WARNING:
DUE TO LIMITED OR NO EXCURSION LIMIT APPLIED TO THE PEERLESS XLS 12" DRIVER
USED IN THIS APPLICATION - PEERLESS THEMSELVES HAVE DISAPPROVED OF THIS
DESIGN. AGAIN IT MUST BE STRESSED THESE DESIGN(S) ARE ONLY FOR AUDIOPHILE
USE AND NOT HOME THEATRE. IT IS NOT DESIGNED FOR EXTREME SPL LEVELS BUT
FOR REALISTIC LEVELS AND SUPERB EXTENSION AND FIDELITY.
Is it possible to get a Sub-Woofer that uses NO
servo - and yet attains the performance of a Servo-Controlled Sub-Woofer?
No doubt the best Subs have some kind of Servo. It makes for better
performance, and high cost. It also virtually puts it outside the scope of
DIY. Yet there is a way to achieve this high performance without
the use of any Servo. This leads to far lesser complexity, easy for the
DIY constructor, and a huge saving in outlay. The project described here
will compete with Servo-Controlled Subs costing up to five times the cost,
and do it easily. It does so by using a Sealed Box tuned to a Critical Q
of 0.5 at its Box Resonance. Are you interested?
This
project is based on an idea that has permeated in the back of my head for
some years. It was partly inspired by a friend's 15 inch Tannoys that were
installed in a sealed box some 90 Litres - quite small for such a large
driver.
I had measured the T-S
Parameters, which had very low Qt and Fs, but being 15 inch the Vas was,
if memory serves me right, over 500 Litres. You would not have expected
this to work well into what was a relatively small sealed box for such a
huge 15" driver. But I found
that the Fb of the box was around 50 Hertz and Qb 0.7 which is 2nd order
Butterworth.
Those familiar with T-S Parameters will know that the 15" Tannoy's F3 (the
minus 3dB response) would
be at Fb 50 Hertz
and the roll-off below that is 12 dB/Octave. Consequently at 25 Hertz the
response will only be down -12dB.
These 15" Tannoy speakers, mounted in a
relatively small sealed box, got me thinking as this gave
rise to various possibilities that could be exploited. A driver with a
particular mix of T-S Parameters should be capable of deep bass in a
relatively small box. The Sub-Woofer
presented here are partly a result of this thinking process.
This is where things get a little interesting:
The Collom's Curve* as shown here below gives us a +5dB room boost (this is an
average rather than a strict figure) at 25 Hz. This may not be easily
understood, but speaker responses are known as 2Pi responses, as forward
radiating devices. Yet at lower frequencies the speaker becomes spherical
or omni-directional - literally a pulsating sphere, which is 4Pi response.
Since our room has boundaries which will contain this energy, then at some
low frequency we will have a 4Pi response boost.
This means a +10dB boost, but at what frequency
is difficult to predict. But it is certain that this room boost does exist.
The Cullom's Curve give us an average guide. As Subs usually sits close to
the first boundary (the floor), expect the curve to start rising at a
higher frequency than shown here. Notice too that the centre
of the boost is approximately +5dB/Octave. We'll come back to that.
* The Collom's Curve is named
by me after Martin Colloms, its creator.
Returning to our above example, we now realise
that rather than being -12dB at 25 Hertz, we're closer to being -6dB, much
more respectable. Indeed we can conclude that speakers that are flat down
to sub 30 Hertz will have in room peaks and that the correct response
should be a gradual roll-off and thereby compliment room boost. Not surprisingly sealed boxes
do this almost naturally whereas vented alignments can have huge problems
unless very carefully designed with a
gradual roll-off, Bessel-like alignments are preferred.
But for low frequencies using a relatively compact box, we must think
sealed, a driver with low Fs, low (but not too low) Qt, and large surface
area and long linear excursion. It is apparent that we must have a very
large displacement capability, and basic calculations showed that a 12
inch driver to be nearly ideal and the Tannoy example indicated that this
should be possible with a relatively compact size box. Much smaller than
90 Litres.
Most of the better Subs on the market uses some
kind of servo-control or motional feedback. This is supposed to give tight
control over excursion and equalization (EQ). But, as we know, naturally they tend to
be much more expensive as a result of increased complexity.
This is where my idea comes in. It has been known
for some time that where-ever there is a resonance, if the Q is kept down
to or below 0.5 it can be described as critically damped, so hence the
title, a Critical Q Sub, short for Critically Damped Q Sub-Woofer. This
Sub will have superb transient response with virtually no over-hang and
will start and stop on a dime. This means we can have the same level of
performance as servo-controlled subs but at
substantially less complexity and cost. The only thing we may need to pay
attention to is the EQ'ing of the amplitude. It also would be desirable if
this EQ'ing could be reduced to a minimum.
Many who dabble with speaker design and crossovers, knows that Linkwitz-Riley
2nd and 4th order crossovers have a specified Q of 0.49 - this is no
coincidence as the crossover will be critically damped, so this principle,
as with many other principles, works both in the electrical and mechanical
domain. It was Neville Thiele (of Thiele-Small fame) who first recognised
this, and loud-speaker design has never been the same again. I can
happily say that
Neville is still living here in our wonderful city, Sydney - Australia.
At this point I want to point to a particular
ratio that applies to all sealed box
alignments. As Fs of a driver gets pushed up by the volume (actually a
mechanical spring) to become the Fb of the box, the same ratio applies to
the Qt of the driver. Let's look at an example:
