Speaker box design is an empirical art, not a hard science. There are many articles and books out there, and most of them agree on the broad design parameters, but very often the finer details differ substantially.
Firstly, of course, you need a driver. It's all very well to design a wonderful speaker on paper, then find out that the driver units are not available in your country, or have been discontinued for 5 years.
I managed to find a supplier of Fane speaker units. These are not high-end speakers, Fane being more focussed on live gigs and the like. At that stage (I was a first or second year student) I wanted something *really* *loud*. So the choice was between the 12" and the 15" woofers. The 15 incher needs a cabinet the size of a fridge to work well, and bearing the size of the typical student's room in mind I went with the 12/100C units.
I used the following sources for inspiration (This was before I got a copy of the Loudspeaker Design Cookbook):
Let's assume that we have a speaker (two, actually) and that we want to design a box to give the "best" (typically best = lowest) bass from this speaker.
You will need the following parameters (called Thiele-Small parameters) for the speaker:
Firstly, calculate the Efficiency Bandwidth Product:
EBP = fs/Qe.
If EBP < 50, this indicates that the speaker is better suited for a sealed box design than for a vented box. If EBP is around 100, this indicates that a vented box would be a better choice.
If you have Qe and Qm, you can take external
resistance
into account when calculating QT.
QT = 1/((1/Qm) +
Rs/((R+Rs)Qe))
where R is the resistance of the wiring, typically 0.5 ohm.
Alternatively, use QT as specified in the TS parameters.
Davies suggests that Qe=1.25QT and Qm=5QT (approximately) but I have not seen this in practice.
Thiele's method is to choose an alignment based on QT. The following table comes from the EA article.
| Alignment | Box design | ||||||
|---|---|---|---|---|---|---|---|
| No | Type | Ripple(dB) | f3/fs | fB/fs | VB/VAS | QT | |
| 1 | QB3 | --- | 2.68 | 2.000 | 0.0954 | 0.180 | |
| 2 | QB3 | --- | 2.28 | 1.730 | 0.1337 | 0.209 | |
| 3 | QB3 | --- | 1.77 | 1.420 | 0.2242 | 0.259 | |
| 4 | QB3 | --- | 1.45 | 1.230 | 0.3390 | 0.303 | |
| 5 | B4 | --- | 1.000 | 1.000 | 0.7072 | 0.383 | optimally flat |
| 6 | C4 | --- | 0.867 | 0.927 | 0.9479 | 0.415 | |
| 7 | C4 | 0.13 | 0.729 | 0.829 | 1.372 | 0.446 | |
| 8 | C4 | 0.25 | 0.641 | 0.757 | 1.790 | 0.518 | |
| 9 | C4 | 0.55 | 0.600 | 0.716 | 2.062 | 0.557 | |
| 9.5 | C4 | 1.52 | 0.520 | 0.638 | 2.60 | 0.625 | |
Note: This table is for an ideal box. Small recommends that the volume be increased by 30% to compensate for losses.
Davies shows that fB in Small's table can be estimated by
the following formula when QT < 0.5:
fB=0.38fs/QT for an ideal box
fB=0.4fs/QT for a lossy box with
QB = 7
My interpretation of Davies' explanation of the choice of
box volume is as follows: Small worked with a simple
two-dimensional graph, where the speaker Q determines
fB and VB (in terms of fs
and VAS, of course).
Davies expands this into a three dimensional "graph"
for VB. The resonant frequency is still a function
of QT, but the box volume can vary. The box response
is calculated as
a function of the box volume and the "best" volume is
determined. Davies recommends that the box volume should
be between 2 and 10 times
VAS(QT2).
The -3dB frequency f3 will then be approximately
f3 = 0.84fs *
SQRT(VAS/VB)
For an ideal box:
Box volume VB = 0.7072 * VAS (about 57 liters)
Tune the box to fB = fs = 52 Hz
The -3dB frequency will be f3 = fs = 52 Hz
Moving to the real world and using Davies' formulas:
fB = 0.4fs/QT = 53.7 Hz
VB > 2 * VAS(QT2) =
24 liters and
VB < 10 * VAS(QT2) =
120 liters
I initially chose a volume of 70 liters, giving
f3 = 0.84 * fs *
SQRT(VAS/VB) = 41 Hz.
I then designed the box so that the panels could be cut
from a standard sheet of particle board with as little
waste as possible. The total volume came out at 73.5 liters,
without taking the internal bracing and driver displacement
into account. The true box volume is probably closer to
68 liters.
I used fairly generic midrange drivers and piezo tweeters. The crossover is also off-the-shelf. I later replaced the piezo tweeters with larger units, and I recently replaced the mids as well. The new mids sound a little bright, I might have to pad them down.
Looking back: I built these speakers ten years ago, in 1990. I now think that the bass is too "hollow", or, to use a term that gets many people upset, not fast enough :-)
I think a smaller box will give tighter bass, at the expense of a higher f3.
JL Audio 10150 (note: this is a locally produced speaker.)
Looking at the table, this QT suggests alignment 3, giving
VB = 28 liters
fB = 43 Hz
f3 = 53 Hz
So, in an ideal box, this speaker's -3dB point is the same as the dW1, but the box is about half the size. Interesting :-)
So, lets put this woofer in a box, and see what falls out:
fB = 0.4fs/QT = 48.8 Hz
VB > 2 * VAS(QT2) =
15.6 liters and
VB < 10 * VAS(QT2) =
78 liters
| VB | 15.6 | 20 | 25 | 30 | 32 | 35 | 40 | 45 | 50 | 55 | 60 | 65 | 70 | 75 |
| f3 | 72.5 | 64.1 | 57.3 | 52.3 | 50.7 | 48.4 | 45.3 | 42.7 | 40.5 | 38.6 | 37.0 | 35.5 | 34.2 | 33.1 |
In this case, I would go for VB = 30 to 40 liters, giving
f3 (approx) = 50 Hz
Using the golden ratio (this works because of the unique property of
the golden ratio that 0.618 * 1.618 = 1)
x3 = 35000000 (cubic millimetres, i.e. 35 liters)
x = 327mm
0.618x = 202mm
1.618x = 529mm
But... I don't particularly like the shape of this box. I'd rather have a taller, more narrow box. So:
x3 = 17500000 (17.5 litres, "stack" two of these)
x = 260mm
0.618x = 160mm
1.618x = 420mm
260mm turns out to be a very interesting number -- it's also the diameter of the woofer, and as such the narrowest that the front baffle can be. The depth becomes 160mm and the height is 840mm. Note: These are minimum internal dimensions.
When measuring voltages or currents, 6dBs represent a doubling. The
equation is
dB = 20 log (V2/V1)
When measuring power, the equation becomes
dB = 20 log (P2/P1)
Absolute values of signals can be expressed in dBm or dBV, which specifies the ratio between the signal and 1mW (dBm) or 1V (dBV). What makes it more confusing is that the load impedance for dBm measurements is rarely specified, and is normally, but not necessarily, 50 ohm for RF and 600 ohm for audio.
OK, let's wave some hands here. If you have a rectangle of 1.618 x 1, and you cut a 1 x 1 square off the one side, the remaining rectangle will be 0.618 x 1. The ratio of the long side to the short side is the same as that of the parent rectangle. In other words, you can keep on lopping off squares, and the "shape" (i.e. the ratio of the sides) of the remaining rectangle stays the same. Draw it, and you'll see you get a spiral. Mathematically, make the rectangle sides X and 1. Cut the square, the remaining rectangle is 1 by (X-1). Resize this to be Y by 1, by dividing by (X-1) both sides, so that Y = 1/(X-1). Now, if the original rectangle and the proportionally resized rectangle are the same, X = Y = 1/(X-1). X^2 - X - 1 = 0. Solve that and guess what pops out? :-)