High quality point source or stereo sound
from an array of cheap drivers
by Andre Jute
WHAT IS THE BESSEL ARRAY GOOD FOR?
The interest of the Bessel array is that a bunch of cheap drivers can be used to give the same illusion as a high quality point source speaker (like a Quad ESL-63 electrostat or Lowther concentric driver). Since only a little power, relative to the single-driver case, is applied to each driver for the same SPL, the voice coil will always stay in the magnetic gap and the driver will operate in its most linear range. SPL is made by the number of the drivers, not by running any one of them out of band.
WHAT IS THE BESSEL ARRAY?
It is possible to simulate a point source by a line array of drivers, when the power output and polarity of the drivers represents the values of the mathematical Bessel row. The simulation will be perfect for an infinite number of drivers in the line array. But even an array of 5 drivers will result in a good approximation of the point source. The drivers are arranged in an equally spaced line, or in a square, so that the array may be 5 or 6 drivers, or 25 or 36. The array of 6 is actually a Bessel array of 7, with the centre position left blank (put a tweeter in it for coincident sound!).
Though it is possible with some contortions to use a single amplifier to drive a Bessel array of any size, two or more amps are more commonly used to drive a Bessel array the easy way.
SMALL BESSEL ARRAYS
Here is the power allocation from the amplifiers for arrays of 5 and 6 (7 including blank) drivers:
D: -2 (reverse polarity)
Six (7) elements:
D: 0 (not needed, leave blank space)
E: -2 (reverse polarity)
G: -1 (reverse polarity)
The line array can be constructed as a serial or parallel circuit of drivers. For a Bessel array with drivers of 8 ohm the aggregate impedance will thus be 28 Ohm or 2.3 ohm. Spacing, though equal, should be as close as possible.
BIG BESSEL ARRAYS
Bessel array with 25 elements:
1 2 2 -2 1
2 4 4 -4 2
2 4 4 -4 2
-2 -4 -4 4 -2
1 2 2 -2 1
Bessel array with 36 elements including 13 "dummy" drivers:
1 2 2 0 -2 2 -1
2 4 4 0 -4 4 -2
2 4 4 0 -4 4 -2
0 0 0 0 0 0 0
-2 -4 -4 0 4 -4 2
2 4 4 0 -4 4 -2
-1 -2 -2 0 2 -2 1
The impedance of the array will be the same as the impedance of a single driver. Spacing should be about 1cm between edges.
STEREO WITH A BESSEL ARRAY
It is possible to make stereo sound using 5 drivers in a Bessel array:
A : 0.5 * (L+R)
B : L-R
C : L+R
D : - (L-R)
E : 0.5 * (L+R)
wherein L and R stands for the left and right channel, and the 0.5 indicates that drivers A and E receive only half the power that the other drivers receive. The easiest implementation uses four power amplifiers (one inverted) to drive the array.
This one, having so few drivers, could be an expensive solution to the wall of sound we all dream of: five Quad ESL-63 in a Bessel array driven by four 300B or 845 or Svetlana SV572-3 or -10 or -30 SE amplifiers.
By putting the amplifier distribution into a pre-amp, it is possible to use only two amplifiers, one for drivers A, C, E, and the other for B,D -- if proper power distribution to the drivers can be arranged.
CAN YOU BUILD ONE?
For a commercial application, get a license from Philips, who hold the patent. To build one pair or one stereo "speaker" for your own enjoyment as a hobbyist, go right ahead.
SHOULD YOU BUILD ONE?
As always with speakers, it depends on a number of variables. A Bessel Array integrates the sound, that is, works as intended, at a distance of about ten times the length of the array. This natural limitation of its form doesn't matter overly much if a Bessel array is used for the purposes for which it was designed (outdoor sound, huge stadia, architectural applications, large venues like theatres) but in a domestic environment it means that Bessel arrays of any substantial size are suitable only for the largest rooms or garden use.
Adventures in Bessel Arrays
One domestic application I have found for this clever design is multimedia speakers. At first this seems an outrageous idea but there is no reason computer speakers should be on the desk with the computer.
Specifically, I used five two-inch Coral drivers (too good for Bessels, really, but that was what I had to experiment with) to build the array, no-name surplus sealed "sound modules" for amps and a kustom-kludged box for a distribution "preamp". This "speaker" was useless under my Mac because it simply sounded like five separate speakers interfering with each other; I have close relations of the same drivers in coconuts (made by a Swiss designer and sent to me for an opinion) and close up and personal the coconuts won hands down. The tiny Bessel array was then hung in the angle of the ceiling and the wall at the short end of the room furthest from my desk and angled to beam down the length of the room over my computer screen. Suddenly it integrated and became a speaker, a single unit of sound. The sound was of superior quality but that is no surprise: the Corals are a known-good quantity and priced accordingly. This tiny Bessel array with the Coral drivers worked so pleasingly at well beyond the minimum correct distance that I decided to see how big a Bessel array would work in the same room.
Next I rigged up a standard commercial public address array, five patently cheap and nasty oval no-name drivers each about 3x5 inches in an open-backed box about 30 inches long, as a Bessel array by simply rewiring and adding amps as required. This proved to be the size limit of a Bessel array in this particular application where the distance between the far wall and the "listening" position is 24 feet.
An experimental 6ft6in long stereo Bessel array with five 12in fullrange guitar drivers was too big for a domestic setting but was stunningly realistic when I took it along to a record club in a public hall.
Of course, your house might be bigger than mine, or you may want speakers to hang on the far side of your pool from the barbeque. I have proved experimentally to my own satisfaction that ten times the length of the Bessel array is a good room size.
I had several cartons of the two inch Coral drivers, so next I tried a 5x5 stereo square (not an official Bessel configuration, so don't blame Mr Bessel and Philips if in your hands it turns out an experiment too far!). Correctly angled near the ceiling so that it beamed over the computer screen, and with some further in-computer EQ fiddling to sort out anomalies created by room irregularities, it created a high-quality soundstage with width as well as depth; it placed the listener in the centre of the soundstage, a most impressive ability indeed. The problem was not the sound but that what started as an experiment in el cheapo mimicry of a Quad ESL63 was becoming expensive; I anyway have real Quad ESL63 and Lowther horns. Besides, I'm not big on artificially wide soundstages; in fact, I am often happy with mono, and find that most people with active imaginations agree with me. The Stereo Square Mini-Bessel was therefore broken up and the fine drivers reapplied.
However, with cheaper drivers such as the MTM aluminum-coned 4- and 5-inchers, a Stereo Square Midi Bessel Array would be a possibly economical and certainly space-saving alternative to, for instance, a pair of my Impresario speakers or other big floorstanders in even medium-sized living rooms (from about 17ft for the 4-inchers, 21ft for the 5-inchers). As an experimenter's econonomy, the flat baffle design for these drivers which I published in Glass Audio (Volume 9, No. 6, 1997) with my review of SEX amp kit can easily be reconfigured as a Bessel stereo amp.
So, is a Bessel Array any good for hobbyists?
The answer is yes -- and no. As outdoors party motivators, Bessel Arrays can bring real quality to your barbeques at a surprisingly modest price. A tiny Bessel array can make a most superior multimedia speaker. A modest Bessel stereo square can be stunning in a large room. But anything bigger than a modest Bessel array is suitable only for use outdoors or in large venues. The key consideration is always the size of the space. In addition, Bessel Arrays are intended to use many cheap drivers to give high quality sound at substantial volume. But the people who live in rooms of the size required to make Bessel Arrays work inhabit an income bracket where the saving between real Quad ESLxx and a Bessel Array faux point source speaker looms much less large than the pleasure of having the real thing. In short, the Bessel Array isn't really wanted in (nor was ever intended by its inventor for) any everyday domestic niche.
We have to conclude that the Bessel Array comes into its own as a public address speaker of quality, and is a curiosity for audiophile DIYers.
"Bessel panels - high-power speaker systems with radial sound distribution" Philips Technical Publication 091, Eindhoven. Released 15 March 1983.
"Hi-Fi Performance from Small Speakers", by Charles F. Mahler, Jr., Audio, December 1959. He described building up 32 x 6 inch speaks into an array, equivalent area of five 15 inch speaks, -1dB at 10Hz, bandwidth to 11kHz.
"Dipole Radiator Systems" by R.J. Newman, JAES Vol 28 #1/2, 1980 January/February. He states, pg. 37: " The basic driver of interest would then appear to be one with a Qt approaching 1 and with a Vas being as large as reasonably possible." He builds an evaluation system with drivers having a Qt of 0.85 at 32 Hz.
Sound System Engineering by Don Davis & Carolyn Davis, Focal Press (Butterworth-Heinemann), Newton, MA. ISBN 0-240-80305-1
Bodo Kalthoff, Tom Dunker, Dan "Doc Bottlehead" Schmalle, Jean-Michel Le Cleac'h, Robert Levrault, Kurt Gabitzsch, Dave Dlugos, and Tony Weimar.
All text and illustration is Copyright © Andre Jute 1995, 2000, 2006
and may not be reproduced except in the thread KISS xxx on rec.audio.tubes