636 Chapter 17
Note the separation of right side of the equation for
pressure response into two parts. The first contains
amplitude information resulting from the driving
voltage, woofer parameters, and distance from the
source, and the second provides frequency response
information. A voltage excitation of the form of
is assumed.
From the first term in the equation, we can see
several ways in which the system’s output can be
increased for a given distance and driving voltage:
- Increase the flux density, B. Increasing magnet size
will accomplish this up to the point at which the
pole piece is saturated. - Increase the length l of the conductor in the gap.
This will increase Re, however, if all we do is to add
turns to the voice coil. - Increase the diaphragm surface area, Sd. Doing so
without changing the density of the material will
also increase m, however.
Changing any of the above will potentially have an
effect on the value of Qt. If the total system Q has a
value of 0.707, the response of the system will be maxi-
mally flat, also known as a Butterworth alignment. If
the Q is higher than this, there will be a peak in the
response just above the cutoff frequency.
If total Q is lower than 0.707, the response will fall
off, or sag, in the region above cutoff, Fig. 17-59.
17.10.2.2 Vented Boxes
Prior to the existence of analytical models for a
vented-box woofer, it was understood that an opening
could be cut in a low-frequency enclosure, creating a
Helmholtz resonance. The vent itself functions as an
additional radiator in this case, and its radiation can add
constructively to that of the woofer over a limited range
of frequencies. A. N. Thiele developed the original
published analytical model for vented box radiators, and
his work was later supplemented by that of Richard
Small.
The effect of the enclosure on the spring constant of
the woofer is the same as in a sealed enclosure. The
vent functions as a passive radiator coupled to the
woofer cone via the air in the enclosure. In modeling the
response of a vented enclosure woofer, we must account
for the motion, and therefore the acoustic radiation, of
the vent. The air in the vent is assumed to move as a
unit to allow the mathematics to remain manageable.
The following expression gives the farfield half-space
acoustic pressure from a vented enclosure at low
frequencies:
(17-25)where,
Z is 2Sf,
Z 0 is ,Zv is.The first portion of the right side is identical to its
counterpart in the sealed-box equation. The second part
describes a fourth-order high-pass filter. There are three
general alignment classes for such filters: Butterworth,
or maximally flat, Chebychev, or peaked; and Bessel, or
maximally flat group delay.
A comparison of the attributes of sealed and vented
enclosures is in order. The sealed system has the advan-
tage of an intrinsic excursion-limiting mechanism—the
addition to the woofer’s spring constant due to the air in
the chamber—for frequencies below the system cutoff.
The vented system, on the other hand, can allow exces-
sive woofer excursion if excited with out-of-band signals,
so an electrical high-pass filter is a desirable protective
element. The higher-order nature of the vented system
renders it more susceptible to misalignments caused by
production variations in woofer parameters and changes
in atmospheric conditions, but it has the advantage ofEE= me^ jZtFigure 17-59. Response of closed-box system versus Q and
normalized frequency relative to system resonance.20100
10
20
30
40Relative response–dB0.1 0.2 0.4 0.6 1.0 2.0 4.0 6.0 10
f/f 0 where f 0 is the system resonanceQT = 102
1
0.5
0.2
0.14pEmElU 0 Sd
2 SrRemcdr---------------------------Z
©¹Z------ 0§·^4Z
Z 04--------- Q^1
t----- Z
Z 0
©¹§·------(^3) Zv^2 +Zd^2
Z 02
------------------------ Z
Z 02
©¹
̈ ̧
§·
- Q^1
t
----- jZv2Z 02----------
©¹̈ ̧§·Z
Z 0
++©¹§·-----------------------------------------------------------------------------------------------------------------------------------= uZdZvkvemv