"The Application of Broadband Constant Beamwidth Transducer (CBT) Theory to Loudspeaker Arrays," presented at the 109th Convention of the Audio Engineering Society, Los Angeles (Sept. 2000).
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.
Keele - CBT Paper #1 (Sept. 2000) (Application of CBT Theory to Loudspeaker Arrays)
"Implementation of Straight-Line and Flat-Panel Constant Beamwidth Transducer (CBT) Loudspeaker Arrays Using Signal Delays," presented at the 113th Convention of the Audio Engineering Society, Los Angeles (Oct. 2002).
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.
Keele - CBT Paper #2 (Oct. 2002) (Implementation of CBT Loudspeaker Arrays Using Signal Delays)
"The Full-Sphere Sound Field of Constant Beamwidth Transducer (CBT) Loudspeaker Line Arrays," J. Audio Eng. Soc., (July/August 2003).
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.
Keele (2003-03 AES Preprint) - CBT Paper3
"Practical Implementation of Constant Beamwidth Transducer (CBT) Loudspeaker Circular-Arc Line Arrays," presented at the 115th Convention of the Audio Engineering Society, New York (Oct. 2003).
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.
Keele (2003-10 AES Preprint) - CBT Paper4
"Ground-Plane Constant Beamwidth Transducer (CBT) Loudspeaker Circular-Arc Line Arrays," presented at the 119th Convention of the Audio Engineering Society, New York (Oct. 2005).
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.
Keele (2005-10 AES Preprint) - CBT Paper 5
“A Performance Ranking of Seven Different Types of Loudspeaker Line Arrays,” presented at the 129th Convention of the Audio Engineering Society, San Francisco, Paper Number 8155, (November 2010).
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.
Keele (2010-11 AES Preprint) CBT Paper 6 Performance Ranking of Loudspeaker Line Arrays
Use of Ground-Plane Constant Beamwidth Transducer (CBT) Loudspeaker Line Arrays for Sound Reinforcement Presented at the 141st Convention 2016 September 29–October 2 Los Angeles, USA
Ground-plane circular-arc CBT line arrays with wide horizontal coverage offer a very viable, high performance, simple, and thrifty alternative to the usual sound reinforcement setup where loudspeakers are elevated or hung overhead. Due to the broadband constant beamwidth/directivity/coverage characteristics and narrow vertical coverage of the CBT array, the ground-plane version offers a number of strong performance and operational advantages even when they are located on stage behind the performers. Among these are: even coverage, minimal front-back variation in sound level, flat-energy response, less energy directed upwards towards ceiling, improved intelligibility, less prone to feedback, and greater performer freedom to move around on stage. In addition, these arrays minimize the use of stage monitors, require minimal installation voicing and on-site equalization adjustments, and result in a much simpler system i.e. fewer speakers, fewer power amps, and fewer processing channels.
Keele - CBT Paper #11 (Sept. 2016) Use of Ground Plane CBT Arrays for Sound Reinforcement
Time/Phase Behavior of Constant Beamwidth Transducer (CBT) Circular-Arc Loudspeaker Line Arrays Presented at the 139th Convention 2015 October 29–November 1 New York, USA
This paper explores the time and phase response of circular-arc CBT arrays through simulation and measurement.
Although the impulse response of the CBT array is spread out in time, it’s phase response is found to be minimum
phase at all locations in front of the array: up-down, side-to-side, and near-far. When the magnitude response is
equalized flat with a minimum-phase filter, the resultant phase is substantially linear phase over a broad frequency
range at all these diverse locations. This means that the CBT array is essentially time aligned and linear phase and as
a result will accurately reproduce square waves anywhere within its coverage. Accurate reproduction of square
waves is not necessarily audible but many people believe that it is an important loudspeaker characteristic. The CBT
array essentially forms a virtual point-source but with the extremely-uniform broadband directional coverage of the
CBT array itself. When the CBT array is implemented with discrete sources, the impulse response mimics a FIR
filter but with non-linear sample spacing and with a shape that looks like a roller coaster track viewed laterally. An
analysis of the constant-phase wave fronts generated by a CBT array reveals that the sound waves essentially radiate
from a point that is located at the center of curvature of the array’s circular arc and are essentially circular at all
distances, mimicking a point source.
Keele AES139th Paper ID #181 (Time-Phase Behavior of CBT Arrays)