[sdiy] speaker power limit and speaker protection for synth sounds

[Czech Martin]

We often read or hear: oh, my tweeter evaporized during
playing my synth, or my woofer voice coil got bumped.
This is because synths can generate tones that are very different
from the standard chassis test signals.

We have three dangerous things:

-maximum mebrane amplitude for woofers and low-mid range
-long term thermal power
-short term thermal power

The first one will damage the voice coil in woofers and low-mid range.
The membrane amplitude of a dynamic chassis will look like a second
order low pass. There can be a resonance, and the amplitude will fall
of with 12db/oct. If we have 1cm amplitude at 20 Hz, it will be only 
-68 dB @ 1000 Hz, or 0.4 mm. This is only a rough estimation,
there are vented speakers with resonances, but we see that high mid
and tweeter chassis have no membrane amplitude problem when used in the
proper frequency domain.

All chassis get problems if the voice coil gets too hot.
A short burst can be allowed if the chassis can cool down afterwards.
Thus we have a short time power. For infinitely applied power we
get a much lower rating. The coil will heat up to thermal equilibrium.

--

What to do?

We can play via headphones or very silently.
If you do not like this, the membrane amplitude can be computed via
analog circuits , as well as the voice coil power.
If the limit is reached, a limiter must turn down the amplitude.

--

How to derive the critical parameters?

--

Membrane amplitude is often given in data sheets.
It is also easy to measure, which amplitude leads to which 
sound pressure wave distortion. At some amplitude the
distortion will come up, this would then be the allowed maximum.

A tuned analog 2nd order lowpass can compute the amplitude if the
speaker chassis voltage is given. For vented boxes this is more complicated.

Power could also be measured by analog means.

In most chassis data sheets the RMS power is given.

I think it is measured with pink noise,
in 1 min on, 2 min off intervalls.
The figure then applies to the 1 min on time, not the
average of the whole cycle (which would be 1/3 of the rating).
The measurement uses noise to determine the thermal stress
capability, not maximal membrane amplitude capability.

Also for mid range and tweeter the manufacturers assume that
a passive crossover network is apllied to the chassis.
for a tweeter this is a HP with e.g. 4 kHz.
Now, pink noise means equal power per octave.
We have ~ 9 octaves from 20 Hz to 20kHz.
>From 4kHz to 20kHz is only a span of ~ 2.3 octaves.
Thus the power for the tweeter should be 2.3/9= 0.26 of the
total power.

If we combine the time average of 1/3 and the frequency band
factor of 1/4 of the tweeter, we get:

actual power capability for tweeter: 1/12 of rated RMS.
If the tweeter is speced with 120W, you really have 10 W
capability of the tweeter.
Important if sine waves are played.

Is this interpretation correct?

Now, 1/3 of the RMS rating is maybe too pessimistic for the
thermal power capability of the chassis.
The voice coil will perhaps need less then a minute to heat up
to maximum, and during the pause the chassis will cool down 
faster then 2min.
What would you assume to be the constant thermal power dissipation
that can be applied -say- for 2 hours?

Cheers
m.c.