How Loudspeakers Work  39

away from the pulpit were delayed by 5, 10, and 15 ms, explicitly making use of the Haas effect. The delays were implemented by tape heads contacting a rotating magnetic disc. For the time it was a remarkable system.

CBT Line Arrays

CBT stands for “constant beamwidth transducer”. It is a technique developed by Don Keene [27] [28] and is proprietary to JBL. CBT combines amplitude tapering with steadily increasing time delays to the outer loudspeakers in the array, giving a much wider and smoother coverage off-axis than amplitude tapering alone. The technology originated in beam-forming systems for submarine sonar. The tapering and delays can be conveniently implemented as a passive lossy delay line, which means much less hardware than differing digital delays feeding multiple power amplifiers. JBLhave produced an excellent introductory guide to this technology. [29] One of the patents that cover it is EP2247120A2, [30] which is assigned to Harman International.

Figure 2.7 shows an eight-box CBT array, similar to the JBLCBT-40 array. The undelayed signal directly feeds boxes 4 and 5, which are connected in series. Boxes 3 and 6 are fed in series with a delayed signal after L1 and C1, boxes 2 and 7 are in series after the second delay stage L2-C2, and the outer boxes 1 and 8 are fed in series after the final delay section L3-C3. The European patent gives a full description of the delay process, but is rather vague about how the amplitude tapering is done; it seems likely that in part at least it relies on losses in the series resistance of the inductors. The inductance and capacitor values increase steadily from the input to the end of the delay line.

Diffraction

Diffraction affects loudspeaker operation for the simple reason that high frequencies have shorter wavelengths than long frequencies. At high frequencies, a loudspeaker cone radiates sound mostly in a forward direction, into what is called “half-space”: a hemisphere facing forwards.At low frequencies, the longer wavelengths of the sound bend, or diffract, around the sides and rear of the enclosure, so radiation occurs into “full-space”, which is a sphere with the loudspeaker at its centre. In other words the loudspeaker becomes more or less omnidirectional. The difference between these two modes appears as a lower output on the forward axis at low frequencies. In the quite unrealistic conditions of an anechoic chamber the low-frequency loss is 6 dB, halving the SPL. In the special case where the loudspeaker enclosure is spherical, the transition between the two modes is smooth and can be approximated by a 1st-order shelving response, as shown in Figure 2.8, which is derived from the classic paper on the subject by Olson in 1969. [31]

This effect is sometimes called the “6 dB baffle step” or the “diffraction loss” of the enclosure (“step” is not a very good description—it is actually a very gentle rise). The frequency at which this occurs is proportional to the enclosure dimensions, and the effect can be compensated for by simple shelving equalisation.

While spherical loudspeaker enclosures are perfectly practical, a notable example being the Cabasse

La Sphère, [32] which claims to be “Atrue 4-way co-axial point source”, they are never likely to be very popular. Apart from anything else, they need special stands to stop them rolling around the room.

40  How Loudspeakers Work

Figure 2.7: CBT line array with passive delay line gives wider and smoother coverage off-axis. Based on European Patent EP2247120A2.

There are also problems because the internal reflection paths are all the same length. I once knew a chap who built a pair of spherical loudspeakers out of GRP, using full-range drive units. He was unable to resist the temptation to paint them like a giant pair of eye-balls, which did not create a restful effect.

For any shape other than spherical, or perhaps ellipsoidal, the diffraction business becomes more complicated. Any other shape has some sort of edge or edges, and when the sound waves from the drive unit strike them, a negative pressure wave is formed which radiates forward and sums with the direct output from the drive unit. This creates an interference effect which adds wobbles to the basic frequency response with its 6 dB rise; these wobbles can be as large as the step itself. This edge effect is illustrated in Figure 2.9.

42  How Loudspeakers Work

Figure 2.10: Serious response disturbances due to corners, superimposed on 6 dB rise; cylindrical­ loudspeaker enclosure 24 inches in diameter and 24 inches long (after Olson, 1969).

Figure 2.11: Reduced response disturbances due to corners, superimposed on 6 dB rise; cubic loudspeaker enclosure 24 inches on a side (after Olson, 1969).

as the frequency increases; this is simply because the graph has a logarithmic frequency scale, but the diffraction effect, being based on multiples of wavelength, is linear. Although the response to be corrected should be constant, because it depends on the mechanical dimensions of the enclosure, clearly any attempt to equalise away these variations would take quite a bit of doing. The obvious conclusion is that this shape of enclosure is of no use to man or beast, and should be shunned.

Rectangular (or to be strictly accurate, rectangular parallelepiped, i.e. with all edges parallel) boxes are of course much easier to fabricate than spheres or cylinders, and are correspondingly more popular. The simplest shape is the cube, which has the advantage over the cylinder that the path length from the drive unit to the front edges varies. This helps to smooth out the response wobbles, but as Figure 2.11 shows, they are still substantial, the difference between the first peak and the first dip being about 8 dB.