Computer Aided Sound System Design 1365f is the frequency,
is the angular resolution.
As an example, these limits correspond roughly to a
measurement setup where the acoustic source is not
farther away than ca. 0.15 m from the POR. Phase data
points will be close enough up to a frequency of 8 kHz,
if the frequency resolution is at least octave (or
475 Hz) and the angular resolution is at least 5 degrees.
Such conditions are well within what is possible with
modern measurement platforms.
Data Acquisition. Although loudspeaker performance
data and directivity patterns have been measured for
several decades, no definitive standard has emerged
from that practice. Also for some years now, the AES
standards committees try to unify the variety of existing
methods and concepts to reach some commonly
accepted measuring recommendations.
The accurate measurement of loudspeaker polar data
is one of the issues of the ongoing discussion. Espe-
cially the acquisition of complex frequency response
data, which asks for significantly higher accuracy in the
measurement setup, and better control of the environ-
ment than the measurement of magnitude-only data. To
determine the exact phase response of the loudspeaker
under test relative to the POR, it is inevitable to measure
and compensate the measuring distance as well as the
environmental conditions that influence the propaga-
tion of sound along that path. For example, to be exact
within a quarter of a wavelength at 8 kHz, all distance
measurements must be accurate within less than a centi-
meter of length. Although this is not a trivial task,
professional acoustic laboratories have been built at the
factories of manufacturers, at universities, and by inde-
pendent service providers.^40 As a result, today many
loudspeaker systems are measured using measurement
platforms that can provide high-resolution impulse
response or complex frequency response data.
But it is important to note that gathering measure-
ment data as described above only slightly increases the
overall effort. To build a measurement setup capable of
acquiring complex balloon data means a high initial
effort, but with respect to automated polar measure-
ments, the subsequent measuring durations are the same
as for magnitude-only data. The measurement of the
individual components of a loudspeaker cabinet or array
is obviously connected with longer measurement times.
However, in many cases the angular resolution for a
transducer measurement may be lower than for the full
multiway device because its directivity behavior is much
smoother. In the same manner, the frequency resolution
can be chosen adequately. Finally, the acquisition of
phase data also means that the so-called acoustic center
does not have to be determined in a time-consuming
procedure. Mounting the loudspeaker for a measure-
ment is therefore much simpler. The measurement of
different transducers of the same loudspeaker does not
require remounting the device anymore, as well. Addi-
tionally, as we will show below, loudspeaker designers
and manufacturers gain direct benefits from advanced
measurement data, such as directivity prediction, cross-
over design, and verification capabilities.
Figs. 35-30, 35-31, and 35-32 show some of the
advantages gained by using complex data for individual
components. Fig. 35-30 shows a comparison of
measurement versus prediction for a stacked configura-
tion of two two-way loudspeakers, arranged horn to
horn (HF-HF). Its vertical directivity pattern at 1 kHz is
displayed in Fig. 35-30, measured data (+ curve) and
calculation based on complex data (solid curve) are in
good agreement. Calculations with magnitude-only data
(dashed curve), provide erroneous results. In this case,
the port of the loudspeaker (FR) was chosen to be the
POR. A similar discrepancy between measurement and
prediction using magnitude-only data can be seen in the
arrangement of woofer to woofer (LF–LF), Fig. 35-31.
To illustrate the sampling problems described before,
Fig. 35-32 shows the same configuration at 4 kHz. Here
measurements (+ curve) can only be imaged properly by
a computation at angular increments of 2.5q The dashed
curve is using individual components measured at 5q.
Computations or measurements at a too coarse resolu-
tion of 5q(dashed curve) fail completely to describe the
properties of the system when being interpolated.
Due to the complexity of establishing an accurate
and phase-stable measurement setup, a set of alternative
approaches is practiced. This includes, in particular, the
modeling of the wave front radiated at the loudspeaker
by elementary point sources according to the Huygens
principle. Other models are based on the idea of
deriving the missing phase response from the magnitude
response, such as by the minimum phase assumption.
Some of these implementations work quite well for a
subset of applications, such as in the vertical domain or
within some opening angle relative to the loudspeaker’s
axis. But generally these ideal models lack the means to
depict the sound radiating properties of the loudspeaker
in those domains where it is not so well behaved and
analytically treatable.35.2.1.3.3 Configurable LoudspeakersIn the previous sections an overview about the crucial
parts of modeling modern loudspeaker systems was
given. In turn, the acquisition of complex directivity'-(^1) » 12