Handbook for Sound Engineers

Loudspeakers 629

Given this simplification, the extended transfer func-
tion of a loudspeaker may be characterized on the
surface of a sphere of some arbitrarily chosen radius
with the source at its center. The number of independent
variables is then reduced to two, yielding a transfer
function that may be represented as a function of S and
two angles —i.e., F(s,T, ). Even with this simplifica-
tion, the number of single-point transfer functions
remains uncountably infinite. Clearly, further simplifi-
cation will be required if the task of measuring and
describing a loudspeaker’s performance is to be made
practically realizable.

Currently available software for the simulation of
sound system performance requires data to be presented
with a fixed angular resolution. The polar coordinate
system that has been adopted for this purpose is most
easily described as that of a globe with the loud-
speaker’s axis aimed at the North pole. Typically, the
plane of horizontal coverage is defined as 0° rotation
angle, with the lines of constant rotation equivalent to
longitude and radius angles analogous to latitude. One
advantage of this approach is that data points are at
maximum density near the on-axis position. There is
still debate regarding the angular resolution required to
show relevant details of device performance. Incre-
ments as fine as 1° have been suggested. Practically
speaking, even with 10° increments, a complete set of
measurements on a device with mirror-image symmetry
(i.e., requiring measurements in only one quadrant)
requires 172 response measurements of the device. An
asymmetric device (e.g., Altec VIR, IMAX PPS,
requiring two quadrants of measurement) requires 325
measurements to characterize with 10° resolution.
One possible compromise is to use one angular
increment for measurements taken within the intended
coverage pattern of the loudspeaker and another,
broader, one for other measurements. This has the
advantage of providing greater detail in the angular area
in which the loudspeaker’s response has the greatest
audible effect. It would, however, complicate the
process of interpolation that is required to approximate
the response of a speaker at angles that fall between the
angles at which measurements were taken. This variable
resolution is unavailable in currently array prediction
software.

Due to the large amount of measured data that is
required to meaningfully characterize the performance
of a loudspeaker, it is highly impractical, if not alto-
gether impossible, to provide the data in a hardcopy
format. In order to conveniently view loudspeaker data
of this complexity, one must employ a computer
program. For many years, the only available programs

for this purpose were those that were primarily designed

for sound system modeling and prediction. These

programs have capabilities that go far beyond the

display of loudspeaker data, are not optimized for that

use, and are typically quite costly.

Recently, a format specifically for presentation of

loudspeaker performance data, called the common loud-

speaker format, or CLF, has been developed. This

format is supported by a consortium of loudspeaker

manufacturers. Due to the amount of data accommo-

dated by the format, it is optimized for electronic, rather

than hardcopy, presentation of data. It requires a data

viewer program, which is available for download free at

http://clfgroup.org. The displays in the CLF viewer

include 3D amplitude balloons, traditional polar plots,

normalized off-axis response plots, impedance versus

frequency, as well as other data. Figs. 17-52 and 17-53

are screen captures of a CLF display.

17.9.5 Impedance

The impedance of a loudspeaker is very seldom

constant with respect to frequency. For this reason, the

nominal impedance provided in the specification

sheet—typically 4: , 8: , or 16:—is often useless as

a figure of merit. Because power amplifiers have

limited ability to drive excessively low impedances and

because loudspeaker cabling may have nonnegligible

series resistance, it behooves the prospective purchaser

of a loudspeaker to examine its impedance versus

frequency curve. Of greatest interest is the minimum

impedance seen in the device’s bandwidth and, to a

lesser extent, the frequencies and magnitudes of any

peaks in the curve.

17.9.6 Distortion

The concept of a transfer function assumes a linear

system. In a linear system excited by a single frequency,

the output will contain only that frequency, possibly

changed in amplitude and/or phase. By extension, the

output of a linear system excited by a signal containing

multiple frequencies will contain only those frequen-

cies present in the original signal.

There are a number of nonlinear mechanisms in any

loudspeaker. These include nonlinearities in the motor,

suspension, and air (e.g., in a phasing plug or the throat

of a horn). For this reason, all practical loudspeakers

have nonnegligible levels of harmonic and intermodula-

tion distortion. By comparison with modern electronic

signal processing devices and amplification, loud-

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