NON-LINEAR THERMAL DISTORTION - A SOLUTION IS SOUGHT

[This is an old article and still good]

Much has been said and discussed re the mechanism to describe thermal distortion in speakers. The fact is that speakers are rarely 1% or more efficient and the conclusion is that 99% plus is usually expended as heat. Indeed, most of your amplifier's Watts are not actually used, the process is extremely lossy.

But the question is posed, since 99% of the power fed to the Voice Coil is dissipated as heat, then your very guts tells you that somehow it causes some form of non-linear distortion. It just has to!

Add to that, many claim to hear an improvement when speakers are designed to deal with heat in an organised way. And I agree with them.

Here we need to distinguish between Linear Thermal Distortion (LTD) and Non-linear Thermal Distortion (NTD). Evidence of LTD is easy to prove, but NTD is an entirely different matter. LTD is easy to measure even with basic instruments and also easy to model, all of which has been done.  

LTD results in a loss of sensitivity, here is how:

The Voice Coil (VC) is made of Copper (rare if anything else). It has a Thermal Coefficiency of 0.4% per single unit of Centigrade. So if a VC has a coil resistance, called "Re" in T-S parlance, then each C degree of increased heat will cause 0.4% increase of Re. So if Re is 6 Ohm at 20C, then at 21C Re has increased to 6.024 Ohm. If the VC is increased by 100C (not unusual) then Re would now be 8.4 Ohm, a 40% increase. The Qe will also be raised by the same 40%.

This lessens the sensitivity of the driver but not necessarily efficiency as the nominal current is decreased. But in terms of calculating sensitivity it is the effect on Qe that lowers the BL factor - the force factor of the Voice Coil in the gap.

So the result can be viewed two ways, that Qe increases proportionally to the increase in Re and that the 'No' (nominal sensitivity of driver) will be reduced. But even easier to understand is that the RMS current drawn from the 'voltage' amplifier will be reduced and the same result, less power is drawn (unlike "current" amplifiers). The driver will now be less loud by a known amount and this is LTD.

BUT...

It is not proved non-linear. The reduction in output is very gradual and due to the thermal mass of VC and to a certain extent the motor/magnet assembly, the Re's rate of increase is too slow to show up at audio frequencies, way too slow! Earl Geddes has expressed this thought clearly and yet believes that NTD may be for real and designs with that in mind.

The mechanism causing LTD has not yet been directly linked to NTD, there is no explanation where or how heat becomes or causes NTD. Does that mean that NTD does not exist. Most of us interested in this subject still insist that it must. Somehow!

At least some of this heat finds itself radiated into the motor assembly. I tried input a 500 Hertz 10V RMS into an 8 Ohm driver with 1" Voice Coil - and after some time the motor assembly went double the ambient temperature.

Interesting that not all parts of the motor assembly stabilises at the same temperature. This was noted with some interest as the heat is clearly radiated across the gap, the only origin. This leads to an interesting train of thought.

Hence we have a mystery, one that has persisted for decades. But I will reveal one mechanism that may help to or lead to a resolution. This mechanism is now being discussed here in Sydney that may well be the breakthrough we seek. If this mechanism is correct, then both driver manufacturers and system designers (like ourselves) will be able to deal with this factor in a much more focussed way!

There is an assumption that the Voice Coil gets heated linearly across its length, yet the observation has been made that speakers failing due to thermal overload tends to fail in higher proportion at a certain point - the front of the Voice Coil. This tells us that sinking heat is less successful at that point and varies across the length of VC, probably approximating as U or more likely a J shape. Just as all parts of the motor assembly did not heat up the same.

This would indicate that the VC temperature is not a "constant" versus its length and hence a VC thermally loaded up at higher frequencies where there is little amplitude (cone in low piston mode or flexing mode where cooling may well be less efficient) and then when any subsequent lower frequencies (piston mode) comes along and become non-linear as the Re fraction of the VC's Re that is in the gap will be modulated at audio frequencies, If both low frequencies and high frequencies are reproduced together, as we would find in music, will they both become non-linear?

"Re" modulated at audio frequencies modulates Qe and hence BL also at audio frequencies.  If this is the case we now do have a non-linear mechanism, we have NTD; and LTD is only limited to static signals. Music has a broad spectrum that can excite in a way static measurements cannot capture.

Any system that lessens thermal load of the VC, such as increasing its size and mass,  and also reducing the need for pistonic cone movement will lessen NTD. The latter means the area of the cone or "Sd" will need to be as large as possible or at least increased, too lessen cone movement away from its static position. Small driver with small VCs and small cone area Sd will be at a disadvantage as they attempt to move air. Indeed larger drivers with larger Sd are also perceived as sounding more effortless and lower sense of strain - exactly what you would expect. The lowering LTD may well prove to also lower NTD and treating LTD will also do the same for potential NTD.

It's interesting that at least one designer, Troels Gravesen, has heard audible effects from the type of former that the VC is wound on, preferring Aluminium over Kapton. Could it be that the former has a significant effect over the VC's heat distribution? He also notices the same effects on drivers he considers having an inadequate Sd, the cone area. If the conceptual theory is correct, then larger Sd will lessen the audible effects of non-linear VC heat distribution. Please read his article: Vocals.

It is still early days and there is still much to do. But I believe that we have made a good start in developing a conceptual model (hypothesis) and then see if a mathematical model can be developed. As in all things of similar nature, this needs testing.

The Elsinores already benefits from this thinking as thermal load on the Voice Coils are far less than average systems and in the order of 16 times below 500 Hertz, four times in the midrange and at least two times at high frequencies. This performs well above most commercially available systems. It is also a notably dynamic speaker system.

In time other designers will also be able to apply this thinking to their designs. In many ways they are, at least the good ones are, but mostly because of gut instinct. We may now finally get some proof of that instinct and power of observation.

Joe R.