Handbook for Sound Engineers

Loudspeakers 637

requiring less woofer excursion for a given acoustic

output in the lowest portion of its usable bandwidth. In

general, a sealed system will have more highly damped

low-frequency transient response when compared to a

vented system with the same cutoff frequency. This effect

is most noticeable for frequencies in the neighborhood of

the system lower cutoff frequency.

The design and modeling of vented and sealed

woofer enclosures has been greatly simplified in recent

years due to the ready availability of computer software

developed specifically for the purpose. The following

Thiele-Small (in honor of A. N. Thiele and Richard

Small) loudspeaker parameters are required as

minimum input to an enclosure design program:

1. QT is the total loudspeaker Q.


2. FS is the free-air cone resonance of the loudspeaker.


3. VAS is the equivalent volume compliance of the
   suspension.


4. Xmax is the maximum linear excursion.


5. Pmax is the maximum thermal power handling.

Most manufacturers provide the above parameters as
per Audio Engineering Society (AES) recommended
practice on loudspeaker specifications.

Loudspeaker enclosures can have resonances, or
standing waves, caused by internal reflections. The
characteristic frequencies (fb) of these standing waves
are given by:

(17-26)

where,

x, y, and z are the three box dimensions,

l is the designated dimension of the box,

n takes on all possible integer values (n = 0, 1, 2, 3,...).

If the lowest modal frequency found by setting n=0

for all but the longest box dimension is above the band

of use, there will be no standing waves inside the enclo-

sure. In the more common case of a woofer being used

above the first mode frequency, acoustic absorption can

be added to damp these unwanted resonances. It should

be understood that the addition of large amounts of

damping material can have an adverse effect on the

box/port tuning, so a balance must often be struck

between control of standing waves and optimal low

frequency response alignment.

17.10.2.3 Measurement of Thiele-Small Parameters

The most accurate way of determining fS is by observa-

tion of a Lissajous pattern on an oscilloscope of voltage

versus current with the speaker in free air. When the

pattern collapses to a straight diagonal line, the phase of

the impedance is zero, which indicates resonance. Once

this condition has been achieved, the frequency should

be measured with a frequency counter that is accurate to

0.1 Hz or better.

VAS may be determined with the loudspeaker

suspended in free air as follows:

1. Find total moving mass (m) by attaching an extra
   mass (MX) to the cone (as close to the voice coil as
   possible) and observing the new resonant frequency,
   fSX. MX can be putty or clay; measure mX accurately.
   The total mass can then be found by the equation

(17-27)

2. The suspension spring constant is then

(17-28)

3. From the effective diaphragm area of the loud-
   speaker, SD, VAS is given by

(17-29)

One means for determining the effective diaphragm

area is to excite the woofer near its resonant frequency

and observe its motion using a strobe light tuned almost,

but not exactly, to the frequency of excitation. The

resulting apparent slow motion of the woofer will allow

an accurate determination of the portion of the cone that

is moving.

QT may be found using the following procedure:

1. Determine the impedance of the woofer, Zmax, at its
   resonant frequency. This is simply the applied
   voltage divided by the current in the coil.


2. Identify the frequencies, f+ and f–, above and below
   fs, respectively, at which the magnitude of the
   applied voltage divided by the magnitude of the
   current in the coil is equal to.


3. Mechanical Q is given by

(17-30)

4. The total Q is then

fn c

2

---

nx

lx

©¹§·---- -

(^2) ny
ly
©¹§·-----
(^2) nz
lz
©¹§·----
2
= ++
mc
Mx
fS
fSX

©¹
§·
2
1–
=------------------------
k= 2 Sfs^2 mc
VAS
U 0 c^2 SD^2
k
--------------------=
Qm
f 0
f+–f

©¹
̈ ̧
§·Zmax
Re
= -----------