linearity?
If the temperature changed fast enough that one half of the wave were treated differently or caused a change over a few cycles, then maybe so.
What you do see in a woofer is the frequency response changes reflecting the increased Qt via Qe from the larger Rdc hot. One normally gets dips in the frequency response where low impedance points are.
Also, if one used a broad band pink noise signal, one see’s the SPL begins to fall nearly immediately.
In one of the ancient papers below, I had measured a number of speakers that way, using band limited pink noise and setting up the TEF machine to be a 20 second broad band level recorder. Woofers of that day, driven at rated power with band limited pink noise experienced power compression that reached 3-6 dB in less than 15 seconds (the most was 8dB), the coil heats up very fast..
Modern woofers have even better VC adhesives and some can get to 350C for a short time so one would expect all the “heat” related effects to be even larger.
With the thermal time constant being so much shorter on an hf driver, it (although I never measured one) should show a similar effect in a much shorter time period.
This is where your investigation is interesting as i haven't looked at anything but woofers. I suspect some kind of envelope analysis of a real speaker's output relative to the drive signal would be a good place to look. I would think your looking for things on the order of 1/10 second to a second or two as a rough guess.
Anyway, a cool subject (well, hot subject) but my question would be how does a slowly (relative to each cycle) changing Rdc, cause a basic non linearity leading to harmonic distortion?
Would it be more likely that a change in amplitude response as a result of changed parameters, would be the cause of an increase (such as more motion such as resulting from a higher Qe)?
Would it make sense to look for differences in the signal envelopes ( viewing the music or test signal after dsp full wave rectification) comparing the original music and the emitted sound (in near anechoic conditions probably)?
Lastly, at work there was the nagging issue of how do you rate a speaker's power capacity?
It's truly a game for some companies, likewise "peak SPL" figures.
Serving mostly sound system designers and installers, we wanted to be conservative and realistic.
What we (an independent lab) did was to drive our full range speakers with band limited pink noise with a +6dB peak to average ratio, who's level increases every 300 seconds.
The speakers output is monitored (in 1/48 oct resolution i think) and "Maximum power" is determined when any frequency has fallen -3 dB relative to the response shape at 2.8Vrms.
Within this range, there would be essentially no power compression, however in most all loudspeakers one does see harmonic distortion always increases with increasing level, increasing faster than the level. Thus headroom is your friend.
Some related stuff;
http://klippel.net/pubs/Klippel papers/Nonlinear_Modeling_of_Heat_Transfer_03.pdf
http://almainternational.org/2006_symposium_papers/Buck_temperature.pdf
http://www.aes.org/e-lib/browse.cfm?elib=5023
http://www.aes.org/e-lib/browse.cfm?elib=5525
http://www.aes.org/e-lib/browse.cfm?elib=7059
Best,
Tom Danley
I have been thinking about this issue and have a few thoughts / questions.
Specifically, what mechanism causes a driver’s distortion to change as a function of VC temp alone?
If one said, ok, heat causes the Rdc to change, to approximately double at 230C if I recall, how does this change in R effect or cause a non-linearity?
If the temperature changed fast enough that one half of the wave were treated differently or caused a change over a few cycles, then maybe so.
What you do see in a woofer is the frequency response changes reflecting the increased Qt via Qe from the larger Rdc hot. One normally gets dips in the frequency response where low impedance points are.
Also, if one used a broad band pink noise signal, one see’s the SPL begins to fall nearly immediately.
In one of the ancient papers below, I had measured a number of speakers that way, using band limited pink noise and setting up the TEF machine to be a 20 second broad band level recorder. Woofers of that day, driven at rated power with band limited pink noise experienced power compression that reached 3-6 dB in less than 15 seconds (the most was 8dB), the coil heats up very fast..
Modern woofers have even better VC adhesives and some can get to 350C for a short time so one would expect all the “heat” related effects to be even larger.
With the thermal time constant being so much shorter on an hf driver, it (although I never measured one) should show a similar effect in a much shorter time period.
This is where your investigation is interesting as i haven't looked at anything but woofers. I suspect some kind of envelope analysis of a real speaker's output relative to the drive signal would be a good place to look. I would think your looking for things on the order of 1/10 second to a second or two as a rough guess.
Anyway, a cool subject (well, hot subject) but my question would be how does a slowly (relative to each cycle) changing Rdc, cause a basic non linearity leading to harmonic distortion?
Would it be more likely that a change in amplitude response as a result of changed parameters, would be the cause of an increase (such as more motion such as resulting from a higher Qe)?
Would it make sense to look for differences in the signal envelopes ( viewing the music or test signal after dsp full wave rectification) comparing the original music and the emitted sound (in near anechoic conditions probably)?
Lastly, at work there was the nagging issue of how do you rate a speaker's power capacity?
It's truly a game for some companies, likewise "peak SPL" figures.
Serving mostly sound system designers and installers, we wanted to be conservative and realistic.
What we (an independent lab) did was to drive our full range speakers with band limited pink noise with a +6dB peak to average ratio, who's level increases every 300 seconds.
The speakers output is monitored (in 1/48 oct resolution i think) and "Maximum power" is determined when any frequency has fallen -3 dB relative to the response shape at 2.8Vrms.
Within this range, there would be essentially no power compression, however in most all loudspeakers one does see harmonic distortion always increases with increasing level, increasing faster than the level. Thus headroom is your friend.
Some related stuff;
http://klippel.net/pubs/Klippel papers/Nonlinear_Modeling_of_Heat_Transfer_03.pdf
http://almainternational.org/2006_symposium_papers/Buck_temperature.pdf
http://www.aes.org/e-lib/browse.cfm?elib=5023
http://www.aes.org/e-lib/browse.cfm?elib=5525
http://www.aes.org/e-lib/browse.cfm?elib=7059
Best,
Tom Danley
Hi Tom, thanks for all that additional information – very much appreciated.
It will take some time to digest – to say the least.
Flying over Klippels work for a few minutes only – I really admire that math magicians setting up formulas from one end of a page to the other end and not take a breath in between – but its certainly not my way to approach things.
What I could extract is, that Klippel uses more refined modelling but concentrates more on a close relationship towards audibility over the whole spectrum of the speaker (which is a goal).
This is way more than I can predict at the moment with my thermal model.
I'm concentrating on the aspect of intuitively understanding the thermal mechanisms and skip all refinement that didn't show up to be necessary compared to measurements until now.
The impacts of thermal distortion affecting *only* the "resistive" part of the speakers impedance – and its interaction with highly reactive impedance frequencies - seems to play an even bigger role (regarding audibility of effects) than I assumed until now – and I hardly have looked into that.
At current stage, my investigation has produced a thermal model that can predict Thermal Distortion on all time levels – but only if referenced by measurement and at a certain frequency (limitation due to fixed cooling assumption).
We would need a set of TD figures over some neuralgic frequencies to give a better picture.
So, as for your questions – you seem to know even better - from own experience – than me.
It would be guesswork if I'd try to do some answers.
As for Thermal Distortion at the level of wave form deformation you may have a look at #69
http://www.diyaudio.com/forums/showthread.php?postid=1671976#post1671976
and subsequent
But I'm not sure that you'll find any answers there that are at the (distortion) level you are looking for - though I haven't investigated power injection levels at the very limit of current speakers.
I have some hope that Peter may add something in this high power / short time range. My model and suggested measurement procedure should be good enough to reveal things even there.
Michael
It will take some time to digest – to say the least.
Flying over Klippels work for a few minutes only – I really admire that math magicians setting up formulas from one end of a page to the other end and not take a breath in between – but its certainly not my way to approach things.
What I could extract is, that Klippel uses more refined modelling but concentrates more on a close relationship towards audibility over the whole spectrum of the speaker (which is a goal).
This is way more than I can predict at the moment with my thermal model.
I'm concentrating on the aspect of intuitively understanding the thermal mechanisms and skip all refinement that didn't show up to be necessary compared to measurements until now.
The impacts of thermal distortion affecting *only* the "resistive" part of the speakers impedance – and its interaction with highly reactive impedance frequencies - seems to play an even bigger role (regarding audibility of effects) than I assumed until now – and I hardly have looked into that.
At current stage, my investigation has produced a thermal model that can predict Thermal Distortion on all time levels – but only if referenced by measurement and at a certain frequency (limitation due to fixed cooling assumption).
We would need a set of TD figures over some neuralgic frequencies to give a better picture.
So, as for your questions – you seem to know even better - from own experience – than me.
It would be guesswork if I'd try to do some answers.
As for Thermal Distortion at the level of wave form deformation you may have a look at #69
http://www.diyaudio.com/forums/showthread.php?postid=1671976#post1671976
and subsequent
But I'm not sure that you'll find any answers there that are at the (distortion) level you are looking for - though I haven't investigated power injection levels at the very limit of current speakers.
I have some hope that Peter may add something in this high power / short time range. My model and suggested measurement procedure should be good enough to reveal things even there.
Michael
Multiple time constants should arise from several considerations.
First we have the equation that represents the change in VC temp
of the form
dTvc/dt = Q - L.
L (losses to the surrounds) would have several parts, but consider the two basic parts: L1 = heat lost to the pole piece, and L2 = heat lost to the outer magnet structure,
Thus,
dTvc/dt = Q - L1 - L2
but then there are the equations governing the temp of the pole and magnet structure,
dTpole/ dt = +L1 - some losses to other surroundings
and
dTmagnnet/dt = + L2 - some losses to other surroundings
Of course this is a gross over simplification, but we see there 3 coupled equations here which will each have different time constants and which all affect each other, thus Tvc.
Nonlinearity comes in because if the input voltage, V, is a sine wave, for example, the VC Re will vary over the cycle giving rise to a distorted motor force, BL x V / Re(t). The VC temperature, hence Re, will always have a component that is time dependent but the magnitude will depend on the frequency. Also, is the input is a simple sine wave the heat generation term, and therefore the AC component of temperature variation would vary at twice the frequency of the input because, even in the case of constant resistance
Q = V^2/Re = [sin(wt)]^2 / Re = [1-cos(2wt)] /(2 x Re).
Thus we see that for a simple sine wave input, to first order,
Q = 0.5/Re - 0.5 cos(2wt) / Re = Qdc + Qac.
There can be no doubt that VC heating generates nonlinear distortion. The only question is of its magnitude. As I stated earlier, the equations above are basically of the form of low pass filters and the time constants are poles in the temperature transfer function. For any frequency there is always a heat up to a mean temperature determined by Qdc and an oscillation about that mean at twice the input frequency. As the frequency increases, the magnitude of the variation due to Qac decreases due to the low pass nature of the thermal system.
First we have the equation that represents the change in VC temp
of the form
dTvc/dt = Q - L.
L (losses to the surrounds) would have several parts, but consider the two basic parts: L1 = heat lost to the pole piece, and L2 = heat lost to the outer magnet structure,
Thus,
dTvc/dt = Q - L1 - L2
but then there are the equations governing the temp of the pole and magnet structure,
dTpole/ dt = +L1 - some losses to other surroundings
and
dTmagnnet/dt = + L2 - some losses to other surroundings
Of course this is a gross over simplification, but we see there 3 coupled equations here which will each have different time constants and which all affect each other, thus Tvc.
Nonlinearity comes in because if the input voltage, V, is a sine wave, for example, the VC Re will vary over the cycle giving rise to a distorted motor force, BL x V / Re(t). The VC temperature, hence Re, will always have a component that is time dependent but the magnitude will depend on the frequency. Also, is the input is a simple sine wave the heat generation term, and therefore the AC component of temperature variation would vary at twice the frequency of the input because, even in the case of constant resistance
Q = V^2/Re = [sin(wt)]^2 / Re = [1-cos(2wt)] /(2 x Re).
Thus we see that for a simple sine wave input, to first order,
Q = 0.5/Re - 0.5 cos(2wt) / Re = Qdc + Qac.
There can be no doubt that VC heating generates nonlinear distortion. The only question is of its magnitude. As I stated earlier, the equations above are basically of the form of low pass filters and the time constants are poles in the temperature transfer function. For any frequency there is always a heat up to a mean temperature determined by Qdc and an oscillation about that mean at twice the input frequency. As the frequency increases, the magnitude of the variation due to Qac decreases due to the low pass nature of the thermal system.
John
Agreed - there is no doubt that it occurs, what is the level - that takes some real data. It is precisely the time constants that you show that I want to measure. I think that I can do that with some simple signal processing from current and voltage wav files. This is far simpler that the approach used by Marshall Buck in the paper that Tom quoted.
Agreed - there is no doubt that it occurs, what is the level - that takes some real data. It is precisely the time constants that you show that I want to measure. I think that I can do that with some simple signal processing from current and voltage wav files. This is far simpler that the approach used by Marshall Buck in the paper that Tom quoted.
Data *I* have presented not "real" enough ?
#78
http://www.diyaudio.com/forums/showthread.php?postid=1676689#post1676689
#85
http://www.diyaudio.com/forums/showthread.php?postid=1677033#post1677033
Michael
#78
http://www.diyaudio.com/forums/showthread.php?postid=1676689#post1676689
#85
http://www.diyaudio.com/forums/showthread.php?postid=1677033#post1677033
Michael
john k... said:
Agree, but for the tweeters measured you can throw time constants together - meaning there is a higly dominant *one* and the others are almost not counting - OR – for the ferro fluid tweeter - there are two dominant ones at *very* different values and the rest is almost not counting
For the Seas Millennium the two dominating time constants are roughly at 1.6sec and 300sec
May be different for woofers we'll see...
Michael
gedlee said:
I imagine that if you measure V and I you can compute Z(t) and look at the real and imaginary parts to see if only changes in Re occurred. An FFt of I(t) would be indicative of distortion, and if changes in Ze were found to be only in Re then it could be argued that this is of thermal origin.
However, I did some work years ago to look at how VC heating affected frequency response with passive crossover.
An externally hosted image should be here but it was not working when we last tested it.
When discussing the observed response changes with others and then trying to model the effect the results seemed more consistent with excursion related changes in Le than with VC temp;
An externally hosted image should be here but it was not working when we last tested it.
The red curve is a 25% change in Re, the green a 10% change in Le.
First time you can download my enhanced thermal model to simulate TD.
http://members.aon.at/kinotechnik/diyaudio/diy_audio/TD/SPICE_modelling_TD.htm
I have packed it with some additional - new - features and did a general clean-up.
Also there is a legend to indentify how model roughly works.
Have fun !
Michael
http://members.aon.at/kinotechnik/diyaudio/diy_audio/TD/SPICE_modelling_TD.htm
I have packed it with some additional - new - features and did a general clean-up.
Also there is a legend to indentify how model roughly works.
An externally hosted image should be here but it was not working when we last tested it.
An externally hosted image should be here but it was not working when we last tested it.
Have fun !
Michael
If you woiuld like to know to *what degree* the changes you measured are also caused by Thermal Distortion you *have to* know
1. source impedance
2. real / imaginary part of speaker impedance
3. a TD reference measurement for scaling TD at different power injection at a given frequency
- and possibly my thermal model you now can download
Quantifying TD effects is now pretty precise - once you've referenced the model by measurement.
I don't think its any new for you, that all this factors play together.
What role source impedance plays with respect to TD is also outlined in short in my paper for current versus voltage amplifiers.
Michael
1. source impedance
2. real / imaginary part of speaker impedance
3. a TD reference measurement for scaling TD at different power injection at a given frequency
- and possibly my thermal model you now can download
Quantifying TD effects is now pretty precise - once you've referenced the model by measurement.
I don't think its any new for you, that all this factors play together.
What role source impedance plays with respect to TD is also outlined in short in my paper for current versus voltage amplifiers.
Michael
john k... said:
Hey John
I am not sure what you mean, but I don't think that it is possible to define impedance in the time domain, i.e. "Z(t)". And I've tried to find a way to get Re from time domain information directly but I don't think that it is easy (phases, etc. make things a little complicated). For a first cut I'm going to take the FFT of the current and voltage waveforms and find V(w)/I(w) over a limited bandwidth where the real part is dominately Re. To a first order this should be correct. A more accurate calculation would fit the impedance curve to a better model for each block of data - a little more accurate but a lot more calculations (and code).
Since I will then know Power(t) and Re(t) I can correlate the time constants from this data - at least to the extent that this is linear. Linearity is my biggest concern. This gives me the time constants for a real device is a very simple manner.
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