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).
ABSTRACT:
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 discretesource 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 axiallysymmetric 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 StraightLine and FlatPanel Constant Beamwidth Transducer (CBT) Loudspeaker Arrays Using Signal Delays," 113th Convention of the Audio Engineering Society, Convention paper 5653 (Oct. 2002).
ABSTRACT:
Conventional CBT arrays require a driver configuration that conforms to either a sphericalcap curved surface or a circular arc. CBT arrays can also be implemented in flatpanel or straightline array configurations using signal delays and Legendrefunction shading of the driver amplitudes. Conventional CBT arrays do not require any signal processing except for simple frequencyindependent shifts in loudspeaker level. However, the signal processing for the delayderived CBT configurations, although more complex, is still frequency independent. This is in contrast with traditional constantbeamwidth flatpanel and straightline designs which require strongly frequencydependent signal processing. Additionally, the power response rolloff of conventional CBT or delayderived CBT arrays is one half the rolloff rate of competing designs, i.e., 3 or 6dB/octave (line or flat) for the CBT array versus 6 or 12dB/octave for the other designs. Delayderived straightline CBT arrays also provide superior horizontal offaxis response because they do not exhibit the ±90° rightleft offaxis sound pressure buildup or bulge as compared to conventional circulararc CBT arrays. In comparison to conventional CBT arrays, the two main disadvantages of delayderived straightline or flatpanel 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 offaxis 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 FullSphere Sound Field of Constant Beamwidth Transducer (CBT) Loudspeaker Line Arrays," J. Aud. Eng. Soc., vol. 51, no. 7/8., pp. 611624 (July/August 2003).
ABSTRACT:
The fullsphere sound radiation pattern of the CBT circularwedge curvedline loudspeaker array exhibits a 3D petalor eyeshaped 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 offaxis angle and reaches a minimum at right angles to the primary listening axis. This is in contrast to a straightline 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 CircularArc Line Arrays," presented at the 115th Convention of the Audio Engineering Society, New York, Convention paper 5863 (Oct. 2003).
ABSTRACT:
To maintain constant beamwidth behavior, CBT circulararc 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 3dB 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 passivelyshaded prototype CBT arrays using miniature wideband transducers.
[5] D. B. Keele, Jr. and D. J. Button,"GroundPlane Constant Beamwidth Transducer (CBT) Loudspeaker CircularArc Line Arrays." presented at the 119th Convention of the Audio Engineering Society, Convention paper 6594 (Oct. 2005).
ABSTRACT:
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 freestanding 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 freestanding array, the groundplane 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 nearfar variation of SPL. This paper explores these characteristics through soundfield simulations and overthegroundplane measurements of three systems: 1. a conventional twoway compact monitor, 2. an experimental unshaded straightline array, and 3. an experimental CBT Legendreshaded circulararc curvedline 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).
ABSTRACT:
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 offaxis frequency response, 7) Sound pressure rolloff versus distance, and 8) Nearfar polar pattern uniformity. Line arrays analyzed include: 1. Unshaded straightline array, 2. Hannshaded straightline array, 3. "J"line array, 4. Spiral or progressiveline array, 5. Unshaded circulararc array, 6. CBT circulararc array, and 7.CBT delaycurved straightline array. All arrays were analyzed assuming no extra drive signal processing other than frequencyindependent shading. A weighted performance analysis yielded the following ranking from best to worse 6, 7, 5, 4, 3, 2, 1, with the CBT Legendreshaded circulararc array on top and the unshaded straightline array on the bottom.
