From Power Compression towards Thermal Distortion / developing on a point of view

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soongsc said:

I like the way you put it.:)


Me too ;)

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Earl, I am happy we finally sorted out the "temperature delay" issue.
:)


Its kind of a mental hurdle people have when it comes to thermo-dynamic as you can also see at many postings in the other thread (even crystal clear math whizz John seems to be sort of undecided here ;) ).

As for the concept of linear or nonlinear behaviour there is in fact sort of semantic problem .

I have checked back and been told that in German speaking areas there isn't the same feeling about the difference in the term "distortion".

Basically around here "distortion" is to be meant both linear and nonlinear – so I'd rather not like to follow your suggestion to differentiate between LTD and NTD in general, as to me this seems to become too much of a science speech somehow meaningless to most of us (I think we are already splitting hairs here with the whole Thermal Distortion thing :D ).


For the purpose of the discussion and for sorting things out - I certainly agree on this terms you would like to use (LTD / NTD), Earl.


At this point I have to go back one step and to correct something mentally misleading (me too).



If again we look at the simplified simulation


An externally hosted image should be here but it was not working when we last tested it.


we clearly can see that the rise time and the decay of thermal distortion basically is *symmetric* !!
In this simplified model its basically a low pass behaviour or – seen different - an integrator with loss.
This may describe TD much more accurate than the slew rate analogy I used before.
Most scientifically put, it might be called a "time variant system" – including all sorts of weird effects on very different time scales.



The feeling – or the picture in our mind – we have about decay many orders of magnitude slower than TD raise only happens at the very first period of the green trace.

Which is the case if we throw an enormous amount of energy on our speaker the motor cant dissipate quick enough – and as long as we are far from thermal equilibrium.


In that sense the cooling mechanism is *always* in the equation - unless we make "R-thermic" zero – meaning completely isolating the VC thermally – which hardly is our aim.


Also as soongs pointed out we should come to a point where we can predict sonic interference.

It's pretty hard to setup a simulation that is more correct without any measurements to compare with.
On the other hand it will become a challenge of its own to get TD measured without other effects at the same time scale.

If Thermal Distortion low pass behaviour is happening in the sub audio band its even hard to get any sidebands displayed by measurement.

On the other hand if I measure DC resistance by a multimeter and throw a hf load on the speaker it may not be posssible to measure short term variations.

Any good ideas about the measurement dilemma?


My idea so far would have been to use a low level sinus as the measurement signal and overlay bursts of high energy. This way we could possibly observe the complete TD effects bunch in the most intuitive time domain.

But at what frequencies to set our measurement for a first attempt?


john k... said:

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,



Yes sure a VC temperature change takes time – like it also takes time to inject energy into the voice coil (remember the time term in "Watt * seconds") - but again – temperature change starts *instantaneously*.
This is also reflected in my simple simu – the resistance raise starts immediately and *also* the rate of change starts immediately (bending the raising curve as a result of increased cooling due to increased temperature difference).


Michael
 
I would think that measuring distortion and harmonics at 1W, drive a driver to higher temperature and then immediately measure at 1W again would be the first step to confirm what temperature does to distortion. In the process, log the rate of rise in driver demperature via current change to calculate the temperature change of the coil to actually see how fast temperature change can modulate at.
 
Yes Earl, I agree that what I was saying was similar to your thoughts. I just though it may be helpful to expresses things in terms of the time averaged temperature and the short term fluctuations.

I can't say if these fluctuations will introduce nonlinear distortion or not, only that they will give rise to nonlinear terms in the equation for dT'/dt. These terms arise form cross terms involving products of the fluctuation of current and Re. And the variation in temperature about the mean will follow the the time variation of thr current.

Conside for argument only conduction and convection as the means of heat loss to the suroundings where the temperature of the surroundings is Ts.

Then we can write

Cv x M x dT/dt = Q - c(T-Ts)

as the representative equation. Or in simpler form,

c1 x dT/dt = Q - c2 x T + c2 xTs

rearranging,

(Q +c2 x Ts) = c1 x dT/dt + c2 T


Notice that this is similar to Newton's Law, F = ma for a damped mass system;

F = M x dV/dt + b x V

where V = velocity, and a = dV/dt. We already know how this system behaves in the linear case. If the applied force (or Q) varies sinusoidally, at low frequency the damping term (or heat conduction term ) dominates the result and we would expect large variations in v (or T) which are in phase and at the same frequency as the variation of F (or Q). At higher frequency the mass term dominates and we see a 90 degree phase shift between the chnage in V (or T) and F (or Q). Additionally, the magnitude of the vaiation will decrease with increasing frequency. You may think of the temperature variation about the mean as behaving like the cone velocity above the driver resonance. The magnitude of that velocity goes like 1/f.

Translating all this says to me, that thermal compression of transients dominated by higher frequency components is not really of much concern. Yes, the temperature variations will be of the same frequency as the input signal, but, while the rate of change (DT/dt) can be large, the time interval over which they occur is so short that the temperature change due to the transient is still small. An every day example of this behavior is testing an iron to see if it's hot. We don't place out hand on it and wait to see what happens. If we did we would burn our hand. Rather we touch for a fraction of a second. In other words we apply a large heat source to our hand for a very short time over which a small change in temperature occurs.

Can these small temperature changes introduce nonlinear distortion? I believe Hawksford has already addressed some of these and the answer is yes. As I have stated, there will be, by necessity, variation in temperature which faithfully follow the frequency of the input signal. The question is only of the magnitude. However, since even small temperature changes will result in changes in Re, if the VC is driven by a voltage source then this will affect the VC current.

Looking further, (I could have errors here as I am writing while thinking so you may want to just follow the logical though and think about the details your self), the force applied tot he driver through the VC is

(BL) I(t)

where t is time. Assuming BL is constant, then if the source is a voltage source we have,

I(t) = V(t)/Re(t)

With a current source, I(t) is not affected by VC temperature. But for the voltage source, if T(t) is 90 degree out of phase with I(t) then Re(t) could be expressed as Re(t) = Reave + Re' cos(wt) when I(t) = sin(wt) since Re(t) goes like T(t).

Now, it to first order I(t) is in phase with V(t) thus we can write the crude expression

I(t) = A sin(wt) /(Reave + Re' x cos(wt))

and we see that the driving current is no longer simply sin(wt).

as the amplitude can be expressed as A' = A/(Reave + Re' x cos(wt)) and

I(t) = A' sin(wt).

Again, realize that I am thinking as I write and these details aren't exactly correct, but I believe things trend this way.

So I did a little analysis of I(t) = A' sin(wt) where A' = 1 + 0.05 cos(wt) and the FFt of the result showed generation of harmonics degreasing rapidly in amplitude.

So I would conclude that for a voltage driver system that VC heating will definately introduce nonlinear distortion, but whether or not it is audible I would question without further analysis.

Here is a plot showing the effect (exaggerated) when A = 1 + 0.5 cos(wt). The distortion is clear.

An externally hosted image should be here but it was not working when we last tested it.

The question is that, when realistic changes in Re about the mean occur how big is the distortion and how significant would it be compared to BL nonlinearity, suspension nonlinearity, etc?
 
gedlee said:
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.

As a early mentor was fond of saying "when the facts are sufficient, argument is useless".

Sheldon
 
Actually, for me the deal is sealed as soon as I write

I(t) = V(t)/(Re(t))

and I let Re(t) = Re ave + Re'(t).

There can be no argument that Re'(t) MUST have the same spectrual content as V(t) and therefore, I(t) must have nonlinear distortion components in it arising from the VC heating. It's just a matter of magnitude.
 
very interesting discussion. but at some posts I roll my brain here :)
what does it mean for us not very math oriented diy'ers?
drivers with large diameter/gauge voice coils sound more dynamic than
drivers with smaller coils/gauge coils?
I'd like to see comparison in voice coil gauge, say scan speak revelator (IMO very dynamic driver) vs some cheap woofer. If scanspeaks have heavier gauge, than I'll know what to look for in my next driver :) apparently large voice coil drivers like HiVi D8.8 should be the best sounding.
 
nickmckinney said:
My 1st cent = heat sinking capability of the motor, the better the lower the problem

My 2nd cent = voice coils do not heat up linearly along their path, they are usually hotter at the edge closest to the spider unless you have a really well designed motor.
If the temperature rise comes from Joule heating, then the heat input should be uniform across the copper, correct? Are you saying that the cooling coefficient is higher at the top side of the coil?

I suppose that makes sense, but I didn't think that the motor steel made that big of a difference; the copper has a high thermal conductivity.
 
nickmckinney said:
My 1st cent = heat sinking capability of the motor, the better the lower the problem

/B]


Ah! Another point in favor or OB speakers. The motor has to dump heat to the ambient. With the motor exposed to the ambient, as in an OB system, they will run cooler than a driver in a sealed box stuffed with damping material that is also thermal insulation, with result that the motor structure (magnet, pole piece...) will run warmer which leards to higher VC temp.
 
454Casull said:

If the temperature rise comes from Joule heating, then the heat input should be uniform across the copper, correct? Are you saying that the cooling coefficient is higher at the top side of the coil?

I suppose that makes sense, but I didn't think that the motor steel made that big of a difference; the copper has a high thermal conductivity.

Remember that like water, heat flows from high to low. With a VC heat is initially generated uniformly, but is rejected, for example, by conduction along the VC former and so fourth. Thus, the ends of the VC will have greater heat rejection than the center and the center would run hotter as a result. Thus the resistively of the VC wire will increase greater in the center giving rise to even greater heat generation at the center......

Simple analyses only lets us look at what the trends are. When we want to make predictions the models need to consider the details of the structure. That's why guys like me whose job is to develop simulations tools for such problems get paid well, well before I retired anyway. ;)
 
You are faster than light speed, John – amazing!


Here is what it looks like when I go one steps further with the simu I've set up.


An externally hosted image should be here but it was not working when we last tested it.



Again the scaling is meaningless as stated before.
Basically I have adapted the simu to show how the voice coil resistance drops over time (RED trace) when a 100Hz sine burst (BLUE trace) injects energy into the VC.

All restrictions about simplification apply as stated – again - its only to have a *qualitative* impression what may happen.


Next plot shows us the same but zoomed into the first half interval


An externally hosted image should be here but it was not working when we last tested it.



Next plot shows us the FFT of the burst signal


An externally hosted image should be here but it was not working when we last tested it.



Well "maybe" ( :D ) a little bit too much side bands here but basically we see the effect.


Michael
 
diyAudio Member RIP
Joined 2008
454Casull said:

If the temperature rise comes from Joule heating, then the heat input should be uniform across the copper, correct? Are you saying that the cooling coefficient is higher at the top side of the coil?

I suppose that makes sense, but I didn't think that the motor steel made that big of a difference; the copper has a high thermal conductivity.



They are hotter at the top as there is usually no pole piece to wick the heat off. You can see the extra burn on the top portion of the coil on well burnt speakers. That was my primary reasoning to have such a long extended pole when I designed the TD drivers. The TD drivers are one of the few overhung designs that always have a solid pole piece at full xmax and in really rare territory to also have the pole completely covered with a thick copper sleeve the full length to lower the heating problems of the voice coil.

Realizing that a good high eff driver needs to shed about 95% of its input power as direct heat in a small enclosed area I used the most heatsinking I could design in rather than the other route of making the coil so physically large it could absorb the heat and not break down the glues.
 
Ups – sorry

Instead of:

Basically I have adapted the simu to show how the voice coil resistance drops over time (RED trace) when a 100Hz sine burst (BLUE trace) injects energy into the VC.


It should have been:

Basically I have adapted the simu to show how the voice coil resistance raises over time (RED trace) when a constant voltage 100Hz sine burst (BLUE trace) injects energy into the VC.
The shape of the 100Hz sinus bursts reflect the loss of driver sensitivity due to voice coil heat up - coming back to some extent after each cooling down period.


Michael
 
Most of this discussion is about the longer term LTD since the time scales of the heating have not been considered.

The heating is a rectified signal remember, and not a linear one. The heat results from the RMS current where it is not clear what the time cosnstant of the RMS average should be.

The test that got me thinking about this was a result from some Harman guys who showed sub-harmonics in the output. Now nonlinear theory says that sub harmonics are not possible in a time invarient nonlinear system. Thus the sub harmonic must be coming from some time-variant aspect of the problem, but what? What could be time variant on the scale of the audio signal? Then it dawned on me that the VC temperature could varry in this manner which would be a time variant aspect to the nonlinear loudspeaker problem and could generate subharmonics. Now subharmonics in a signal would never be masked as the higher harmonics would so our thory of nonlinear distortion masking would not hold.

The more I thought about this the more I came to conclude that a small VC, and this test was done on a car speaker, could change its temperature fast enough to be a time varying term in the Diff-EQ. Then it also is clear that a large VC could probably NOT have these kinds of effects and indeed I have never seen a subharmonic in a large woofer.

John - clearly there is always nonlinear effects from VC heating, but at what magnitude? I am convinced that unless the voice coil can heat and cool at rates comparable to the audio frequencies in the signal then this nonlinearity, NTD, is small (although LTD could still be large). But if, for example, the VC temp could change significantly within the period of a LF signal, then this signal WOULD modulate the HFs with a time-variant term in the nonlinear Diff-EQ. This would be a completely different animal than most loudspeaker nonlinearities since, as I said, it could generate subharmonics. This kind of thing could be far more audible than the normal nonlinearities that we are used to thinking about, which from my research are not that audible at all.
 
mige0 said:
Earl, how far from the signal were the sub harmonics you measured with that car speaker?

Michael


They weren't my measurements as I said. They were from Harman Motive. They started a conversation about how subharmonics were possible in a nonlinear system as the theory doesn't allow them. They were 1/2 order as I recall.

Oh, and I did want to mention that I think that measuring temp performance should be quite easy. The VC is a temp probe in that Re can be used to track the temp. But Re is just the ratio of the complex voltage to the compex current plus some other lessor effects like resonance etc. But the fact is that a fitting equation to this complex ratio can easily determine Re to very high accuracy. Now there will be time constants that we will want to know in the thermal circuit - how to get those.

I am going to create a noise signal with a random amplitude modulation. I will use the audio frequencies to find Re but then I will take Re(t), t is the time, and cross correlate that with the amplitude modulation of the RMS of the signal. This will give me the time constants for the thermal model.

The only potential problem will be exactly what I am looking for and that is a cross modulation of Re(t) with the time signal rather than the RMS amplitude signal. If this occurs then it shows NTD is a factor - although it dramatically complicates the analysis. If it does not occur then NTD - in that device - is not a factor.
 
Nick, thats quite true of the speaker, but not nearly as true of the actual VC. And at any rate, even if it does not cool as fast as it heats, the ratcheting effect could cause nonlinearities if this happens fast enough. It makes the Diff EQ have time variant coefficients and this can cause all kinds of wierd things.

I suspect that the problem is somewhat complex, but I haven't seen anyone do a really accurate job of analysis.
 
If I would speculate from my first TD measurements presented below, I would guess that it's not been Thermal Distortion what people of Harman Motive have measured.

But have a look by yourself


First lets pick the time domain – where the parallels to my simulation are most striking
Pictures show a 10 kHz sinus test signal.


CD15_10k_10W.gif


What we see here is the voice coil current of a sine voltage over time.
We clearly can observe the raise of the voice coil resistance – and subsequent fall of the VC current due to heat up.
This first plot shows a (no-name) 1.5" compression driver measured at roughly 10W power injection



CD15_nak_10k_10W.gif


In the plot above we can see the same VC taken off the gap and measured in free air – again at roughly 10W power injection



CD15_nak_10k_1W.gif


In the plot above we can see the same VC taken off the gap and measured in free air – this time at roughly 1W power injection



Now lets switch to the frequency domain



15_CD_1W.GIF


This measurement was taken "live" – its not a processed graph from the measurements above.
We clearly can see that there are side bands at roughly 8 Hz.
The sideband are way down
It was tricky to catch 'em at all. This is due to three reasons

- first it takes some time to do a 262144 points FFT with a resolution of 0.17 Hz
- second the VC resistance flattens out towards equilibrium
- third the measurement was taken with roughly 1 W power injection only (VC *in* the gap)

now we have nailed both thermal long time behaviour and thermal short time behaviour
The 8 Hz side bands should pretty precisely reflect the thermal time constant of that compression driver.


QED or as John likes to say – the deal is sealed
:D


Whups – pretty lovely, no?

Hope someone is coming up with additional measurements soon to verify my results.
To capture TD at the very beginning of the time line seems to be the biggest hurdle.

Would especially love to see if your cross correlation approach can dig even deeper into that, Earl .


nickmckinney said:
I haven't seen a speaker that can cool down as fast as it heats up unless it has a serious heat sink capability. Once you get the steel core of the motor hot it tends to want to stay that way.

Sometimes we get surprised – will see this possibly more clearly from further measurements !?

If we look some closer to the real world – the simu also isn't correct in the way that there are several "reservoirs" on the way of heat dissipation.
Usually this would better be modelled with a R-C-R-C ladder (a delay line in other words)


gedlee said:
I suspect that the problem is somewhat complex, but I haven't seen anyone do a really accurate job of analysis.

No? consider that world wasn't built in a single day.....
And until now I haven't seen that much substantially supporting from your side either...




Michael
 
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