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slope of the loudspeaker response with the upward slope of equaliser boost, but there are two major complicating factors. First, when the LF response of a loudspeaker is rolling off, the cone excursion is at its greatest. Adding equalisation increases the excursion further, and it is all too easy to exceed the safe limits of the drive unit. Second, a much increased amplifier power capability is required.

It has been claimed that not only is the LF response extended, but the time response may also be improved, because the ringing and overshoot caused by an underdamped LF response can be cancelled by a matching dip in the response of the equalisation circuit, since we are dealing with a simple minimum-phase system. The final LF roll-off is determined by that of the equaliser. It is questionable if this can really be counted as “equalisation” as such, because the intent is not so much to correct an error as to extend the performance beyond what would otherwise be physically possible. The biquad equaliser is a good choice for this form of equalisation, giving great freedom of parameter variation.

Because of the low frequencies at which this kind of equaliser operates, large capacitor values are required if impedance levels are to be kept suitably low, and this puts up the cost.

4  Diffraction Compensation Equalisation

We saw back in Chapter 2 that the diffraction of sound from the corners of a loudspeaker enclosure can have profound effects on the frequency response. A somewhat impractical spherical loudspeaker is free from most response irregularities but still has a gentle 6 dB rise with frequency, because at low frequencies, the long sound wavelengths diffract around the sides and rear of the enclosure,

so radiation occurs into “full-space”, while at high frequencies, the drive unit cone radiates mostly forwards, into what is called “half-space”. This rise in response is sometimes called the “6 dB baffle step” though it is actually a very smooth transition between the two modes. Since the frequencies that define it are constant, being derived from the enclosure dimensions, it can easily be cancelled out by

1st-order shelving equalisers, such as those described later in this chapter.

Spherical loudspeakers are, however, very rare, and for practical reasons the vast majority of loudspeaker enclosures are rectangular boxes, as seen in Figure 14.2, which is derived from the alltime classic paper by Olson in 1969. [2] The lengths of the edges of the rectangular box were 2 feet and 3 feet, the drive unit being mounted midway between the two side edges and 1 foot from the top short edge. Olson comments that the dips at 1 kHz and 2 kHz are induced by diffraction from the top and side edges, the frequencies being relatively high because the distances from the drive unit to these edges are small; the broader response minimum just below 600 Hz is due to the longer distance to the bottom edge. It is obvious that equalising away these three minima. as well as compensating for the 6 dB baffle-step rise, is a fairly ambitious undertaking, requiring at least four equaliser stages. There are also minor dips of about 1 dB at 1.5 kHz and 2.5 kHz, which are at multiples of the frequency of the minimum due to the distance to the bottom edge and are due to the path containing whole wavelengths.

Olson suggested a more sophisticated enclosure, as in Figure 14.3, that would give blunter edges and much reduce the response irregularities, while still fitting into a living room better than a sphere would.

The graph shows response deviations reduced to about 2 dB. This is a great improvement, and this sort of box has had some popularity, though it is of course more difficult to make and not everybody likes the shape. The response could be made almost flat by correcting the inherent 6 dB rise and then applying a little cut at 1 kHz and 2 kHz.

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middle of a large field, which can be useful for measurements but is less so for actual listening) is said to be working into “whole-space”.As we saw in the previous section, the low-frequency output will tend to diffract around the loudspeaker enclosure and travel backwards away from the listener, while the high-frequency output will mostly be radiated forwards.

If we now mount the loudspeaker in the middle of a large vertical wall, with the front baffle flush with the wall, it is working in “half-space”, and the low-frequency output can no longer travel backwards— it has to go forwards, and so more low-frequency energy reaches the listener. The high-frequency output is unchanged because it was all going forwards anyway, so the relative rise in LF level is about

6 dB. If we put the loudspeaker at the junction between a vertical wall and the floor, the effect is enhanced, and this is called “quarter-space” operation. Finally, we can put our loudspeaker in a corner, where the floor and two walls at right angles meet, and this is known as “eighth-space” operation.

If this progression was taken further by adding more enclosing surfaces, we would end up with something like a horn loudspeaker.

From the point of view of crossover design, the important thing is that the low-frequency acoustic output is boosted relative to the high-frequency output each time we move from whole-space to halfspace to quarter-space and then to eighth-space.Aloudspeaker/crossover system designed to give a flat “free-space” response, typically for an outdoor sound-reinforcement application, will sound very bassheavy indoors. Some studio monitor speakers have “half-space” and “quarter-space” settings which switch in a low-frequency roll-off, the frequency at which it starts depending on the enclosure size.

A suitable equaliser might be the LF-cut circuit described later in this chapter.

While studio monitor speakers are mounted very carefully, often flush with a surface to give true “half-space” operation, more compromise is usually required in the domestic environment, and it is quite possible to encounter a situation where one loudspeaker is against a wall (quarter-space) while the other has to be in a corner (eighth-space). This is obviously undesirable, but sometimes in life one must make the best of a non-optimal situation, and providing separate open/wall/corner equalisation switches for the left and right channels of a crossover might be worth considering.

Things get more complicated when we contemplate a loudspeaker standing on the floor and not flush (or nearly so) with a wall but some distance from it. If the loudspeaker is one quarter of a wavelength away from a reflective wall at a given frequency, the low-frequency energy that diffracts backwards is reflected, so that its total path length is one half-wavelength, and it will reach the loudspeaker again in anti-phase so that cancellation occurs. If the front of a loudspeaker is 1 metre from a wall, the first cancellation notch will be at about 86 Hz, as this frequency has a quarter-wavelength of 1 metre. How complete the cancellation is depends on how accurately the speaker-wall distance is one quarterwavelength and on the reflection coefficient of the wall.Alower frequency means a greater distance for a quarter-wavelength, and the amplitude of the reflected signal reaching the speaker will be lower because there is more opportunity for diffusion, and so the cancellation will be less effective.

If the loudspeaker is half a wavelength away from a the reflective wall, the total path length is a whole wavelength, and it will in arrive in-phase and reinforce the direct sound, theoretically giving a +6 dB increase in level. The effect on the sound reaching the listener will vary from complete cancellation to +6 dB reinforcement depending both on the relationship between the sound wavelength and the total path length via reflection and on the wall reflection coefficient. This effect is not confined to one frequency, because there can be any number of whole wavelengths in the go-and-return path;

Figure 14.4 shows how this gives a “comb-filter” response, with the reinforcement peaks and the

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Reinforcement peaks

+6 dB

0 dB

Cancellation notchs

86 Hz 258 Hz 430 Hz

Figure 14.4: Comb-filter effect produced by reflection from wall behind loudspeaker. The amplitude of the peaks and the notches reduces with increasing frequency because more

sound is radiating forward and less is diffracting to the rear.

cancellation notches reducing in amplitude with increasing frequency because more sound energy is being radiated forward and less is diffracting to the rear. The peaks and notches get closer together because the graph is drawn in the usual way with a logarithmic frequency axis, but the reinforcement/ cancellation process is dependent on a linear function of frequency.

Calculating the actual path length is complicated by the fact that the low-frequency radiation has to go round a 180-degree corner, so to speak, as it diffracts around the front of the enclosure, and it is a question as to how sharp a turn it makes in a given situation.

This comb-filtering loudspeaker-room interaction has been examined here because it is a very good example of a mechanism that it is not possible to correct completely by equalisation, for both theoretical and practical reasons. Practically, boosting the gain at all the notch frequencies would be

very hard to do, because of the need to line multiple boost equalisers up with multiple narrow notches, an alignment that would become grotesquely incorrect as soon as the loudspeaker was moved by a few inches. You will however note that the gain variations become less as the frequency increases, so what can be done is to make some compensation for the really big response variations at the LF end.

The other important point that stands out here is that the loudspeaker-spaced-from-a-wall situation is extremely common, giving rise to the sort of frequency response shown in Figure 14.4, and yet we still listen quite happily to the result. It is not necessary to have a ruler-flat frequency response to enjoy music.

Another important property of a listening space is the amount of high-frequency absorption it contains.

Aroom with hard walls and floors will reflect high-frequency energy, and a proportion of this will reach the listener as reverberation. On the other hand a room with wall hangings, thick carpets, and comfy sofas will absorb some of high-frequency energy, and the effect will be less treble. The more absorbent room will give the more accurate sound, as a greater proportion of the energy at the listener