The Constant Beamwidth Transducer (CBT) topology was originally invented by US Navy researchers in the 1970s who were seeking to create a sonar transducer whose frequency response would remain unaffected vessel speed or direction.
The declassified US Navy research papers describing the CBT topology can be found here.
Don spent much of his career developing large constant directivity horns for ElectroVoice (including the legendary HR9040), Klipsch, and Harman. He discovered the US Navy CBT research in the late 1990s and saw the potential of a CBT array to overcome the frequency and time domain limitations of horns. Don has been developing, researching, publishing, and presenting his work on CBT line arrays since 2000, resulting in critically acclaimed commercial CBT implementations by JBL, PreSonus, Acoustic Artistry, Dayton Audio, and others. Don's CBT papers published in the Journal of the Audio Engineering Society and presented at multiple meetings of the society are available below.
- "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.
- "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.
- "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.
- "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.
- "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.
- “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.
Don recorded a 9 part video lecture series demonstrating the unique features and performance in 2016 which can be found below.