Sourced from Andy Wehmeyer:
Sourced from Andy Wehmeyer
Consider the following Thiele and Small parameters:
Cms = The compliance of the suspension--how easily it's moved
Vas = Cms expressed as a volume of air that has the same compliance
These two are a measure of the suspension's restoring force--how much the suspension pushes back when the motor moves the cone.
Q is a measure of the amount of overshoot allowed at resonance. High Q
means that the speaker keeps moving after the signal goes away. Low Q
means that the speaker stops moving more quickly when the signal goes
away.
Qms is the amount of overshoot that the suspension allows
Qes is the amount that the motor allows
Qts is the total and the formula for Qts is the product of Qms and Qes over the sum of Qms and Qes--like resistors in parallel.
Now...if you look at the parameters for 99% of the speakers that are
available you'll see that the Qms is always MUCH higher than the Qes.
That means that the suspension allows MUCH more overshoot than the
motor. Thinking a little further, you'll discover that what that really
means is that the MOTOR controls the motion of the cone and the
suspension contributes very little control. Both the motor and the
suspension work to overcome the inertia of the moving MASS. The motor
does a better job than the suspension. essentially, the suspension
screws things up. The suspension is there mostly to keep the coil from
leaving the gap and should be designed to apply very little force until
that is about to happen.
Resonance is the point where the motor and suspension make the hand-off.
Above resonance, the motor provides nearly all the control and below
resonance, the suspension does more work. Above resonance we say a
speaker is mass controlled and below we say it's stiffness controlled.
Above resonance the motor overcomes the inertia of the moving MASS and
below resonance the motor overcomes the COMPLIANCE of the suspension.
Here's an example: a super-ball is a high Q device and one of those
squeezable things in the check out line of Bed Bath and Beyond is a low Q
device. When you drop the super ball, it bounces back nearly to the
same height as from where it was dropped. That squeezy thing falls with a
thud and doesn't bounce at all.
The super ball bounces back because the rubber has a VERY HIGH restoring
force--very low compliance or very low VAS. The squeezy thing has a
very high compliance--very high VAS. It ABSORBES the force of the
impact.
Now, back to the boxes. A woofer by itself with no box is controlled
mostly by the motor but the restoring force of the suspension causes it
to bounce around a bit at resonance after it should have come to a stop.
When we put the woofer in a box, we ADD restoring force because the
cone compresses (and rarefies) the air in the box when it moves, causing
it to bounce around even more--it's a stiffer super ball. The Q is
increased (and so is the frequency of resonance). If the box is bigger,
there's less force applied to the cone when the air is compressed and
more if the box is smaller. The box RAISES the Q. A small box raises the
Q more than a large one. For a small sealed box, you need a woofer with
a very low Q. A woofer with a higher Q will need a larger box. The box
provides the additional overshoot necessary to achieve the desired Q.
Here's how sealed box design works. The box raises the Qms of the
speaker and we choose a box volume that raises it enough to produce the
desired response. Qtc is a measure of how much overshoot the whole
system of box and woofer allow at resonance. A Qtc of .707 provides the
best combination of flat response and low frequency extension. However,
there is some overshoot involved. A Qtc of .5 is critically damped or
"transient perfect". There's less overshoot.
Before you freak out and decide that you should always build a box with a
Qtc of .5 for best accuracy, we have to think a little further:
Choosing .7 is like saying, "well, I know it can't be flat, so I'll
choose to make it as flat as possible to the lowest frequency possible
and i'll deal with the group delay (inaccuracy) below the cutoff
frequency." Choosing a lower Q is like saying, "Well, it can't be flat
and I don't care about low frequency extension, so I'll minimize the
SLOPE of the rolloff for less group delay. I'll make it more inaccurate
at some frequencies and less inaccurate at the lowest frequencies."
Why would we want overshoot? Because if the woofer contnues moving, it
makes bass. We want the woofer to continue moving a little bit at
resonance, to boost the bass at the bottom of the response for better
low-frequency extension and flatter response. Choosing a lower Qtc is
essentially managing the compromise a little differently.
The reason we care more about flat response and low frequency extension
more than minimizing overshoot is because flat frequency response from
the system IS transient accuracy, by the Fourier Transform. Choosing a
Qtc of .7 is like saying "I want perfection down to the lowest
frequency possible". Choosing .5 is like saying, "I'd prefer to have the
transient accuracy be less screwed up at the very lowest frequencies
and in order to get that I'll let it be a little scewed over a wider
range of frequencies"
The easiest and best rule is to choose flat response and wide bandwidth if it's accuracy that you're after.