CBT Theory

CBT, which stands for Constant Beamwidth Transducer, is a loudspeaker line array technology pioneered by Don Keele in six Audio Engineering Society technical papers, and is based on unclassified military underwater sound research. See http://www.dbkeele.com/CBT.php for in-depth information on the CBT concepts.

System Description

Each CBT36 contains 18 each 3-1/2" full-range drivers, used as mid woofers, and 72 each 3/4" diameter wide-band tweeters, that are crossed over at 1 kHz. Initially, the system will only be available in a bi-amped version but later a passive crossover may be offered. The drivers are mounted on a front panel that has a 36° circular-arc with the system standing about five feet tall and a width of about 7 inches, and a depth at the base of about 25 inches.

Drivers

The 3-1/2" drivers are Dayton Audio's ND91, which were designed specifically for the CBT36 system. The ND91 utilizes a Neo-Balanced 1" underhung motor that is capable of over 10 mm of peak excursion and features a shorting ring to help keep distortion under control. The 3/4" diameter tweeters are also made by Dayton Audio, and are mounted on pc boards in groups of four to ease assembly and optimize center to center spacing.

Specifically Designed to Eliminate the Detrimental Effects of Floor Reflections

The CBT36 has been specifically designed to operate over a reflective ground plane and does not suffer from destructive floor-bounce effects. The curved line array of 72 tweeters extends all the way down to the floor to take advantage of the ground-plane acoustic reflection. Effectively the floor provides a reflective surface that acoustically extends the array below floor level and thus creates an array that is over 10 feet tall and controls vertical coverage and directivity down to below 160 Hz!

The Vertical and Horizontal Coverage of the CBT36 Greatly Reduces Ceiling and Wall Reflections

The above-the-floor vertical coverage of the CBT36 is a narrow 28° which is extremely stable with frequency. This greatly reduces ceiling reflections as compared to a typical box style system. In addition, the horizontal coverage which is very broad narrows as you go around the side of the system, which also significantly minimizes side wall reflections.

Extremely even Coverage with no Sweet-Spot Listening Axis

The system has extremely well-behaved and smooth coverage from locations well above the array to points even down at floor level, and at distances from directly in front of the speaker to points in the rear of the listening room. The horizontal coverage is extremely broad and uniform even out to plus-minus 90 degrees. The CBT36's variation of loudness with, distance is also very unique. At standing height, the system's volume level hardly changes over a range from directly in front of the system to points 10 feet away!

Maximum SPL and Distortion

The system can be played extremely loud and remains very clean and effortless at all levels. The large number of drivers minimizes distortion, and driven with powerful amplifiers the system can generate very-high instantaneous peaks.

System Requirements

The system must be bi-amped and requires a DSP-based speaker processor along with two stereo power amplifiers. For extended bass response below 45 Hz, one or two powerful subwoofers are required.

Part Number: 301-980

The CBT36 is designed to have an extremely even and well-behaved frequency response no matter where the response is measured. This includes locations very close and far away from the system, from points near the floor up to points above the system, and locations at extreme horizontal off-axis points out to ±90°. In addition, the system is specifically designed to operate over the floor without incurring the harmful effects of floor bounce. An additional design advantage of the CBT36 is that it effectively compensates for near-far volume level changes from locations very near the array to points 10 to 12 ft away. These attributes are briefly illustrated in the following. All the following curves were measured over the ground plane (floor). See "B&W 801 vs. CBT36 Ground-Plane Measurements" at: http://www.audioartistry.com/products_CBT.htm for complete measurements and descriptions.

Traditional 1 m Response Curve (1 m from bottom of system, 1 m high)

This frequency response was measured over a reflective ground-plane with the amplifier drive level set for an average level of 85 dB SPL and smoothed with a 1/12th -octave filter. Although this response curve may not be as pristine as the response curves published by other manufacturers, it is honest and represents the average response you get at most other locations in a real environment. Again refer to the "B&W 80 vs CBT36" presentation mentioned above for more detail.

Response vs. Height in Front of System (At Heights of 0, 0.5, 1, 1.5, and 2 m High)

Note how little the response shape changes with different heights!

Response vs. Distance (At Distances of 0, 0.5, 1, 1.5, 2, 2.5, and 3 m (10 ft) Away)

The complex (magnitude and phase) impedance of the individual low-frequency (LF) and high-frequency (HF) sections of the CBT36 are extremely well behaved. This is because the shading of the LF and HF sections is accomplished passively by series-parallel driver connections and resistive attenuators (see schematics earlier in this assembly manual). The resistive portion of the shading network considerable damps the large impedance variations of the individual drivers. This is very fortunate because this considerably tames-down the load presented to the bi-amp power amplifiers by the system. Both LF and HF sections are honest four-Ohm loads with very small impedance and phase variations. This makes the CBT36 an ideal match to both solid-state and tube power amplifiers! Even a large combined amplifier-plus-cable source resistance of two Ohms will only cause less than ±0.5 dB variation in voltage drive to the individual LF and HF sections of the CBT36!

LF Impedance (18 Mid-Woofers with Shading)

The 1 kHz-and-below LF impedance magnitude (left graph) only varies between 3.9 and 5.9 Ohms. The corresponding impedance phase (right graph) only varies over ±12° range. A very benign load!

HF Impedance (72 Tweeters with Shading)

The 1 kHz-and-above HF impedance magnitude (left graph) only varies between 3.6 and 4.6 Ohms. The corresponding impedance phase (right graph) only varies over ±5°. Also very benign!

Background

The CBT36 is based on unclassified "CBT" military under-water sonar research done by the U.S. Navy. CBT, which stands for "Constant Beamwidth Transducer," is a term coined by military researchers in a series of three papers published between 1978 and 1983 [1-3] (see Bibliography at the end of this section for reference numbers in brackets). This research resulted in under-water transducers that exhibit extremely even coverage independent of frequency and distance. The CBT36 is the result of applying this research to high-end home loudspeaker systems.

Application to Loudspeakers

Don Keele applied this theory to loudspeaker arrays in a series of six pioneering Audio Engineering Society papers between 2000 and 2010 [4-9]. Don is a designer and engineer that's been involved with "Constant Directivity" professional loudspeakers and horns that are designed to have extremely even coverage and flat frequency response over wide angles both horizontally and vertically. His goal was to design a line array loudspeaker system for domestic and home theater environments that exhibit the same characteristics.

Design Goals

The design goal of the CBT36 was to create a no-holds-barred high-end line array loudspeaker for home use with extremely even coverage at all points in the listening room and with broadband constant directivity (CD). This type of speaker would have no preferred so-called "sweet spot" listening axis and associated listening distance for optimum sound. It would sound good not matter where you listened to it; whether sitting down, standing up, laying on the floor, listening directly in front of the system from six inches away, or listening to the system way off to one side. An additional goal of the system was to completely eliminate the deleterious effects of floor bounce and create a system that would work located on a hard reflecting surface such as a tiled non-carpeted floor without exhibiting frequency response comb filtering or other aberrations. The design of the CBT36 may be summarized in three design targets.

Extremely Even and Uniform Frequency Response

The CBT36 has very even frequency response from listening points ranging from up and down, side to side, and from near to far.

Up - Down

The frequency response is quite uniform from listening locations on the floor to points significantly higher than the array itself, and all points in between!

Side to Side

The CBT36 has extremely even and wide, but well-controlled, horizontal coverage that extends over very-wide angles from ±90° from directly in front of the system.

Near and Far

The CBT36 has extremely even and flat frequency response from points even as close as 3" (75 mm) from the front panel of the system to points 10 to 14 ft (3 to 4 m) away. The CBT36 can be used as a perfect near-field monitor because the systems can be placed as close as 2 ft (0.6 m) from each other and listened to from a location 2 to 3 ft (0.6 to 1 m) away!

Eliminate the Deleterious Effects of Floor Bounce

Most speakers exhibit comb filtering effects due to the sound of the speaker bouncing off the floor. The floor-bounce effects depend highly on the distance and height of the listener. The vertical coverage of the CBT36 is essentially perfect from points on the floor to above the array and from distances from very close to far away. This is true because the system is a ground-plane design specifically intended to operate over a reflective surface.

Compensate for near-far variation of sound level

The CBT36 compensates for level variations with distance as compared to traditional box-style speaker systems. At seated height, the level only decreases 10 dB from directly in front to 10 ft (3 m) away and stays relatively flat! For standing listeners, the sound level of the CBT36 hardly changes from listening points directly in front of the array to points 10 feet (3 m) away!

The original CBT military under-water sonar research was applied to so-called "spherical-cap" (http://mathworld.wolfram.com/SphericalCap.html) underwater transducers with special frequency-independent "Legendre" shading. This shading provides wide-band extremely constant beamwidth and directivity behavior with virtually no side lobes. The technique works without the need for any special or complex signal processing. The shading is just a simple level adjustment of the individual elements that make up the transducer. The following figure (Fig. 1) shows several illustrations from the original Navy under-water CBT research papers.

Fig. 1. Illustrations from the original U.S. Navy technical papers showing a spherical cap (in red)

• (a) side view
• (b) oblique front view
• (c) side view of a 50° spherical cap with "Legendre" shading (the length of the arrows indicate the strength of the shading which is maximum in the center of the cap and decreases towards the outside of the cap)
• (d) an overlay of several measured polar curves or beam patterns for the 50° spherical cap radiator shown in (c). Fig. 1 (d) illustrates the extreme uniformity of the CBT radiator polar curves with frequency.

Don Keele applied the technology to loudspeaker arrays in a series of six AES papers between 2000 and 2010. The following illustrates the three different types of CBT loudspeaker arrays that were analyzed.

Fig. 2. Three types of CBT loudspeaker arrays analyzed by Keele (the red dots indicate loudspeaker locations)

• (a) circular spherical-cap array
• (b) elliptical toroidal-cap array
• (c) circular-arc line array

The first two arrays (a) and (b) control coverage in both planes, while the third array (c) controls coverage in the vertical plane only but provides wide horizontal coverage. The CBT36 is a circular-arc line array (c) and is the only type of CBT array considered further in this assembly manual.

There are two types of CBT line arrays: 1) a free-standing array and 2) a ground-plane array. The free-standing CBT array can be operated in free space and does not require mounting near any reflecting surface. The ground-plane CBT array is essentially one half a free-standing array that is intended to operate near or very close to a single acoustic reflecting surface, such as a floor, wall, or ceiling. The reflecting surface essentially doubles the size of the array by recreating the missing half of the array. The CBT36 is a ground-plane CBT line array. The following figure illustrates a free-standing array and a ground-plane array with its acoustic reflection along with typical shading values. Shading is explained in the next section.

Fig. 3.

• (a) A free-standing CBT line array with shading
• (b) A ground-plane CBT line array with shading
• (c) A ground-plane CBT line array with acoustic reflection that essentially doubles the size of the array.

In addition to mounting the drivers on a circular arc, a CBT loudspeaker array requires shading or level adjustment of each driver with respect to other drivers that make up the array. This maintains the best coverage independent of frequency. Note that this shading or level adjustment is a simple fixed change of volume of a particular loudspeaker and is independent of frequency. References [4] and [7] go into much detail on the CBT shading. The level adjustment or attenuation value for each driver depends on where the driver is located in the array. For the CBT36 ground-plane array, the drivers on the bottom near the floor are turned on full and the drivers at the top are attenuated the most. The drivers in between the bottom and top have intermediate attenuation values.

The required theoretical shading values are illustrated in the following graph in a continuous curve. The curve starts at 0 dB at the bottom of the array (left) and falls smoothly to -13.5 dB at the top of the array (right). The bottom of the graph shows the location of the 18 individual woofers in the CBT36 array numbered from 1 to 18 going from bottom to top. Details about this truncated Legendre shading method are shown in reference [7].

Fig. 4. Theoretical Legendre truncated (-13.5 dB) continuous shading curve for a ground-plane CBT array [4] [7-8]. The drivers at the bottom of the array (left) are turned on full while the drivers at the top of the array (right) are fully attenuated.

The most straightforward way to implement the driver shading would be to drive each speaker in the array with its own amplifier whose gain could be adjusted appropriately for each driver depending on its location in the array. However, this is complicated and expensive. Fortunately from a practical standpoint, the continuous shading can be approximated by dividing the drivers into multiple banks each of which are attenuated in a series of steps [7]. Furthermore, the attenuation of each bank can often be implemented passively without requiring separate amplifiers for each bank.

The CBT36 uses 18 mid-woofers and 72 tweeters. Note that there are exactly four tweeters for each mid-woofer (4 x 18 = 72). The 18 mid-woofer drivers and 18 four-tweeter PC-board modules of the CBT36 are divided into five banks which are passively attenuated using series parallel connection combinations and resistive attenuators (the CBT36 schematics were shown earlier in the "Wiring" section of this assembly manual). The following table (Table 1) shows the five CBT36 mid-woofer and tweeter banks along with their attenuations

This shading method essentially approximates the continuous shading curve shown in the previous figure (Fig. 4) with a series of steps [7] and is illustrated in the next figure (Fig. 5). The graph shows the actual stepped shading for the 18 mid-woofers with the attenuation shown for each bank. The attenuation levels of the tweeters are exactly the same except there are four tweeters for each mid-woofer.

Fig. 5. CBT36 stepped-shading approximation (blue) of the continuous shading curve of Fig. 4 (red). The drivers at the bottom of the array (left) are turned on full while the drivers at the top of the array (right) are fully attenuated. The five bank attenuations are respectively 0, -2.5, -4.5, -8.0, and -11.0 dB going from the bottom of the array to the top.

The next subsection shows a pictorial view of the CBT36 with side and front views indicating driver shading banks and attenuations.

The following figure shows two views of the CBT36. On the left (a) is a sectional side view while the right (b) shows the front panel with the driver banks and attenuations indicated. The CBT36 schematics are shown in the "Wiring" section of this assembly manual.

Fig. 6.

• (a) Side view sectional line drawing of CBT36.
• (b) Front panel of CBT36 with driver bank organization and shading indicated.

A most obvious question about the enclosure is why is it circularly curved? The reason can be traced back to the original military underwater transducer research where they analyzed a spherical-shaped round transducer. The theory was applied to loudspeaker line arrays by assuming a circularly-shaped line array. This is the shape that results if several loudspeakers are arranged in a straight line and then wrapped around a sphere. This is the configuration analyzed in Keele's first paper of 2000 [4]. The circular-arc array provides very uniform and well controlled vertical coverage with very wide horizontal coverage that is independent of frequency and distance and does not require any complicated DSP processing.

So why keep it curved? Three reasons

• a. Firstly, the circular shape dramatically simplifies the required processing to have constant coverage with frequency. The processing required for a straight-line array to provide the same coverage control as a circular-curved array is extremely complicated! Each individual speaker in the array would require its own power amplifier with complex DSP and delay capabilities built in. Furthermore, the required processing is strongly frequency dependent. The processing required for a circularly-curved array is extremely simple and is not frequency dependent. Just a simple frequency-independent amplitude shading adjustment of each speaker is required. In most cases the processing can be done completely passive with only a single power amplifier required! This is what's done with the CBT36 with the exception that two power amplifier channels are required for each speaker for the LF and HF bi-amplification.

• b. Secondly, the circular shape guarantees circular constant-phase wave fronts in the vertical plane from points very near the array to points very far away. This means that the vertical coverage of the array is essentially independent of distance. The coverage of a CBT circular-arc array is so uniform that it essentially has no near field. Its frequency response is the same at 3 inches away from the surface of the array as it is at 10 feet away!

• c. Thirdly, the circular shape of the enclosure dramatically increases the strength ofthe enclosure and allows thinner materials to be used for the front and back panels which must be bent to conform to the cabinet shape. The thinner front panel allows the front to be easily bent around the front of the enclosure even with all the drivers attached. All though thinner, the cabinet still will be much stronger than if the cabinet were constructed with thicker materials but not be curved.

One inherent characteristic of a curved loudspeaker array is a power rolloff with increasing frequency as compared to a straight-line array. In the case of a curved-arc CBT loudspeaker array, the power rolloff is -10 dB per decade or 3 dB per octave throughout the frequency range where the vertical beamwidth is controlled. For the CBT36, this rolloff commences at about 300 Hz. The power rolloff is down about 7 dB at 1 kHz and 17 dB at 10 kHz. This power rolloff must be compensated with corresponding lift equalization in the DSP active crossover. The following graph shows the simulated power rolloff of the CBT36. Note that the actual response curve of the active crossover includes the inherent responses of the system's drivers.

Fig. 7. CBT36 power rolloff with frequency. This is an inherent characteristic of a curved loudspeaker line arrays and not just curved-arc CBT arrays. The rolloff commences at about 300 Hz and then falls at -10 dB per decade or 3 dB per octave throughout the frequency range where the vertical beamwidth is controlled. This must be compensated by a corresponding lift equalization before the power amplifier.

The following lists the references cited in this "Theory of Operation" section. Numbers in text enclosed in brackets "[6]" refer to papers in this listing. Copies of these papers are available on the Audio Artistry website (www.AudioArtistry.com, Home, Papers and Patents). The reader is also referred to inventor Don Keele's website (http://www.DBKeele.com/) for in depth information on the CBT concepts (http://www.DBKeele.com/CBT.php) and much other interesting information.

Military Prior Art Papers

• [1] P. H. Rogers, and A. L. Van Buren, "New Approach to a Constant Beamwidth Transducer," J. Acous. Soc. Am., vol. 64, no. 1, pp. 38-43 (1978 July).

• [2] J. Jarzynski and W. J. Trott, "Array Shading for Broadband Constant Directivity Transducer," J. Acous. Soc. Am., vol. 64, no. 5, pp. 1266-1269 (1978 November).

• [3] A. L. Van Buren, L. D. Luker, M. D. Jevnager, and A. C. Tims, "Experimental Constant Beamwidth Transducer," J. Acous. Soc. Am., vol. 73, no. 6, pp. 2200-2209 (1983 June).

Keele CBT Papers

• [4] D. B. Keele, Jr., "The Application of Broadband Constant Beamwidth Transducer (CBT) Theory to Loudspeaker Arrays," 109th Convention of the Audio Engineering Society, Preprint 5216 (Sept. 2000).

• [5] 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, Preprint 5653 (Oct. 2002).

• [6] 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 (2003 July/August).

• [7] 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, Preprint 5863 (Oct. 2003).

• [8] 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, Preprint 6594 (Oct. 2005).

• [9] 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, Preprint 8155 (Nov. 2010).