I started this thread on request of Earl about "in depth" discussing the topic of Thermal Distortion / Power Compression as I have outlined in the paper linked below.
Basically this is a *my* focused summary of several postings and some additional ideas having evolved in a discussion with nickmckinney, John_E_Janowitz, EarlGeddes, Charles Hansen and others about impacts of voice coil wires used today at Lynn's thread.
Michael
Basically this is a *my* focused summary of several postings and some additional ideas having evolved in a discussion with nickmckinney, John_E_Janowitz, EarlGeddes, Charles Hansen and others about impacts of voice coil wires used today at Lynn's thread.
Michael
The main point here is that a thermal change that happens slowly is still a "linear" phenomina because the time rate of the change is slower than the signal rate. The system can only be non-linear if the time rate of the thermal change is within the signals bandwidth. Now the voice coil changes CAN BE within this range depending on two basic factors, the thermal mass and the current. There is no way that anything beyond the voice coil will have time rates fast enough to be nonlinear. The long term thermal aspects like voice coil cooling and magnet temperature will affect system tuning etc, but they will not generate nonlinear distortion of any kind.
Only the voice coils mass and the current through it has any nonlinear component and these factors are almost completely determined by the voice coils size and nothing else. A large voice coil tends to have lower current and a greater thermal mass so it is unlikely that there would be a nonlinear effect. However smaller voice coils (smaller woofer etc.) such as have become popular, need more current, because they have less copper and they have lower thermal mass, hence these speakers would be very likely to have thermal nonlinear effects.
I hypothesis that this is what people hear in the larger speaker as greater dynamics. Its a simple situation - the bigger the voice coil the lower the thermally generated distortion. This is why I like compression drivers over dome tweeters. There is a lot more copper in a compression driver voice coil than a dome tweeter - a lot more! And a 4" voice coil woofer is going to be a whole lot better in this regard that a 2" voice coil woofer. Bigger simply is better in a lot of ways.
Only the voice coils mass and the current through it has any nonlinear component and these factors are almost completely determined by the voice coils size and nothing else. A large voice coil tends to have lower current and a greater thermal mass so it is unlikely that there would be a nonlinear effect. However smaller voice coils (smaller woofer etc.) such as have become popular, need more current, because they have less copper and they have lower thermal mass, hence these speakers would be very likely to have thermal nonlinear effects.
I hypothesis that this is what people hear in the larger speaker as greater dynamics. Its a simple situation - the bigger the voice coil the lower the thermally generated distortion. This is why I like compression drivers over dome tweeters. There is a lot more copper in a compression driver voice coil than a dome tweeter - a lot more! And a 4" voice coil woofer is going to be a whole lot better in this regard that a 2" voice coil woofer. Bigger simply is better in a lot of ways.
gedlee said:
Earl, thanks for pointing out what is the meaning of "distortion" in a strict scientifically context.
I very much appreciate your input at the topic and I perfectly agree with you that "tings ain't that simple"
My point about TD / Thermal Distortion is that it gives us kind of semantic "alarm" message on the topic.
Leaving semantics aside for a moment, I'd like to know where *exactly* to draw the line on interaction .
As I understand your argumentation – you are saying there is non "distortion" (in the strict scientific sense) happening as there is no bandwidth intersection where the thermal caused resistance change could possibly interfere with the audio signal.
Maybe you are right .
On the other hand - digging deeper into this we can see that both – heat up and cooling down are *immediately* happening.
Not exactly correlated with the audio signal itself - but with the envelope of the amplitude of the audio signal.
And to make things even more complicated – there is kind of asymptotically slew rate limitation behaviour involved for the cooling down part .
From this point of view I could agree that there is no bandwidth intersection at all – as there are no two *frequencies* to compare with and hence calling the effect sort of "distortion" would in fact be wrong - at least in a more strict scientific sense -
- OR - looking at a pulse signal only – I could say - that this pulse is "distorted" (in the strict scientific sense) as there is *immediate* rise of resistance at the raising side of the pulse and also there is *immediate* fall of resistance (at a different scale) at the falling side of the pulse.
Summing together I tend towards looking at the effect of Power Compression from a Thermal Distortion point of view .
We also have to stay clear about two things :
- first, Thermal Distortion doesn't have any lag / delay – though it might not be "linear" over time
- second, Thermal Distortion occurs as well for *any* given frequency – though the effect on a single sine wave swing would be rather small as there is the cumulative effect of envelope behaviour at the raising side and the sort of asymptotic slew rate limitation behaviour at the decay side – nevertheless this is more about quantity than about the quality of the effect
Michael
Hi Mige0,
Some good points were raised in this discussion :
http://www.diyaudio.com/forums/showthread.php?s=&threadid=102587&perpage=25&highlight=&pagenumber=1
See some data in Philippe Lasage's paper which is quoted in one of the posts.
Some good points were raised in this discussion :
http://www.diyaudio.com/forums/showthread.php?s=&threadid=102587&perpage=25&highlight=&pagenumber=1
See some data in Philippe Lasage's paper which is quoted in one of the posts.
soongsc said:
If you follow my example in the paper linked below you can see that – from plain calculation – it affects even home and car audio.
But yes - sure – there never will be any 100% consensus about ranking of speaker design goals.
Pro Audio stuff is usually both – more sensitive and equipped with bigger voice coils than standard audio gear.
The background why they are doing so is to optimise first SPL capability and second reliability.
Fortunately bigger voice coils and top notch sensitivity improve *also* Thermal Distortion.
Compared to home-fi, PRO stuff always run at way higher SPL levels – hence home-fi and PRO stuff actually work in comparable Thermal Distortion ranges.
To put things into perspective you can also read about Keith Howard findings
http://stereophile.com/reference/1106hot/
Though I don't exactly agree with his conclusions at the end of his article it nevertheless might put another shade of light onto the subject
Michael
You mention a lot about voice coils reaching 120 degC. May I ask how much continous audio power is necessary for it to reach that temperature? I do not see it possible in most home audio conditions. I would probably turn the volume down long before this kind of temperature is reached.mige0 said:
soongsc said:
Not sure what you are asking for – as you can read it in my paper.
Basically its like having guests for tee – you will need more time for preparing tea than at breakfast as you will have to get more water boiled.
Same with speakers. To reach a certain VC temperature it takes the time needed to heat up the VC mass (plus the energy to cover the losses due to cooling – which at some point will balance to a thermal equilibrium *if* VC can handle that temperature).
Your water gets boiled very fast with a beefy stove or slowly on the flame of a single candle
Same with speakers.
In the example given it takes a 10W input to increase VC temperature by roughly 100 °C for only 10 seconds.
Is this something you will have occasionally happen with your home speakers?
Brian Ding of rythmikaudio has given an other example if you like to have a second source.
But again – the discussion about perceptional threshold is a different one than about "is it happening at all" or how should we name it
Michael
Michael
Your incorrect on one important point. The VC does not change temperature instantaneously. It begins to heat instantaneously, but there is a thermal mass that delays temperature changes and its temperature that affects the voice coils resistance. Further temperature rise and temperature fall at different rates being dependent on two different things.
IF the rise and fall time of the VC TEMPERTURE has a time constant that is significantly lower than any signal frequency then the Dif EQ is linear and there is no IMD of THD ("Nonlinear distorion"). There will always be effects of VC changes on the crossover and output power over the longer term and these things depend mostly on the thermal disidation capability of the device.
But no where that I have seen does anyone look at the effect that could occur with smll drivers where the VC heating and cooling could happen at rates fast enough to follow the signal. This aspect seems to be overlooked.
To me its mostly about these time constants as a very slow time constant of temperature effects would simply cause slow and small variations is the frequeny response and would not be heard dynamically. In fact they would be hard to hear at all. But changes on the time scale of the musical dynamics could seriously affect the perceived dynamics of the music.
Your incorrect on one important point. The VC does not change temperature instantaneously. It begins to heat instantaneously, but there is a thermal mass that delays temperature changes and its temperature that affects the voice coils resistance. Further temperature rise and temperature fall at different rates being dependent on two different things.
IF the rise and fall time of the VC TEMPERTURE has a time constant that is significantly lower than any signal frequency then the Dif EQ is linear and there is no IMD of THD ("Nonlinear distorion"). There will always be effects of VC changes on the crossover and output power over the longer term and these things depend mostly on the thermal disidation capability of the device.
But no where that I have seen does anyone look at the effect that could occur with smll drivers where the VC heating and cooling could happen at rates fast enough to follow the signal. This aspect seems to be overlooked.
To me its mostly about these time constants as a very slow time constant of temperature effects would simply cause slow and small variations is the frequeny response and would not be heard dynamically. In fact they would be hard to hear at all. But changes on the time scale of the musical dynamics could seriously affect the perceived dynamics of the music.
gedlee said:
Well, I guess if we look at VC temperature change – and subsequent resistance change - from a pure scientific point of view - it actually *does* change instantaneously.
There is no delay whatsoever as I pointed out in my last posting. The wire of the voice coil heats up according to the electrical power (in Watt seconds) put into the speaker minus the thermal losses due to cooling.
I am with you, that it takes time to reach temperatures that might be significant (what ever that may be) but I am strict, in that there is instantaneously temperature change. This is simply a distinction between the quality and the quantity of this effect – don't mix !
If you look at it from a "conservation of energy" point of view, you will immediately become clear about that there is no reservoir of energy without temperature rise, Earl.
To put things into perspective I have set up a quick simulation.
Starting from an ambient temperature equilibrium things look like below
This is how VC temperature changes with five cycles of constant energy injection (where heat up can be observed) interrupted by zero energy injection (where cooling can be observed).
The duty cycle was set to 50%
In the first plot the three traces reflect three different values of constant power injection :
An externally hosted image should be here but it was not working when we last tested it.
In the second plot the traces reflect three different leakages due to more or less efficient VC cooling:
An externally hosted image should be here but it was not working when we last tested it.
we can see is that there is a difference in how traces look like (the shape).
- If we set different input power the traces are more or less congruent.
- If we set different cooling capabilities the traces change from what we are familiar with at capacitor charging and discharging (no surprise looking at the equivalent electrical model I used
)What we also can see is that there is equilibrium after a certain time for any trace and condition we set.
Please don't look at the scales as this are *very* simplified simulations and nothing is calibrated in any way.
It doesn't make any sense to model leakage due to radiation, convection, forced convection, conduction and resistance corrected power injection etc in detail at this very early stage.
But even so - above simus could make a good start for coding a TD feed forward correction if we can refine models accordingly to measurements.
Regarding modulation of signals I'm not able to put it more clear as I already have outlined.
There is – undoubtedly - modulation of audio signals in the short term as I have outlined with my pulse example – but I agree the effect is small as the area under the RMS envelope is small for short intervals. Again its a distinction between the quality (if it happens at all) and the quantity of this effect.
If we look at what is perceptible or not – I'd rather not go too deep into that.
All I an confident about is when some people tend to talk about a certain issue and it seems to correlate well with sublime second order effects like TD for example.
That Thermal Distortion is measurable is nothing new and Brian Ding has already posted valuable plots.
Michael
I'm sorry but I don't follow your simulations so I can't comment on them.
You seem to be lumping "heat" with "temerature" and this is incorrect. The "heating" begins immediately, and there is an instantaneous temperature "change", but the temperture rise depends on the "heat capacity" of the voice coil. In other words it will be slower for a large VC than for a small one.
You need to explain your sims terms better before they can be followed.
Could you point to those Ding plots.
On looking at your plots again, I think that where I would disagree is that the duty cycle time is way too long. I would not expect the system to reach equilibrium in anything like a few cycles, more like hundreds or thousands of cycles. Then I think that you would agree that the temperature curve would begin to look like a smooth line of growth to an asymptotic value much much larger than the incremental changes of temperature along this curve.
Unless the instantaneous incremental changes are significant AND happen faster than the RMS envelope trace there will not be any significant signal modulation.
Also, on you curves the temperature seems to grow and fall at about the same rate. These two rates would be orders of magnitude different. That would seriously change your curves.
You seem to be lumping "heat" with "temerature" and this is incorrect. The "heating" begins immediately, and there is an instantaneous temperature "change", but the temperture rise depends on the "heat capacity" of the voice coil. In other words it will be slower for a large VC than for a small one.
You need to explain your sims terms better before they can be followed.
Could you point to those Ding plots.
On looking at your plots again, I think that where I would disagree is that the duty cycle time is way too long. I would not expect the system to reach equilibrium in anything like a few cycles, more like hundreds or thousands of cycles. Then I think that you would agree that the temperature curve would begin to look like a smooth line of growth to an asymptotic value much much larger than the incremental changes of temperature along this curve.
Unless the instantaneous incremental changes are significant AND happen faster than the RMS envelope trace there will not be any significant signal modulation.
Also, on you curves the temperature seems to grow and fall at about the same rate. These two rates would be orders of magnitude different. That would seriously change your curves.
gedlee said:
Sorry for confusing you more than enlightening the subject with my simu – please don't take it for more than I have stated – its *very* simplified (first take on the subject) - as outlined above.
Basically it shows the effect of applying a signal to a loudspeaker for some time (1 sec to choose something but not meaning anything) – taking a break for some time and again applying a signal for some time.
The intend is to show - in qualitative terms - how TD will come and go. It already correlates pretty good to the plots of Ding at the thread Forr pointed us to – I assumed you have read it, so I didn't dive deeper into the findings there.
The plots of Brian are here:
http://www.diyaudio.com/forums/showthread.php?postid=1229129#post1229129
and here is how I translated the thermal voice coil behaviour into simulation
- the constant energy input into a speaker is simulated by the constant current source switching on and off several times
- there is energy exchange from electricity to heat in the VC occurring
- heat and temperature subsequently raise at a slope determined by the input power, the thermal mass and thermal leakage – modelled here by the capacitor (thermal mass) and the resistor (thermal leakage) in parallel
Sure, you are right that the slopes for raise and decay are much more different in reality – I already have outlined that and calculated some figures in my paper.
In the simu I concentrated on an intuitive grasp of TD over time and – especially for you, Earl – on the very staring point of TD as you seem to have problems with the time domain here.
Anyway lets sort out the temperature delay issue first in order to make some progress
I'm well aware of the different meanings of temperature versus heat – at least if I didn't mix it up during translation which I hopefully didn't
Earl, you stated :
"Your incorrect on one important point. The VC does not change temperature instantaneously."
I state:
Both - temperature and heat of the voice coil *do* change immediately, due to energy injection –
All energy (electrical power multiplied by time) is immediately converted into VC heat (minus the acoustic radiated energy and some mechanical losses of course) and heat is expressed by temperature multiplied by thermal mass (if that's the correct translation ?).
Its simply rock solid physics plus a grain of thermal theory.
You can prove me and the rest of the world wrong – but you will have to provide evidence first for your temperature delay theory – I have referred common theory and visualised it by simulation.
Regarding cycle time – again please don't look at the scale of the axis.
The time when equilibrium will happen depends on the heat dissipation capability and the power input only.
But undoubtedly equilibrium will happen (if the VC doesn't melt down earlier
) and for sure there will be a certain rise time and decay behaviour that may look pretty different if we change variables in the equation as shown by my plots.We will have to perform some useful measurements before we get a good feeling about how all this balances and at which time scale.
Yes, sure I agree that the final curve will look smoother – depending on the axis scales we apply – but its pretty pointless to show a smooth curve when we are *also* interested how – in qualitative terms – raise and decay of TD occur.
Michael
A few things that need to be considered:mige0 said:
Not sure what you are asking for ?as you can read it in my paper.
Basically its like having guests for tee ?you will need more time for preparing tea than at breakfast as you will have to get more water boiled.
Same with speakers. To reach a certain VC temperature it takes the time needed to heat up the VC mass (plus the energy to cover the losses due to cooling ?which at some point will balance to a thermal equilibrium *if* VC can handle that temperature).
Your water gets boiled very fast with a beefy stove or slowly on the flame of a single candle
Same with speakers.
In the example given it takes a 10W input to increase VC temperature by roughly 100 °C for only 10 seconds.
Is this something you will have occasionally happen with your home speakers?
Brian Ding of rythmikaudio has given an other example if you like to have a second source.
But again ?the discussion about perceptional threshold is a different one than about "is it happening at all" or how should we name it
Michael
1. If you give a speaker 10W of music, depending on speaker driver count and XO design, in reality you may only get some 2 or 3W to the individual drivers.
2. Very seldom does one listen at 10W per driver listening levels in the home environment for 10 seconds; well, unless one uses the system for karaoke, it would most likly be <5 seconds.
3. Gedlee has mentioned this earlier, unless the temperature is varying, the coil characteristics is still quite linear. According to B&K sound quality metrics, fluctuation strength (which is between 1~20Hz) with 4Hz being the most annoying. So even if the driver takes the power 10W the way you have described, what effects does it have on sound reproduction? What will it sound like? Additionally, according to a JBL paper presented in 1984 at the 76th AES convention, temperature fluctuation can be about 1Hz, which I assume to be with pro audio.
454Casull said:
Sure, but again don't look at the scales when you draw conclusions.
Cooling is pretty simple at a first take but extremely complex for a loudspeaker in reality.
There are basically only three ways to transfer heat
- radiation (goes basically by the temp difference power 4 and some surface color constants)
- convection (depends strongly on airflow speed)
- conduction (basically linear like a resistor)
If we don't have a ferro fluid speaker only convection and radiation is left (if we don't take the VC former, the spider and the membrane into account).
But what makes it that immense complex is that we have *very* different conditions depending on the sound material and how the in and out strokes of the membrane / dust-cap / voice coil accelerate convection and subsequently the thermal sink capability of the motor as a whole before the motor can hand over the heat into the almost infinite thermal sink of a room (in case of OB).
So we will have to break down complexity into some more or less usefully simplifications. This is the creative fun part
.Discussing basic knowledge in front of any consensus might be necessary but slows down the process heavily and also needs some mental investment.
Its kind of a challenge to bring all this down to possibly create some useful treatment in the end – not knowing if the sonic improvement is worth the effort until we can audition it in our listening room – hopefully not only with subwoofers.
Michael
Michael
Yes, I mistated the first time, but not the second time. The heat appears instantly and rises from zero and follows the current in the voice coil instantaneously. The temperature will *change* instantaneously but its rate of change is dictated by the thermal mass for rising and it cools at a different rate dictated by several complex factors (as you mention), but suffice it to say that it will be much slower than the temperature rise. It might be safe to say that the temperature rise will be very fast and the cooling very slow such that the temperature will be a staircase upward towards the asymptotic value of quescence for any steady state input.
I think that its your term TD (thermal distortion) that bothers me because you don't seperate out the linear from the nonlinear and to me it's the fact that these two are quite different that is the crux of the whole problem.
If we continue then we need better terms or we will get lost. Lets let LTD (Linear TD) be that effect which depends on the long term temperature of the VC. LTD will be dominated by the loudspeakers cooling mechanisms. Lets let NTD (Nonlinear TD) be the effect that is the modulation of one tone by the thermal changes in the voice coil due to a much lower frequency signal, maybe even just the signals envelope (very low frequency). The time scales for NTD to be a factor are very very short compared to LTD. NTD will depend almost exclusively on voice coil copper mass. It will not depend on any cooling mechanisms since these have time scales far too long to influence NTD.
Does this make sense to you?
I found some Klippel measurements by Dan Wiggens in a post, is this waht you were refering to? Thise are strickly LTD. Just look at the time scale.
Yes, I mistated the first time, but not the second time. The heat appears instantly and rises from zero and follows the current in the voice coil instantaneously. The temperature will *change* instantaneously but its rate of change is dictated by the thermal mass for rising and it cools at a different rate dictated by several complex factors (as you mention), but suffice it to say that it will be much slower than the temperature rise. It might be safe to say that the temperature rise will be very fast and the cooling very slow such that the temperature will be a staircase upward towards the asymptotic value of quescence for any steady state input.
I think that its your term TD (thermal distortion) that bothers me because you don't seperate out the linear from the nonlinear and to me it's the fact that these two are quite different that is the crux of the whole problem.
If we continue then we need better terms or we will get lost. Lets let LTD (Linear TD) be that effect which depends on the long term temperature of the VC. LTD will be dominated by the loudspeakers cooling mechanisms. Lets let NTD (Nonlinear TD) be the effect that is the modulation of one tone by the thermal changes in the voice coil due to a much lower frequency signal, maybe even just the signals envelope (very low frequency). The time scales for NTD to be a factor are very very short compared to LTD. NTD will depend almost exclusively on voice coil copper mass. It will not depend on any cooling mechanisms since these have time scales far too long to influence NTD.
Does this make sense to you?
I found some Klippel measurements by Dan Wiggens in a post, is this waht you were refering to? Thise are strickly LTD. Just look at the time scale.
The simple form of the equation for temperature in the VC is
dT/dt = Q - L
or in works, the time rate of change in temperature is equal to the rate of heat generation, Q minus the loss of heat to the surrounds. Q can change instantaneously. L is related to the difference between the temperature of the VC and that of the surroundings. L can not change instantaneously unless T VC changes instantaneously. BUT the equation says that even if L and Q change instantaneously, it is only the rate of temperature change that changes instantaneously. Not the VC T. A change in VC T takes time,
T(t2) – T(t1) =Integral of (Q -L) over the time period dt.
If you rewrite the equation in terms of T, Re and I, and express them as long term mean values plus a fluctuation, for example, for T,
T(t) = Tmean + T'(t)
you will find that there is a steady mean temperature about which there are time dependent fluctuations. The equation for the fluctuations in temperature about the mean will have both linear and nonlinear contributions. These nonlinear terms mean that the time rate of change of the temperature fluctuation will be nonlinear and can give rise to nonlinear distortion.
Thermal compression, on the other hand, is more associated with the mean, steady temperature rise in the VC which will be proportional to the mean current squared. This is reflected as a loss in efficiency, due to increased VC Re. The lower the "cold" efficiency of the driver, the less severe the thermal compression will be when trying to reproduce a given SPL for a "long" period of time.
Now, you can fool around with models and equations all you like and make them show anything you like. But to have a sense of what is really going on the models have to be based on parameters which are representative of real drivers.
dT/dt = Q - L
or in works, the time rate of change in temperature is equal to the rate of heat generation, Q minus the loss of heat to the surrounds. Q can change instantaneously. L is related to the difference between the temperature of the VC and that of the surroundings. L can not change instantaneously unless T VC changes instantaneously. BUT the equation says that even if L and Q change instantaneously, it is only the rate of temperature change that changes instantaneously. Not the VC T. A change in VC T takes time,
T(t2) – T(t1) =Integral of (Q -L) over the time period dt.
If you rewrite the equation in terms of T, Re and I, and express them as long term mean values plus a fluctuation, for example, for T,
T(t) = Tmean + T'(t)
you will find that there is a steady mean temperature about which there are time dependent fluctuations. The equation for the fluctuations in temperature about the mean will have both linear and nonlinear contributions. These nonlinear terms mean that the time rate of change of the temperature fluctuation will be nonlinear and can give rise to nonlinear distortion.
Thermal compression, on the other hand, is more associated with the mean, steady temperature rise in the VC which will be proportional to the mean current squared. This is reflected as a loss in efficiency, due to increased VC Re. The lower the "cold" efficiency of the driver, the less severe the thermal compression will be when trying to reproduce a given SPL for a "long" period of time.
Now, you can fool around with models and equations all you like and make them show anything you like. But to have a sense of what is really going on the models have to be based on parameters which are representative of real drivers.
John
Thanks for the analysis. You basically said what I said, although the sentence "The equation for the fluctuations in temperature about the mean will have both linear and nonlinear contributions." could be misleading. Its not the temperature change being linear or nonlinear, but its effect on the signal output. I believe thats what you meant, but the wording makes it confusing.
My intent is to do a model in Mathcad which contains all these factors and to use this to actually listen to real signals modified by real parameters. Then I'd like to use this model in a subjective test to find the significant perceptual thresholds.
Thanks for the analysis. You basically said what I said, although the sentence "The equation for the fluctuations in temperature about the mean will have both linear and nonlinear contributions." could be misleading. Its not the temperature change being linear or nonlinear, but its effect on the signal output. I believe thats what you meant, but the wording makes it confusing.
My intent is to do a model in Mathcad which contains all these factors and to use this to actually listen to real signals modified by real parameters. Then I'd like to use this model in a subjective test to find the significant perceptual thresholds.
In order for fluctuation in tempaerature to give rise to non-linear distortion, this fluctuation needs to be much higher in frequency of the signal it's distorting. With current available information, temperature would more likely cause fluctuation in the audio frequency.john k... said:
I like the way you put it.
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