Additional information on the use and application of Thiele's
alignments for the vented loudspeaker cabinet is presented.
A rewritten alignment table which has all the frequency
terms normalized to the speaker resonance frequency is
included. Computer-run frequency responses for all the
alignments are displayed along with a new fourth-order
Chebyshev alignment beyond no. 9. Variations and sensitivity
functions for the vented cabinet output with respect to
various system parameters (both Thiele system parameters
and driver physical parameters) are derived and plotted.

The current high usage of frequency-equalized sound systems
in the commercial sound and recording fields places increasing
demands on the user-operator of the system to ensure that
the overall system holds its designed value of spectral
flatness during normal day-to-day operation. An inexpensive
generator of pseudo random pink noise with adequate spectral
purity is described which can be used as a stable known
test source for quick on-site sound-system tests. The
generated pink noise is accurate enough for use with an
elaborate real-time spectrum analyzer (if available) for
quantitative measurements or can be used for qualitative
operator subjective measurements in the absence of other
test equipment.

FURTHER
ON SIMPLE PSEUDORANDOM PINK NOISE GENERATOR

Additional information on the use and application of Thiele's
alignments for the vented loudspeaker cabinet is presented.
A rewritten alignment table which has all the frequency
terms normalized to the speaker resonance frequency is
included. Computer-run frequency responses for all the
alignments are displayed along with a new fourth-order
Chebyshev alignment beyond no. 9. Variations and sensitivity
functions for the vented cabinet output with respect to
various system parameters (both Thiele system parameters
and driver physical parameters) are derived and plotted.

Loudspeaker exponential horn computer model studies indicate
that there is an optimum mouth size for a horn of specific
cutoff to minimize mouth reflections. Evaluation of the
reflection coefficient at the horn's mouth reveals how
large the mouth must be to optimally radiate into different
size solid angles.

Computer-generated tables greatly simplify the selection
of vent dimensions for a vented loudspeaker enclosure.
Fine adjustment of vent length may be guided by a simple
partial derivative expression relating resonance frequency
to vent length.

A loudspeaker test technique is described which depends
on nearfield pressure measurements

made in a nonanechoic environment. The technique allows
extremely simple

measurements to be made of frequency response, power response,
distortion, and

electroacoustical efficiency.

The maintenance of constant directivity with frequency
in high-frequency exponential horns is quite difficult.
Two main sound industry solutions are the multicell and
radial/sectoral horns. While the multicell exhibits fairly
constant directivity, both designs suffer from mid/high-frequency
polar lobing and midrange narrowing, and the radial shows
continually decreasing vertical beamwidth as frequency
increases. A new series of horns which optimally joins
a modified conical horn with an exponential throat section
corrects these problems, while offering very well behaved
polar patterns and constant directivity up to 16 kHz.

A new and useful set of low-frequency assisted alignments
contain Thiele's sixth-order Butterworth (B/6) alignment
as a central member. The new alignments provide the same
low cutoff with moderate amplifier boost (+6 dB) and low
out-of-band driver excursion as the assisted B/6 alignment
15 of Thiele. The method of alignment generation is based
on shifts of driver suspension compliance.

The old cut and try methods of direct radiator loudspeaker
system development have been minimized by the recent work
of Australians Thiele, Small, and Benson. The operation
of systems in the so-called low-frequency piston range
where the wavelength is larger than the radiator is now
quite predictable and predetermined. The Australians have
contributed substantially to the storehouse of information
that can aid and direct a systems designer. Well developed
theory has been made available, permitting a designer
to proceed from the specification of important end goals
(such as efficiency, system size, low frequency limit,
and power output) to a usable system with a minimum of
empirical investigation. Applications of this theory to
the design of several loudspeaker systems will be discussed.

Evaluation of the efficiency constant for exponential
horns reveals that the horn is quite wasteful in its use
of enclosed volume when compared to direct-radiator systems.
The main advantage of horns lies in the realizability
of rather high efficiencies in the 10% to 40% range which
is beyond the capabilities of most direct radiators. Use
of direct radiators in arrays increases the low frequency
efficiency but not without a decrease of high frequency
bandwidth. The areas discussed in this paper are illustrated
by comparative experimental measurements on three low
frequency systems: 1) A dual driver front loaded folded
horn, 2) a single driver direct radiator vented-box system,
and 3) a four-driver vented-box system consisting of a
2x2 array of a single driver system of item #2.

The design formulas for low-frequency horns which yield
various physical and performance related horn data can
be recast in a form which utilizes the Thiele/Small direct-radiator
driver parameters. This conversion simplifies computations
of items such as required back cavity volume and throat
area for desired performance. Performance data such as
operating bandwidth, upper rolloff frequencies and low-frequency
maximum acoustic output power are easily calculated.

A report on the preliminary version of a general purpose
computer program for the analysis and simulation of two-dimensional
acoustic spaces under steady-state sinusoidal conditions.
The program employs finite element methods to predict
the sound pressure magnitude and phase in an arbitrary
region at any desired frequency. AWASP is similar to concept
and usage to well known electronic circuit analysis programs
such as ECAP and SPICE. The program has wide application
in the analysis and design of a large number of electro-acoustic
situations including: sound in ducts, horn propagation,
sound in enclosures, diffraction effects, etc. Appications
analyzed include: sound in straight and bent pipes, sound
in a live room, and simulation of a Helmholtz resonator.

An automatic polar response measurement and analysis system
controlled by an industrial/small business grade microcomputer
is described. A Z80 microprocessor based S100-buss computer
(a Cromemco System 3) interfaced with a one-third octave
realtime analyzer and remote controlled turntable is used
to gather response spectra at different angles. The disk
stored spectral data is subsequently analyzed to generate
polar/frequency response curves and beamwidth/directivity
data. This paper emphasizes the practical aspects and
problems encountered in development of the system's hardware
and software.

The usual procedure for direct-radiator low-frequency
loudspeaker system design leads to the calculation of
the driver's fundamental electromechanical parameters
by an intermediate specification of the Thiele-Small parameters.
A reformulation of the synthesis procedure to eliminate
the intermediate Thiele-Small calculation leads to a set
of equations that yield the driver's electromechanical
parameters directly from the system specifications. These
equations reveal some moderately surprising relationships
when the different system types (closed box, fourth-order
vented box, and sixth-order vented box) are compared.
For example, for a specified low-frequency cutoff f(3),
midband efficiency, and driver size the fourth-order vented-box
driver is found to be roughly three times more expensive
(judged on the amount of magnet energy required) than
the closed-box driver. Conversely for a given f(3), enclosure
volume V(B), maximum diaphragm excursion X(max), and acoustic
power output P(AR) the fourth-order vented-box driver
is some five times cheaper than the closed-box driver.
It is also found that for direct-radiator systems in general,
specified f(3), V(B), X(max), and P(AR) lead to the total
moving mass M(MS) depending inversely on the sixth power
of the cutoff frequency, that is, a one-third-octave reduction
in f(3) results in a fourfold increase in mass. Furthermore,
the same conditions reveal that the sixth-order vented-box
driver moving mass is some 42 times lighter than that
of the closed-box driver, providing the same midband acoustic
output and f(3). If cone area and efficiency are held
constant, the direct-radiator system driver actually gets
less expensive as the low-frequency limit is extended.

As the recording industry enjoys the benefits of both
digital and advanced analog recording technology, attention
is appropriately focused on the use of compression driver
and horn designs which are some 25-30 years old. Evolutionary
improvements in woofers, compression drivers, and dividing
networks combined with new constant-coverage horn designs
have resulted in a frequency response more consistently
uniform at all coverage angles (yielding flat power response)
along with lowered distortion and increased acoustic power
output at the frequency levels.

A microcomputer program is described which accurately
calculates the direct-field SPL at points on a seating
area generated by an arbitrary configuration of loudspeakers.
The program solves inverse square losses as seen through
the loudspeaker's directional pattern at up to 230 points
on the searing plane. When multiple loudspeakers are used,
their coverage patterns are merged by two strategies:
phasor summation takes into account interference phenomena,
while non-phasor combination provides the maximum envelope
of response that can be expected of the combination of
loudspeakers. When acoustical data is provided, direct-to-reverberant
ratios can be calculated, and estimates of intelligibility,
using the method of Peutz, can be made. A graphics portion
of the program provides front, side, and top orthographic
views of the loudspeaker array.

A constant-directivity defined-coverage loudspeaker horn
that approximately covers a flat rectangular area from
an oblique angle is described. The horn compensates roughly
for the inverse rolloff of sound pressure in the forward-backward
direction by varying the horizontal coverage as a function
of the elevation angle. The horizontal coverage angle
of the horn at the 6-db-down points at each elevation
angle is matched to the required horizontal angle of the
rectangular area as seen by the horn. Measurements on
a prototype horn which covers a two by three unit area
from a point one unit above the center of the narrow end
are shown. This horn roughly covers a 70-deg vertical
angle with the horizontal coverage smoothly changing from
90 deg at 0-deg elevation (straight down) to 38 deg at
70-deg elevation.

A study of the effects of interaural crosstalk on normal
spaced-speaker stereo listening environments is presented.
Interaural crosstalk detrimentally affects both imaging
and frequency response. Imaging is affected by restriction
of the sound stage to between the speakers and by the
loss of realism and preciseness of the sonic images. Interaural
crosstalk also creates very severe comb filtering in the
frequency response of the direct sound field in which
the listener's ears are placed. Furthermore, the amplitude
and frequency characteristics of the response comb filtering
are found to depend heavily on the positions of the panned
images, and are at their worst for a centered image. The
interaural crosstalk signal can be thought of as a high
level early reflection coming from the direction of the
opposite speaker, but whose timing and amplitude depend
on the signal in the opposite channel. Current studio
monitoring design techniques tend to accentuate the problems
of interaural crosstalk. Preliminary psychoacoustic test
results of a simple method to minimize the effects of
interaural crosstalk in a nearfield stereo/binaural loudspeaker
monitoring setup are described. The results show accurate
horizontal imaging and localization over a 120° frontal
angle for both intensity-difference and delay-difference
stereo program material. The method depends on the use
of a flat vertical boundary erected between two front-positioned,
side-by-side nearfield monitor loudspeakers. The listener
is situated facing the monitors with his/her ears on opposite
sides of the boundary. Advantages include: independent
control of amplitude, phase, and delay at each ear; solid
frontal out-of-head imaging for side-to-side head shifts
and head rotations; extremely good center image; creation
of realistic lateral beyond-the-speaker acoustic images;
minimization of crosstalk frequency-response comb-filtering
effects; and excellent results with both stereo and binaural
program material.

Recent investigations into the measurement of speech intelligibility
using large listener groups (three groups of 30 each)
in a cathedral, a concert hall, and a classic motion picture
theater of the early 1930s suggest that a listener's subjective
intelligibility score will be best matched in objective
testing by dividing the sound considered to be direct
sound from sound considered to be reverberant sound at
the highest level return within the first 50 ms. This,
in a majority of cases, results in using only the first
arrival and no integration of early sound. Evidence will
be presented that indicates that the use of impulse squared
measurements that fail to process the signal as a complex
analytic signal often fail to properly record major reflective
signals unless extensive spatial averaging is resorted
to. The paper will be supported by actual postprocessing
of data taken with a Techron TEF analyzer using the Heyser
technique for energy time curve measurement. In such measurements,
minor movements of the microphone dramatically affect
the impulse and doublet responses while the same change
barely affects the energy time curve measurement, thus
demonstrating the need for the complex analytic signal
in such analysis.

The literature shows that the modulation transfer function
(MTF) and speech transmission index (STI) can be computed
from the squared impulse response of a linear passive
system. This paper describes an extension of this method
to measurements of systems using time delay spectrometry
(TDS). The new method makes use of both the real and imaginary
parts of the complex analytic impulse response of the
system (the energy-time response). This allows more accurate
determination of STI and MTF because the calculations
are based on measurements that more closely follow the
true energy decay in the room.

The Bessel array is a configuration of five, seven, or
nine identical loudspeakers in an equal-spaced line array
that provides the same overall polar pattern as a single
loudspeaker of the array. The results of a computer simulation
are described, which uses point sources to determine the
effective operating frequency range, working distance,
efficiency, power handling, maximum acoustic output, efficiency-bandwidth
product, and power-bandwidth product of the array. The
various Bessel configurations are compared to one-, two-,
and five-source equal-spaced equal-level equal-polarity
line arrays. As compared to a single source, a five source
Bessel array is 14% (0.6dB) more efficient, can handle
3.5 (+5.4dB) more power, and has 4 times (+6dB) the maximum
midband acoustic output power, and is usable for omnidirectional
radiation up to the frequency where the overall length
is 11 wavelengths long. As compared to a two-source equal-level
in-phase array, a five-source Bessel array is 43% (2.4dB)
less efficient, can handle 1.75 (+2.4dB) more power, has
the same maximum midband acoustic output power, and is
usable for omnidirectional radiation 10 times higher in
frequency. A working distance of 20 times the length of
the Bessel array was assumed, with the length of the Bessel
array (center-to-center distance of outside sources) being
four times that of the two-source array. Analysis reveals
that the three Bessel arrays have equal maximum acoustic
output, but that the five-element Bessel array has the
highest efficiency and power-bandwidth product. The seven-
and nine-source Bessel arrays are found to be effectively
unusable, as compared to the five-source array, due to
much lower efficiency, requirement for more sources, and
poor high-frequency performance. Judging polar peak-to-peak
ripple and high-frequency response, the performance of
the Bessel array is found to improve in direct proportion
to the working distance away from the array. Unfortunately
the phase versus direction and phase versus frequency
characteristics of the Bessel array are very nonlinear
and make it difficult to use with other sources.

Polarity is usually measured by energizing the system
under test with a wide-band asymmetrical test stimulus,
such as a raised cosine pulse, and then observing the
system's output on an oscillioscope. For a well-behaved
flat-response minimum-phase system, such as an electronic
device, the polarity determination is straightforward.
However, for a general band-limited non-minimum-phase
system with non-flat frequency response, such as a loudspeaker,
the policy assessment can be quite difficult due to waveform
distortion. A measurement method is presented that uses
a narrow-band asymmetrical Hann-windowed tone burst, along
with synchronous detection, to evaluate polarity at many
points across a desired bandwidth. For a general system
evaluated with tone bursts over a narrow frequency range,
polarity is not just a simple two-valued function, but
a continuum of values over the range of +/- 180 degrees,
that varies with frequency. A preliminary theory is presented
that allows prediction of the tone-burst phase, and hence
time-constrained narrow-band polarity (herein called polarity
phase), from the systems's conventional steady-state sinusoidal
phase and group-delay responses.

The Thiele/Small method of low frequency direct-radiator
loudspeaker system analysis neglects the radiation impedance
components in the equivalent electric network model. When
these components are included some surprising results
are evident. Due to the definition of efficiency widely
used in direct-radiator loudspeaker analysis, the absolute
maximum efficiency is limited to 25%. With voice-coil
inductance neglected, inclusion of the radiation impedance
components transform all responses from high-pass into
band-pass functions. Fow low frequencies, the maximum
achievable nominal power transfer efficiency is found
to be proportional to cone diameter. For a specific diameter,
the maximum efficiency depends only on the moving mass
to air-load mass ratio. Relationships and graphs are presented
which relate the true nominal power-transfer efficiency
to the Thiele/Small derived efficiency.

A comprehensive system for doing production testing of
loudspeakers and systems is described. Multiple TEF analyzers
can be controlled by a single host computer to create
elaborate test environments. The software allows the test
engineer to orchestrate very complex test sequences while
simultaneously minimizing the perceived complexity of
the system as viewed by the test operator. Tests that
can be incorporated in the test sequence, with pass/fail
window parameters, include any or all of the following
(in any order): frequency response, phase response (polarity),
harmonic tracking, harmonic distortion (of specific harmonics),
THD, THD and noise, spectrum analysis (FFT), and impedance.
Options include the capability to completely store all
the raw data from a test run for after-the-fact review
and analysis.

The analytic impulse is used as a complex-excitation signal
to produce the energy-time curve (ETC) of a system. The
ETC, usually displayed on a wide-dynamic-range log scale,
is the envelope of the system's impulse response and is
loosely related to the energy decay in the system. Additional
information is presented, using heuristic arguments and
simulations, to show that: 1) The ETC is acausal in the
same sense that the time response of a theoretical zero-phase
filter is acausal; 2) a time-derivative-based complex-excitation
signal (rather than Hilbert-transform-based signal) does
not work to extract the envelope of a system's impulse
response; and 3) even though the ETC is a good general
approximation of the energy decay in a system, it does
not predict details of the decay such as exact timing
and roll-off behavior. The intent here is not to present
any radical new information in this debate, but to explain
and clarify some of the concepts.

The theoretical design and the preliminary practical implementation
issues of an anechoic chamber designed specifically for
spherical-wave propagation are described. Conventional
anechoic chamber design methods dictate that the acoustic
impedance of the chamber's boundaries should be purely
resistive (complete absorption) over the whole operational
range of the chamber. For good loudspeaker measurements
at low frequencies, this means large chambers and long
absorptive wedges. Theory suggests that a relatively small
spherically shaped chamber, with the source constrained
to the center of the sphere, could be designed that operates
down to any arbitrary frequency, if the chamber walls
are mass reactive at lower frequencies where the wavelengths
are much larger than the chamber dimensions, and absorptive
at higher frequencies where the wavelengths are much shorter
than the chamber dimensions. A first-order mechanical
model of the wall impedance is a massless plate for the
sound waves to impinge upon, connected to a free-standing
mass through a damper. At low frequencies the whole assembly
moves, thus presenting a mass reactance to the wave, while
at high frequencies the mass would be essentially immobile,
and thus energy would be absorbed by the damper. The crossover
point between the two modes of operation occurs at the
frequency where the wavelength is equal to the circumference
of the sphere, or equivalently, the radius of the sphere
is about one-sixth wavelength. Derivations show that the
total movable mass of the chamber's walls should be exactly
three times the mass of the air contained in the sphere.
These ideas are explored.

The impulse response of real-world physical systems decays
faster at high frequencies than low frequencies. This
is due to the approximately constant Q behavior of the
resonators that often make up these systems. Considerable
efficiency can be obtained in digitizing, storing, and
manipulating impulse-response data that has been sampled
at a rate that starts high initially, and then falls inversely
with time. This paper explores the concept, and develops
an efficient log-log time-frequency transform that converts
back and forth directly between log-spaced time samples
and log-spaced frequency samples. A very efficient FIR
convolver/equalizer configuration with logarithmically
spaced time taps is described.

A cycle-octave time-frequency display is created by plotting
the magnitude of the wavelet transform, using a Morlet
complex Gaussian wavelet on a log-frequency scale versus
time in number of cycles of the wavelet's center frequency.
This type of display is quite well suited to plotting
the decay response of wide-band systems, such as the impulse
response of a loudspeaker, because the time scale is long
at low frequencies and short at high frequencies. If the
response of typical filters is plotted on this display,
the resultant 3-D responses are independent of the filter's
center frequency, i.e., the decay response shape of a
particular filter remains the same as its center frequency
is shifted up and down in log frequency.

A brief tutorial review of Constant Beamwidth Theory (CBT),
as first developed by the military for underwater transducers
(JASA, 1978 July and 1983 June), is described. In this
paper the transducer is a circular spherical cap of arbitrary
half-angle with Legendre function shading. This provides
a constant beam pattern and directivity with extremely
low side lobes for all frequencies above a certain cutoff
frequency. This paper extends the theory by simulation
to discrete-source loudspeaker arrays, including: 1) circular
wedge line arrays of arbitrary sector angle, which provide
controlled coverage in one plane only; 2) circular spherical
caps of arbitrary half-angle, which provide controlled
axially symmetric coverage; and 3) elliptical toroidal
caps, which provide controlled coverage for arbitrary
and independent vertical and horizontal angles.

The EIA-426-B standard: "Loudspeakers, Optimum Amplifier
Power" (April 1998) specifies a test CD that contains
the calibration and test signals for all the tests defined
in the standard. This CD is intended to improve the consistency
and convenience of the standard and will be made available
through the EIA and other sources. This paper describes
the development process of the signals placed on the CD
with emphasis on the spectral-shaped random noise signal
used for life testing and the variable-rate sine-wave
sweep test signal used for power compression tests. All
signals were generated analytically using a signal processing
and data analysis program. In the process of creating
the signals, a couple of errors were detected in the standard
in its description of the method for generating the variable-rate
sweep signal. The paper also develops the math for generating
variable-rate sweeps whose spectrums roll-off at an arbitrary
given rate. Complete statistics and measurements are described
for the signals as placed on the CD and for the signals
as played back on a typical CD player. Also described
are a series of 6.5-cycle shaped tone bursts that are
included on the CD. These are intended for use as a test
stimulus for short-term power assessment of loudspeakers
and electronics, and for testing the frequency response,
energy decay and narrow-band phase/polarity of systems.

The stiffness of a progressive suspension is fairly constant
for small excursions and then gets progressively stiffer
for larger excursions. When the moving assembly enters
the region of increasing stiffness, forces are generated
that rapidly reverse its motion much the same as when
a bouncing ball hits the ground. Contrary to the common
wisdom that predicts a squared-off displacement waveform,
the bouncing-ball analogy predicts that the displacement
waveform will be turned into a triangle wave. Under some
conditions, the moving assembly will repetitively bounce
at a frequency tens of times higher than the excitation
frequency with acoustic output that exhibits high-level
harmonics several times higher in amplitude and frequency
than the fundamental. Time-domain simulations and experiments
are presented to illustrate the effects.

Conventional CBT arrays require a driver configuration
that conforms to either a spherical-cap curved surface
or a circular arc. CBT arrays can also be implemented
in flat-panel or straight-line array configurations using
signal delays and Legendre function shading of the driver
amplitudes. Conventional CBT arrays do not require any
signal processing except for simple frequency-independent
shifts in loudspeaker level. However, the signal processing
for the delay-derived CBT configurations, although more
complex, is still frequency independent. This is in contrast
with conventional constant-beamwidth flat-panel and straight-line
designs which require strongly frequency-dependent signal
processing. Additionally, the power response roll-off
of the delay-derived CBT arrays is one half the roll-off
rate of the conventional designs, i.e., 3- or 6-dB/octave
(line or flat) for the CBT array versus 6- or 12-dB/octave
for the conventional designs.

The full-sphere sound radiation pattern of the CBT circular-wedge
curved-line loudspeaker array exhibits a 3D petal-shaped
sound radiation pattern that stays surprisingly uniform
with frequency. Oriented vertically, it not only exhibits
the expected uniform control of vertical coverage but
also provides significant coverage control horizontally.
The horizontal control is provided by a vertical coverage
that smoothly decreases as a function of the horizontal
off-axis angle and reaches a minimum at right angles to
the primary listening axis. This is in contrast to a straight-line
array that exhibits a 3D sound field that is axially symmetric
about its vertical axis and exhibits only minimal directivity
in the horizontal plane due to the inherent directional
characteristics of each of the sources that make up the
array.

To maintain constant beamwidth behavior, CBT circular-arc
loudspeaker line arrays require that the individual transducer
drive levels be set according to a continuous Legendre
shading function. This shading gradually tapers the drive
levels from maximum at the center of the array to zero
at the outside edges of the array. This paper considers
approximations to the Legendre shading that both discretize
the levels and truncate the extent of the shading so that
practical CBT arrays can be implemented. It was determined
by simulation that a 3-dB stepped approximation to the
shading maintained out to '12 dB did not significantly
alter the excellent vertical pattern control of the CBT
line array. Very encouraging experimental measurements
were exhibited by a pair of passively-shaded prototype
CBT arrays using miniature wide-band transducers.

Recently Vanderkooy et al. [1, 2] considered the effect
on amplifier loading of dramatically increasing the Bl
force factor of a loudspeaker driver mounted in a sealed-box
enclosure. They concluded that high Bl was a decided advantage
in raising the overall efficiency of the amplifier-speaker
combination particularly when a class-D switching-mode
amplifier was used. When the Bl factor of a driver is
raised dramatically, the input impedance magnitude also
rises dramatically while the impedance phase essentially
approaches a purely reactive condition of ±90°
over a wide bandwidth centered at resonance. This is an
optimum load for a class-D amplifier, they note, which
not only can supply power, but can also efficiently absorb,
store, and return power to the speaker. Unfortunately,
the system designed with a high-Bl driver requires significant
low-frequency equalization and increased voltage swing
from the amplifier as compared to systems using typical
much-lower values of Bl. This paper considers the effect
on the driver's efficiency of raising the driver's Bl
factor through a series of Spice simulations. The nominal
power transfer efficiency defined in traditional loudspeaker
design methods is contrasted with true efficiency, i.e.
true acoustic power output divided by true electrical
power input. Increasing Bl dramatically increases the
driver's true efficiency at all frequencies but radically
decreases nominal power efficiency in the bass range.
Traditional design methods based on nominal power transfer
efficiency disguise the very-beneficial effects of dramatically
raising the driver's Bl product.

Small-signal calculations show that the maximum nominal
efficiency of a horn loudspeaker compression driver is
50% and the maximum true efficiency is 100%. Maximum efficiency
occurs at the driver's resonance frequency. In the absence
of driver mechanical losses, the maximum nominal efficiency
occurs when the reflected acoustic load resistance equals
the driver 's voice-coil resistance and the maximum true
efficiency occurs when the reflected acoustic load resistance
is much higher that the driver’s voice-coil resistance.
To maximize the driver 's broad-band true efficiency,
the Bl force factor must be increased as much as possible,
while jointly reducing moving mass, voice-coil inductance,
mechanical losses, and front airchamber volume. Higher
compression ratios will raise high-frequency efficiency
but may decrease mid-band efficiency. This paper will
explore in detail the efficiency and design implications
of both the nominal and true efficiency relationships
including gain-bandwidth tradeoffs.

his paper describes a class of FIR filter/convolvers based
on interpolation that allow sparse specification of the
filter’s impulse-response waveform or equivalently
its frequency spectrum in both linear-and log-spaced domains.
Interpolation allows the filter 's impulse response or
frequency response to be specified in significantly fewer
samples. This is turn means that farless filter taps are
required. Linear-and log-sampled interpolating filter/convolvers
can further be categorized into two types: Type 1, interpolation
in time, and Type 2, interpolation in frequency. Type
1 provides direct specification of the filter’s
impulse response in linear or log time, while Type 2 allows
direct specification of the complex (real-imaginary) frequency
response of the filter in linear or log frequency. Each
form of filter vastly reduces the number of filter taps
but greatly increases the processing complexity at each
tap. Efficient implementations of the log-spaced filter-convolvers
are presented which use multiple asynchronous sample-rate
converters. This paper is a continuation of the author
's" Log Sampling "paper presented to the AES
in Nov. 1994. This paper represents work in progress with
a conceptual description of the convolution technique
with minimal mathematical development.

This paper describes a design variation of the CBT loudspeaker
line array that is intended to operate very close to a
planar reflecting surface. The original free-standing
CBT array is halved lengthwise and then positioned close
to a flat surface so that acoustic reflections essentially
recreate the missing half of the array. This halved array
can then be doubled in size which forms an array which
is double the height of the original array. When compared
to the original free-standing array, the ground-plane
CBT array provides several advantages including: 1. elimination
of detrimental floor reflections, 2. doubles array height,
3. doubles array sensitivity, 4. doubles array maximum
SPL capability, 5. extends vertical beamwidth control
down an octave, and 6. minimizes near-far variation of
SPL. This paper explores these characteristics through
sound-field simulations and over-the-ground-plane measurements
of three systems: 1. a conventional two-way compact monitor,
2. an experimental un-shaded straight-line array, and
3. an experimental CBT Legendre-shaded circular-arc curved-line
array.

In the 1970s, Ray Newman while at Electro-Voice, single
handedly and very successfully promoted the use of the
then new concept of the Thiele/Small parameters and related
design techniques for categorizing loudspeakers and systems
to the loudspeaker industry. This paper posthumously recounts
the contents of three significant Electro-Voice memos
written in 1992 by Ray Newman concerning a comparison
of overhung versus underhung loudspeaker motor assemblies.
The information in the memos is still very relevant today.
He proposed a comparison between the two assembly types
assuming motors that had the: 1. same Xmax, 2. same efficiency,
3. similar thermal behavior, and 4. same voice coil. He
calculated the required magnetic gap energy and discovered
to his surprise that the magnet requirements actually
went down dramatically when switching from an overhung
to an underhung structure and depended only on the ratio
between Xmax and the voice-coil length. This is in contrast
with “common sense” that dictates that longer
gaps mean larger magnets. He showed that for high-excursion
motors, a switch could be made from a ferrite overhung
structure to an equivalent high-energy neodymium underhung
structure with little cost penalty. This paper recounts
this early work and then presents motor predictions using
present-day magnetic FEM simulators illustrating his concepts.
Ray’s original memos and notes will also be included
as an appendix to the paper.

Traditionally, high-accuracy full-sphere polar measurements
require dense sampling of the sound field at very-fine
angular increments, particularly at high frequencies.
The proposed HELS (Helmholtz Equation Least Squares) method
allows this restriction to be relaxed significantly. Using
this method, far fewer sampling points are needed for
full and accurate reconstruction of the radiated sound
field. Depending on the required accuracy, sound fields
can be reconstructed using only 10 to 20% of the number
of sampling points required by conventional techniques.
The HELS method allows accurate reconstruction even for
sample spacing that violates the Nyquist spatial sampling
rate in certain directions. This paper examines the convergence
of HELS solutions via theory and simulation for reconstruction
of the acoustic radiation patterns generated by a rectangular
plate mounted on an infinite rigid flat baffle. In particular,
the impact of the numbers of expansion terms and measurement
points as well as errors imbedded in the input data on
the resultant accuracy of reconstruction is analyzed.

I read with much interest Malcolm Hawksford’s above

paper1 on the design and implementation of what he terms

“micro drive unit” loudspeaker arrays, which
provide constant-

beamwidth sound radiation. The paper’s FIR-filterbased

design procedure for the driver transfer functions

was very useful and informative, particularly given that

the array can be designed to provide multiple beams of

arbitrary size and direction. However, he analyzed only

one type of array and did not provide any references to

past work concerning the design of line arrays that provide

broad-band constant-beamwidth radiation. No mention

was made of other design methods [1]–[3] or other
array

types such as log arrays [4] or the so-called “constantbeamwidth

transducer” (CBT) arrays [5]–[11], both of

which provide wide-band constant-beamwidth acoustic

output.

Various methods exist for crossing over multi-way loudspeaker
systems. These methods include those loosely classified
as Linkwitz-Riley filters, constant-voltage filters, and
D’Appolito configurations. All these methods do
not provide broad-band constant-beamwidth or constant-directivity
operation because their vertical radiation patterns change
shape as a function of frequency. This paper describes
a simple, non-iterative linear-phase crossover filter
design technique that provides uniform frequency responses
vertically off-axis for a given multi-way loudspeaker.
Distances between the individual drivers, and desired
off-axis attenuation are prescribed as input parameters
for the design process, the outcome of which is a set
of crossover frequencies and unique filter frequency responses
in each band. In order to obtain wide-band constant-beamwidth,
a loudspeaker array configuration composed of a single
central tweeter surrounded symmetrically by pairs of lower-operating-frequency
transducers arranged in a vertical line is required. Practical
implementation issues are outlined in the paper by means
of various design examples. Two design methods are presented
in two-parts: Part 1: a general method which emphasizes
flatness of arbitrary off-axis frequency responses and
Part 2: a simplified method that emphasizes frequency
uniformity of beam shape and coverage angle (vertical
beamwidth) of the polar patterns.

Seven types of loudspeaker line arrays were ranked considering eight performance parameters including 1) Beamwidth uniformity, 2) Directivity uniformity, 3) Sound field uniformity, 4) Side lobe suppression, 5) Uniformity of polar response, 6) Smoothness of off-axis frequency response, 7) Sound pressure rolloff versus distance, and 8) Near-far polar pattern uniformity. Line arrays analyzed include: 1. Un-shaded straight-line array, 2. Hann-shaded straight-line array, 3. “J”-line array, 4. Spiral- or progressive-line array, 5. Un-shaded circular-arc array, 6. CBT circular-arc array, and 7.CBT delay-curved straight-line array. All arrays were analyzed assuming no extra drive signal processing other than frequency-independent shading. A weighted performance analysis yielded the following ranking from best to worse 6, 7, 5, 4, 3, 2, 1, with the CBT Legendre-shaded circular-arc array on top and the un-shaded straight-line array on the bottom.