Keele CBT Papers

Brief Overview of CBT Theory


[1] D. B. Keele, Jr."The Application of Broadband Constant Beamwidth Transducer (CBT) Theory to Loudspeaker Arrays," 109th Convention of the Audio Engineering Society, Convention paper 5216 (Sept. 2000).
A brief tutorial review of CBT theory as first developed by the military for underwater transducers (JASA July 1978 and June 1983) is presented. Here 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 sidelobes 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 toriodal caps which provide controlled coverage for arbitrary and independent vertical and horizontal angles.

[2] D. B. Keele, Jr.,"Implementation of Straight-Line and Flat-Panel Constant Beamwidth Transducer (CBT) Loudspeaker Arrays Using Signal Delays," 113th Convention of the Audio Engineering Society, Convention paper 5653 (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 traditional constant-beamwidth flat-panel and straight-line designs which require strongly frequency-dependent signal processing. Additionally, the power response roll-off of conventional CBT or delay-derived CBT arrays is one half the roll-off rate of competing designs, i.e., 3- or 6-dB/octave (line or flat) for the CBT array versus 6- or 12-dB/octave for the other designs. Delay-derived straight-line CBT arrays also provide superior horizontal off-axis response because they do not exhibit the ±90° right-left off-axis sound pressure buildup or bulge as compared to conventional circular-arc CBT arrays. In comparison to conventional CBT arrays, the two main disadvantages of delay-derived straight-line or flat-panel CBT arrays are 1) the more complicated processing required which includes multiple power amplifiers and delay elements, and 2) the widening of the polar response at extreme off-axis angles particularly for arrays that provide wide coverage with beamwidths greater than 60°. This paper illustrates its findings using numerical simulation and modeling.

[3] D. B. Keele, Jr.,"The Full-Sphere Sound Field of Constant Beamwidth Transducer (CBT) Loudspeaker Line Arrays," J. Aud. Eng. Soc., vol. 51, no. 7/8., pp. 611-624 (July/August 2003).
The full-sphere sound radiation pattern of the CBT circular-wedge curved-line loudspeaker array exhibits a 3D petal-or eye-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.

[4] D. B. Keele, Jr. "Practical Implementation of Constant Beamwidth Transducer (CBT) Loudspeaker Circular-Arc Line Arrays," presented at the 115th Convention of the Audio Engineering Society, New York, Convention paper 5863 (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.

[5] D. B. Keele, Jr. and D. J. Button,"Ground-Plane Constant Beamwidth Transducer (CBT) Loudspeaker Circular-Arc Line Arrays." presented at the 119th Convention of the Audio Engineering Society, Convention paper 6594 (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.

[6] D. B. Keele, Jr.,"A Performance Ranking of Seven Different Types of Loudspeaker Line Arrays," presented at the 129th Convention of the Audio Engineering Society, Convention paper 8155 (Nov. 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.


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