I am not at all convinced by that. I can hear to 18kHz (loud, but unmasked) and the effect I hear seems to be stronger at the other end of the range of the tweeter.soongsc said:
That makes the radiation pattern explanation plausible.
Of course we could be talking about two different but equally valid effects. Without some solid measurements I think it time for me to stop.
Ken
Re: Re: Re: Re: Re: Re: Re: thermal compression
I want to be sure that you are distinguishing what I am saying. The "heating" occurs instantaneously, but the "temperature change" takes time. The heating will follow the RMS signal on a very short time scale - virtually instantaneous, but the wire temperature will lag depending on the copper mass. Then the temperature of the VC itself will rise, on a longer time scale and will cool, as you suggest, but on an even longer time scale (no fluid assumed) because this happens through convection not conduction.
The point is that these time scales all differ, but the only one that could track the signal close enough to be heard as a dynamic effect or nonlinearity is the wire temperature change itself because this is by far the shortest.
Thus, I am hypothesizing that we could view the problem as one where the Re changes WITH the signal (squared actually) directly proportional to the wire mass, while the longer term mean Re will change based on all of the other thermal factors, but these will be slow compared to the signal.
If I model this effect then I could do a simulation of its audibility. The longer term effects from the voice coil and magnet are well studied, but I don't think that they considered effects on the time scale of the signal.
kstrain said:
I want to be sure that you are distinguishing what I am saying. The "heating" occurs instantaneously, but the "temperature change" takes time. The heating will follow the RMS signal on a very short time scale - virtually instantaneous, but the wire temperature will lag depending on the copper mass. Then the temperature of the VC itself will rise, on a longer time scale and will cool, as you suggest, but on an even longer time scale (no fluid assumed) because this happens through convection not conduction.
The point is that these time scales all differ, but the only one that could track the signal close enough to be heard as a dynamic effect or nonlinearity is the wire temperature change itself because this is by far the shortest.
Thus, I am hypothesizing that we could view the problem as one where the Re changes WITH the signal (squared actually) directly proportional to the wire mass, while the longer term mean Re will change based on all of the other thermal factors, but these will be slow compared to the signal.
If I model this effect then I could do a simulation of its audibility. The longer term effects from the voice coil and magnet are well studied, but I don't think that they considered effects on the time scale of the signal.
Re: Re: Re: Re: Re: Re: Re: Re: thermal compression
Hopefully I saw what you were saying, and agree in detail but with an addition to the hypothesis.
I expect that, because of significant outflow of heat across the gap, the temperature rise, even within kHz cycles, is significantly less than you'd calculate just from the heat capacity of the copper (~15K/J) and the input power.
I'm saying that with, for example, a single 1000W 10ms burst the temperature does not reach as much as 150K above ambient as even during the burst a lot of heat crosses the gap where it has almost no effect on the magnet temperature. (And to be clear the individual cycles within the burst also have much smaller temperature modulation.)
This thought was inspired by the initial results I was getting before I destroyed my test tweeter. I could be wrong, but suggest including the cooling effect as a parameter in any model. It would also be interesting to pin down the extent to which ferrofluid removes heat compared to air.
I suppose the picture is that the air/ferrofluid in direct contact with the coil adds to the thermal mass but is rather rapidly replaced from a reservoir of cold material. The quantities and dimensions involved are so small that very little flow is needed to achieve that very quickly. (Unless I made a calculation error, conduction alone is by no means adequate to provide the observed cooling. )
Ken
gedlee said:
Hopefully I saw what you were saying, and agree in detail but with an addition to the hypothesis.
I expect that, because of significant outflow of heat across the gap, the temperature rise, even within kHz cycles, is significantly less than you'd calculate just from the heat capacity of the copper (~15K/J) and the input power.
I'm saying that with, for example, a single 1000W 10ms burst the temperature does not reach as much as 150K above ambient as even during the burst a lot of heat crosses the gap where it has almost no effect on the magnet temperature. (And to be clear the individual cycles within the burst also have much smaller temperature modulation.)
This thought was inspired by the initial results I was getting before I destroyed my test tweeter. I could be wrong, but suggest including the cooling effect as a parameter in any model. It would also be interesting to pin down the extent to which ferrofluid removes heat compared to air.
I suppose the picture is that the air/ferrofluid in direct contact with the coil adds to the thermal mass but is rather rapidly replaced from a reservoir of cold material. The quantities and dimensions involved are so small that very little flow is needed to achieve that very quickly. (Unless I made a calculation error, conduction alone is by no means adequate to provide the observed cooling. )
Ken
Re: Re: Re: Re: Re: Re: Re: Re: Re: thermal compression
Where we differ is that my understanding of the problem is that the conduction of the heat through the air to the magnet is very inefficient being mostly convection and radiation. If this were NOT true then ferrofluid would not work. The fact that it dramatically reduces the VC temperature means that without it the cooling has been substantially reduced. I keep making the point that I assume NO ferrofliud (because I simply wouldn't use it in any speaker of mine). I really don't think that your argument is correct when the gap is filled with air. The cooling is slow and inefficient which means that the wire temp changes are far faster and greater than a longer term look at Re will indicate.
This problem has been studied extensively, but always, to my knowledge, by looking on the time scale of 100s of ms, which is way too long to see what I am talking about. You don't see what your not looking for.
I never intended to do a model without the cooling effects - that would be pointless, but modeling the effects using only the long term time constants measured in practice may not be the whole story.
kstrain said:
Where we differ is that my understanding of the problem is that the conduction of the heat through the air to the magnet is very inefficient being mostly convection and radiation. If this were NOT true then ferrofluid would not work. The fact that it dramatically reduces the VC temperature means that without it the cooling has been substantially reduced. I keep making the point that I assume NO ferrofliud (because I simply wouldn't use it in any speaker of mine). I really don't think that your argument is correct when the gap is filled with air. The cooling is slow and inefficient which means that the wire temp changes are far faster and greater than a longer term look at Re will indicate.
This problem has been studied extensively, but always, to my knowledge, by looking on the time scale of 100s of ms, which is way too long to see what I am talking about. You don't see what your not looking for.
I never intended to do a model without the cooling effects - that would be pointless, but modeling the effects using only the long term time constants measured in practice may not be the whole story.
It will be interesting to see the magnitude of the effect you see, if you have a chance to model it.
I don't know how applicable this is, but these audio transistors are designed partially to eliminate distortion that's caused by temperature changes on the time scale of audio signals. The mechanisms (at least some of them) seem different here, as the largest effect is at lower powers. The mass of the elements involved might be considerably smaller than a tweeter coil, but maybe not. But I'd guess that they are of the same order of magnitude, so that seems to make the coil issue worth a look.
http://www.onsemi.com/pub_link/Collateral/AND8196-D.PDF
Sheldon
I don't know how applicable this is, but these audio transistors are designed partially to eliminate distortion that's caused by temperature changes on the time scale of audio signals. The mechanisms (at least some of them) seem different here, as the largest effect is at lower powers. The mass of the elements involved might be considerably smaller than a tweeter coil, but maybe not. But I'd guess that they are of the same order of magnitude, so that seems to make the coil issue worth a look.
http://www.onsemi.com/pub_link/Collateral/AND8196-D.PDF
Sheldon
Sheldon said:
This looks like a great idea for power amps, but I don't see how it applies to loudspeakers.
Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: thermal compression
OK, no ferrofluid (there goes all my direct evidence).
But ...
Is air cooling really so inefficient given the very small gap? I wonder (I really am not sure).
My prejudice, until very recently, would have been to be agree with you without much thought (e.g. the last time this topic came up a few months ago), but I checked that manufacturers who offer tweeters with and without ferrofluid show only a relatively small difference in short or long term power handling (never factors of 10). Now, I don't really trust these figures, but I'd not be so confident that the air cooling is as poor as I previously thought (and you still think). I don't see how the long-term thermal balance works out if the heat flow through the gap is that poor (but I could be missing something in spite of doing quite a few calculations behind the scenes). I don't jave a convincing result to support my case either.
At the moment I very much doubt that you'll find something audible due to VC heating (extrapolating from your own results on other distortion mechanisms), and anyway don't own any working dome tweeters now.
Ken
gedlee said:
OK, no ferrofluid (there goes all my direct evidence).
But ...
Is air cooling really so inefficient given the very small gap? I wonder (I really am not sure).
My prejudice, until very recently, would have been to be agree with you without much thought (e.g. the last time this topic came up a few months ago), but I checked that manufacturers who offer tweeters with and without ferrofluid show only a relatively small difference in short or long term power handling (never factors of 10). Now, I don't really trust these figures, but I'd not be so confident that the air cooling is as poor as I previously thought (and you still think). I don't see how the long-term thermal balance works out if the heat flow through the gap is that poor (but I could be missing something in spite of doing quite a few calculations behind the scenes). I don't jave a convincing result to support my case either.
At the moment I very much doubt that you'll find something audible due to VC heating (extrapolating from your own results on other distortion mechanisms), and anyway don't own any working dome tweeters now.
Ken
gedlee said:
The transistors output, relative to input, can be modulated to some degree by it's temperature. If that modulation occurs on the time scale of an audio frequency wave, then it would result in distortion. Part of the distortion reduction they show (particularly at low levels) may just be due to a higher bias point, but not all of it. Some could be a result of the modulation effect. The thermal elements in the transistor (TO 264 case) might be similar in effective size to a tweeter coil (the actual junctions I would guess to be smaller, but they are in a thermally conductive surrounding). So maybe some analogy to instantaneous coil heating (hereby acknowledged as a stretch).
Sheldon
http://en.wikipedia.org/wiki/Copper
Electrical resistivity rho = 16.78 nΩ·m (20 °C)
Specific heat Cp =385 J/(kg K)
Density (near r.t.) D = 8960 kg / m3
Let's determine the section of the wire in a midwoofer.
SEAS CB17RCY/P midwoofer (sounds nice, btw).
Flux : B = 1.15 (T)
Force Factor : ff = 6.6 (N/A) = F/I
L is the length of wire (m).
We know F = I L B therefore
L = F/(I B) = ff / B = 5.7 m
5.7 meters of wire seems reasonable.
DC resistance if 5.7 ohms, therefore wire section is
S = rho L / R
S = 0.017 mm²
(That's really small wire).
It makes about 0.86 grams of copper.
Moving mass is 10g, reality checks.
Let's send a current through this wire.
Neglecting Skin effect.
Neglecting self-cooling (convection or conduction).
Dissipated power P (W)
Dissipated power per mass unit : Pm = P / m (W/kg)
Temperature delta per second dT/dt = P/( m Cp ) (K/s)
With this woofer, if we send 1W, the voice coil temperature will rise :
1 Kelvin/second
(neat assortment of constants, eh ?)
Now :
delta R / delta T = 0.0039 * R
If we were to send a 100W transient during 1 ms the temperature would rise 0.1 K.
Voice coil resistance would change from 5.7 ohms to 5.7022 ohms, a whooping 0.039 %
So as you can see the idea of suggesting that the voice coil temperature will vary on time scales comparable to audio frequencies is complete nonsense. It is a completely different story of course with solid state devices where you pump watts (or milliwats) into the micrograms (or nanograms) of a silicon junction.
If we were to send 10W average power, however, because we use this midwoofer as a woofer and we like big bass from tiny speakers, the voice coil temperature would rise at 10K/s which means it would quickly reach (after say 10-20 seconds) thermal equilibrium between dissipated power and airflow, at a rather hot temperature. If it heats by 100K, resistance would change from 5.7 ohms to 7.9 ohms, a 39% change ! and it would take longer to cool down.
Electrical resistivity rho = 16.78 nΩ·m (20 °C)
Specific heat Cp =385 J/(kg K)
Density (near r.t.) D = 8960 kg / m3
Let's determine the section of the wire in a midwoofer.
SEAS CB17RCY/P midwoofer (sounds nice, btw).
Flux : B = 1.15 (T)
Force Factor : ff = 6.6 (N/A) = F/I
L is the length of wire (m).
We know F = I L B therefore
L = F/(I B) = ff / B = 5.7 m
5.7 meters of wire seems reasonable.
DC resistance if 5.7 ohms, therefore wire section is
S = rho L / R
S = 0.017 mm²
(That's really small wire).
It makes about 0.86 grams of copper.
Moving mass is 10g, reality checks.
Let's send a current through this wire.
Neglecting Skin effect.
Neglecting self-cooling (convection or conduction).
Dissipated power P (W)
Dissipated power per mass unit : Pm = P / m (W/kg)
Temperature delta per second dT/dt = P/( m Cp ) (K/s)
With this woofer, if we send 1W, the voice coil temperature will rise :
1 Kelvin/second
(neat assortment of constants, eh ?)
Now :
delta R / delta T = 0.0039 * R
If we were to send a 100W transient during 1 ms the temperature would rise 0.1 K.
Voice coil resistance would change from 5.7 ohms to 5.7022 ohms, a whooping 0.039 %
So as you can see the idea of suggesting that the voice coil temperature will vary on time scales comparable to audio frequencies is complete nonsense. It is a completely different story of course with solid state devices where you pump watts (or milliwats) into the micrograms (or nanograms) of a silicon junction.
If we were to send 10W average power, however, because we use this midwoofer as a woofer and we like big bass from tiny speakers, the voice coil temperature would rise at 10K/s which means it would quickly reach (after say 10-20 seconds) thermal equilibrium between dissipated power and airflow, at a rather hot temperature. If it heats by 100K, resistance would change from 5.7 ohms to 7.9 ohms, a 39% change ! and it would take longer to cool down.
Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: thermal compression
Manufacturers! If it were only a small effect they wouldn't spend the money. No its a big effect, but Ferrofluid has its other problems, mostly that it doesn't last very long and turns to gunk.
Air is a good insulator if its not moving. Only when it moves can it conduct off any heat, and thats why they spend so much time ventilating the gap. Again, they wouldn't bother to do this if air was a good heat conductor.
Voice coils get hot - very hot. I've seen them melt, burst into flames, you name it. Your experience with a power bursts is typical. No matter what the "manufacturers" tell you no dome is going to survive a power burst like that and NO I'm not going to argue the point.
kstrain said:
Manufacturers! If it were only a small effect they wouldn't spend the money. No its a big effect, but Ferrofluid has its other problems, mostly that it doesn't last very long and turns to gunk.
Air is a good insulator if its not moving. Only when it moves can it conduct off any heat, and thats why they spend so much time ventilating the gap. Again, they wouldn't bother to do this if air was a good heat conductor.
Voice coils get hot - very hot. I've seen them melt, burst into flames, you name it. Your experience with a power bursts is typical. No matter what the "manufacturers" tell you no dome is going to survive a power burst like that and NO I'm not going to argue the point.
Consider the FDS8878 Mosfet.
30V, 10.2A, 14mΩ,
rDS(on) = 17mΩ @ VGS = 4.5V, ID = 9.3A
SO-8 package
Certainly not suitable for an output device but for my LED driver, should be OK.
Anyway, datasheet says :
Max Tj : 150°C
Single Pulse Maximum Power Dissipation : 100W @ 1 ms
So, if the part that heats in the MOSFET die absorbs 0.1 J of energy, it will heat from 20°C to 150°C, which from the silicon specific heat allows us to calculate its mass, which is :
0.0011 grams
The thermal impedance graph has various poles at audio frequencies too.
Of course for a small signal BJT which only handles a few milliamps, junction mass and thermal capacity will be very much lower than in a mosfet specifically optimized for surviving thermal pulses without a heatsink in a SO8 package. And thermal poles will be smack in the middle of the audio band. But this is never mentioned in BJT datasheets, only for power transistors. For a transistor on a chip (opamp) the effects are, of course, magnified, but then, transistors are so close that thermal coupling between the differential pairs could happen above audio frequencies.
From the formulas in my previous post it would be easy to compute the self-heating in a tweeter coil, it would probably heat more than a midwoofer (having much lower mass) but then, tweeters usulaly handle much less power, unless the crossover is too low in freq, or too low order, in that case you will get crappy sound from the tweeter having too much excursion and getting really badly nonlinear, and ultimately melting its coil if the volume knob is pushed past the party zone.
30V, 10.2A, 14mΩ,
rDS(on) = 17mΩ @ VGS = 4.5V, ID = 9.3A
SO-8 package
Certainly not suitable for an output device but for my LED driver, should be OK.
Anyway, datasheet says :
Max Tj : 150°C
Single Pulse Maximum Power Dissipation : 100W @ 1 ms
So, if the part that heats in the MOSFET die absorbs 0.1 J of energy, it will heat from 20°C to 150°C, which from the silicon specific heat allows us to calculate its mass, which is :
0.0011 grams
The thermal impedance graph has various poles at audio frequencies too.
Of course for a small signal BJT which only handles a few milliamps, junction mass and thermal capacity will be very much lower than in a mosfet specifically optimized for surviving thermal pulses without a heatsink in a SO8 package. And thermal poles will be smack in the middle of the audio band. But this is never mentioned in BJT datasheets, only for power transistors. For a transistor on a chip (opamp) the effects are, of course, magnified, but then, transistors are so close that thermal coupling between the differential pairs could happen above audio frequencies.
From the formulas in my previous post it would be easy to compute the self-heating in a tweeter coil, it would probably heat more than a midwoofer (having much lower mass) but then, tweeters usulaly handle much less power, unless the crossover is too low in freq, or too low order, in that case you will get crappy sound from the tweeter having too much excursion and getting really badly nonlinear, and ultimately melting its coil if the volume knob is pushed past the party zone.
Nice analysis. So indeed orders of magnitude difference between transistor junction mass and VC mass, even for a dome tweeter.
Sheldon
Sheldon
peufeu said:
In the above sample,it looks something wrong....
The BL Product by the "Flux(B)" and the "efficiency length", such "efficiency length" only include the length of the wire in the magnet gap,so the length of the total wire often longer than the "efficiency length". So all of the calculated under length must be recalculate.
🙂
Yeah, you're right.
However, if the wire length is longer, while dissipated power stays the same (since R is known), then the calculated copper wire section gets larger and self-heating becomes even smaller... So, I actually made a worst-case calculation 😉
However, if the wire length is longer, while dissipated power stays the same (since R is known), then the calculated copper wire section gets larger and self-heating becomes even smaller... So, I actually made a worst-case calculation 😉
peufeu said:
I missed this before, but I think that its correct - for a woofer. It would be interesting to do it for a tweeter at much higher powers as would be required from an inefficient dome (very small voice coil mass) playing at high SPL. There the numbers might get to be significant. I haven't taken the time to calculate them, only that it is obvious that there has to be SOME Re change at near signal time frames. I agree that this effect could never track the actual signal such that a nonlinearity occurs, but a 10 ms. tone burst into a small tweeter could be a significant factor and may be audible.
This would not be so hard to measure experimentally :
- Wire tweeter in series with, say, a 8 ohms resistor with a low tempco and high mass (my dumpster-found 8 ohms test resistors, for instance, measure 15 cm x 3 cm diameter, they are good for space heating too)
- Connect digital scope to tweeter
- Send a DC current of a few milliamps to tweeter + resistor
- Send pulse of high current of 10 ms duration to tweeter+resistor, either sine or square
(you can use voltage instead of current, too, as long as you know the resistor's value)
- Look at Voltage on tweeter, before heating it, and after heating it, with the known current of a few milliamps going through it you can calculate its hot and cold resistance.
For obvious reasons this should be done with a digital scope so you don't need to repeat the pulse while you are watching on the screen. Poor tweeter.
Also care should be taken not to clip the scope input, or else you will test if the scope has thermal tails. Gating the scope input with a little mosfet synced to the current pulse is a good idea, or just use a dumb diode and a resistor.
A reality-check with a resistor instead of the tweeter, after the tweeter has blown for instance, would also be a good idea.
All in all this should not need more than 10 bucks in parts and some perfboard. I don't have any suicidal tweeters around, but perhaps someone wants to try ?
- Wire tweeter in series with, say, a 8 ohms resistor with a low tempco and high mass (my dumpster-found 8 ohms test resistors, for instance, measure 15 cm x 3 cm diameter, they are good for space heating too)
- Connect digital scope to tweeter
- Send a DC current of a few milliamps to tweeter + resistor
- Send pulse of high current of 10 ms duration to tweeter+resistor, either sine or square
(you can use voltage instead of current, too, as long as you know the resistor's value)
- Look at Voltage on tweeter, before heating it, and after heating it, with the known current of a few milliamps going through it you can calculate its hot and cold resistance.
For obvious reasons this should be done with a digital scope so you don't need to repeat the pulse while you are watching on the screen. Poor tweeter.
Also care should be taken not to clip the scope input, or else you will test if the scope has thermal tails. Gating the scope input with a little mosfet synced to the current pulse is a good idea, or just use a dumb diode and a resistor.
A reality-check with a resistor instead of the tweeter, after the tweeter has blown for instance, would also be a good idea.
All in all this should not need more than 10 bucks in parts and some perfboard. I don't have any suicidal tweeters around, but perhaps someone wants to try ?
I'd be more interested in you just running the numbers again for this situation. You did a good job! I'll accept the math. You seemed to be good at it.
The thing is that I don't deal with dome tweeters so I don't know them. My assumption is that if a "typical" domes modulation can't be audible then a compression drivers can't be either and we can drop the whole thing. But if the dome COULD be audible, then the interesting question is "would a compression drivers thermal modulation be audible?"
SEAS Excel T25CF001
http://www.seas.no/index.php?option=com_content&task=view&id=54&Itemid=78
R = 4.6 Ohm
BL = 3.5 N/A
B = 1.8 T
Note :
Voice coil height : 1.5 mm
Air gap height : 2 mm
Excursion pp : 0.5 mm
This means the entire coil is in the gap (as opposed to a woofer).
With the same formulas as above :
=> L = 1.9 m
=> S = 0.007 mm²
(wire diameter 13 µm, small !)
=> Copper mass 0.12 grams
Moving mass 0.33 g (consistent).
Temperature rise is :
21.5 K/J
(Kelvin per Joule)
ie. If you give it 1 watt during 1 s it will heat 21.5 °K or °C.
If we suppose the voice coil wire is aluminum instead of copper, we get :
16.5 K/J
So, it will heat much more than the woofer, of course. But it should (hopefully) also receive much less power.
If we were to send a 100W transient during 1 ms the temperature would rise 2.15 degrees K (or °C), this corresponds to a 0.8% change in resistance.
It is significant.
However :
- With a 91 dB efficiency, this would correspond to a 110 dB peak (from one tweeter, 116 dB for both).
- According to this excursion calculator,
http://www.baudline.com/erik/bass/xmaxer.html
at 2KHz, to create a 110 dB@1m sound, the tweeter would have to move 0.87 mm one-way, which is 3.5 times its specified Xmax.
Using the specified Xmax of 0.25mm one-way (0.5mm pp) we get a peak acoustic power level of 100 dB, therefore 10 times less electric power..
- With the recommended 2K crossover, it would really take a very large amplifier, and extremely loud levels, for this kind of peak power to occur.
- Since this tweeter will most likely be used in audiophile speakers, it will be mated to small woofers, of maximum size 8-10", which means that if an amplifier capable of those power levels was used, and pushed to the limit, the woofers would either explode, or distort so much that the tweeter self-heating doesn't matter anyway.
All these reasons come down to :
Self-heating in this tweeter should not really be a problem, because other sources of distortion will dwarf it before it happens, like xmax, and woofer cones being ejected from speakers, etc.
Also, this tweeter (while probably sounding excellent at normal listening levels) would be totally inadequate for Geddes' headbanging levels.
************
Now consider this compression driver :
http://profesional.beyma.com/ENGLISH/pdf/descarga.php?pdf=CP350Ti.pdf
1W-1m is 104 dB with horn.
It is aluminum this time.
L = 5 m
S = 0.02 mm² (22 µm dia)
mass = 0.266 g
self-heating = 3.74 K/J
Of course this one has a much larger coil, much heavier, it is built to handle some violent abuse.
For instance, then, to produce 111dB @ 1m during 1 ms,
- The SEAS would need 100W and would heat 2.15 °C
(but this is purely academic because it would never reach this power level)
- The Beyma compression driver would need about 5 watts so it would heat by 0.0187 degrees.
Xmax would probably not be a problem since it is rated for 70W ABOVE 1.5k (ie. 70W average power from 1.5K to 7K).
The SEAS is rated for 90W "IEC 268-5, via High Pass Butterworth Filter 2500Hz 12 dB/oct." whatever that means, probably 90W before the crossover.
*** Conclusion :
The whole speaker will fail before self-heating becomes a problem in the SEAS tweeter.
Your ears will bleed before self-heating becomes a problem for the Beyma driver.
http://www.seas.no/index.php?option=com_content&task=view&id=54&Itemid=78
R = 4.6 Ohm
BL = 3.5 N/A
B = 1.8 T
Note :
Voice coil height : 1.5 mm
Air gap height : 2 mm
Excursion pp : 0.5 mm
This means the entire coil is in the gap (as opposed to a woofer).
With the same formulas as above :
=> L = 1.9 m
=> S = 0.007 mm²
(wire diameter 13 µm, small !)
=> Copper mass 0.12 grams
Moving mass 0.33 g (consistent).
Temperature rise is :
21.5 K/J
(Kelvin per Joule)
ie. If you give it 1 watt during 1 s it will heat 21.5 °K or °C.
If we suppose the voice coil wire is aluminum instead of copper, we get :
16.5 K/J
So, it will heat much more than the woofer, of course. But it should (hopefully) also receive much less power.
If we were to send a 100W transient during 1 ms the temperature would rise 2.15 degrees K (or °C), this corresponds to a 0.8% change in resistance.
It is significant.
However :
- With a 91 dB efficiency, this would correspond to a 110 dB peak (from one tweeter, 116 dB for both).
- According to this excursion calculator,
http://www.baudline.com/erik/bass/xmaxer.html
at 2KHz, to create a 110 dB@1m sound, the tweeter would have to move 0.87 mm one-way, which is 3.5 times its specified Xmax.
Using the specified Xmax of 0.25mm one-way (0.5mm pp) we get a peak acoustic power level of 100 dB, therefore 10 times less electric power..
- With the recommended 2K crossover, it would really take a very large amplifier, and extremely loud levels, for this kind of peak power to occur.
- Since this tweeter will most likely be used in audiophile speakers, it will be mated to small woofers, of maximum size 8-10", which means that if an amplifier capable of those power levels was used, and pushed to the limit, the woofers would either explode, or distort so much that the tweeter self-heating doesn't matter anyway.
All these reasons come down to :
Self-heating in this tweeter should not really be a problem, because other sources of distortion will dwarf it before it happens, like xmax, and woofer cones being ejected from speakers, etc.
Also, this tweeter (while probably sounding excellent at normal listening levels) would be totally inadequate for Geddes' headbanging levels.
************
Now consider this compression driver :
http://profesional.beyma.com/ENGLISH/pdf/descarga.php?pdf=CP350Ti.pdf
1W-1m is 104 dB with horn.
It is aluminum this time.
L = 5 m
S = 0.02 mm² (22 µm dia)
mass = 0.266 g
self-heating = 3.74 K/J
Of course this one has a much larger coil, much heavier, it is built to handle some violent abuse.
For instance, then, to produce 111dB @ 1m during 1 ms,
- The SEAS would need 100W and would heat 2.15 °C
(but this is purely academic because it would never reach this power level)
- The Beyma compression driver would need about 5 watts so it would heat by 0.0187 degrees.
Xmax would probably not be a problem since it is rated for 70W ABOVE 1.5k (ie. 70W average power from 1.5K to 7K).
The SEAS is rated for 90W "IEC 268-5, via High Pass Butterworth Filter 2500Hz 12 dB/oct." whatever that means, probably 90W before the crossover.
*** Conclusion :
The whole speaker will fail before self-heating becomes a problem in the SEAS tweeter.
Your ears will bleed before self-heating becomes a problem for the Beyma driver.