haphazard processes if
done right. Good design
encompasses a combination
of science, art,
engineering and craftsmanship.
Simply constructing an arbitrary
wooden box and mounting some drivers
somewhere on the front panel will most
likely not produce optimal results.
As would be expected, the theory and
practice of loudspeaker and enclosure design
have been continually developing and
evolving over the decades since the first
loudspeaker was produced and this research
is carried on to this day. But a real
turning point in describing enclosure design
mathematically and predicting performance
before screws and glue were put to wood
came about in the early 1960s with a paper
by A. Neville Thiele, first published in Australia
in 1961 and republished in the Journal
of the Audio Engineering Society (JAES) 10
Thiele investigated equivalent circuits of
loudspeakers in vented boxes and discovered,
according to his paper “Loudspeakers
in Vented Boxes,” that “it is possible to make
the low-frequency acoustic response equivalent
to an ideal high-pass filter, or as close an
approximation as is desired.” His method, he
wrote, “provided a reasonably precise method
of design that was previously lacking.”
A second researcher, Richard H. Small,
took Thiele’s ideas (among others) and expanded
upon them producing multi-part
seminal papers in the JAES in late 1972 and
throughout 1973, “Direct-Radiator Loudspeaker
System Analysis” and “Vented Box
In the first part of the latter paper, Small
credited Thiele’s paper as “the first to provide
an essentially complete, comprehensive,
and practical understanding of vented-box
systems on a quantitative level.”
|Fig. 1: From “Vented-Box Loudspeaker Systems Part 1: Small-Signal Analysis” by Richard H. Small
(JAES June 1973)
The Thiele and Small approach began
with a certain group of parameters for a given
low-frequency (LF) driver. (Their analyses
applied to low-frequency response.) These
parameters came to be known as, not surprisingly,
the Thiele-Small parameters, or T-S
parameters for short (see Fig. 1).
The T-S parameters can be measured in
the lab—some more easily than others—with both Thiele’s and Small’s papers presenting
measurement protocols. Or they can
be provided by loudspeaker driver manufacturers
who have already done the lab work.
If certain parameters of a LF driver are
known, one can then proceed to work
through the equations Thiele and Small provided
to develop the enclosure design. Or a
loudspeaker system manufacturer can work
at this from another direction.
If, for example, they have a certain box
size in mind and specific acoustical, electrical
and physical design goals, they can then
work through the formulas to help develop
drivers with the appropriate T-S parameters.
According to Thiele, a system that has a
good flat low-frequency response down to
a predictable cut-off frequency can be designed
if the following three parameters are
known about a LF driver.
The first is the free-air resonant frequency
of the driver. The next, according to Thiele, is
“the ratio of electrical resistance to motional
reactance at the resonant frequency,” also
called the total Q. And the third is the volume
of air that has the same acoustic compliance
as the driver suspension.
These parameters result from the physical
and electrical construction of the driver.
The free-air resonance frequency is measured
with the driver not mounted in any
enclosure and is a peak in the driver’s LF
response. It is dependent on the weight of
the driver components that move, like the
diaphragm (cone), dust cap and voice coil,
and how much that movement is restrained
by the driver’s suspension elements like the
spider and surround.
The restraining effect of the mechanical
suspension on the driver’s motion also
factors into the total Q number along with
the opposing effect of the electromagnetic
(EM) part (the magnet and voice coil) that
propels the cone back and forth with an applied
The volume of air parameter corresponds
to the stiffness of the driver’s spider and surround.
With these three parameters in hand,
the box design can start. We’re not going to
go into the formulas, as they are well-documented
in the literature, but rather give a
general idea of the design process, which is
much more detailed than presented here.
THE SIZE OF THE BOX
One of the first things we’d like to know
is how big a box is needed. The volume is
calculated using the volume of air and total
Q parameters. This is the actual volume of
air needed in the box to create a maximally
flat high-pass filter. The actual size of the
box will be larger than this volume to allow
for the space taken up by such items as the
drivers, support bracing and the vented port.
The volume of these items should be added
to the calculated volume to give the total
volume of the enclosure.
It’s up to the designer to determine the
length, width and height of the box that provides
the calculated volume. That’s where a
lot of the art of design comes in. In his paper,
Thiele suggested using ratios that would be
used in good acoustical room design.
Another point that Thiele made is that
“the box volume is closely proportional
to the inverse square of cut-off frequency,
which can be varied over a wide range.”
Since the box will act as a maximally flat
high-pass filter, it will have a LF 3 dB down
point. That value is calculated using the free-air
resonance of the driver and the total Q.
These two parameters are used in a different
equation to obtain the resonant frequency
of the box.
As might be expected, a larger LF driver
will require a larger enclosure and have a
lower cut-off (3 dB down) frequency.
Now we turn our attention to the port.
Small’s paper on vented box design provides
guidelines for the area of the vent (port) and
the diameter of a circular vent so that peak
air velocity through the vent will be limited
to avoid air noise. We don’t want any air
whistling or rustling through the tuned port.
Knowing the inside radius of the vent, as
well as the box resonant frequency and box
volume, the duct length can be calculated.
Settling on a port size and duct length can
be an iterative process as can be the design
of the box itself.
Mary C. Gruszka is a systems design
engineer, project manager, consultant and
writer based in the New York metro area.
She can be reached via TV Technology.