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Loudspeaker Technology Part 9: Methods of Controlling Directivity

The need for good directivity in loudspeakers cannot be sufficiently emphasised and remains an area that speaker designers sometimes neglect. The result destroys acoustic realism and makes loudspeakers sound like loudspeakers instead of like the original sound.

To recap from the previous chapters of this series, when listening in a reverberant environment, the HAS (Human Auditory System) soon acclimates to the characteristics of the environment and learns how the reflected sound is modified. With a real sound source, the HAS soon establishes that the reflections it is hearing are actually from the sound source. As they arrive later, they do not distract from locating the true position of the source. That was done using the first versions of any sound emitted that must have come by the shortest route.

In concert halls, we make the walls reflective so that the sound created by the musicians is re-directed to the audience. Typically, a reflector is also mounted above the orchestra. Yet no one in the audience thinks the sound is coming from the wall or the reflector, because the sound from the instruments reaching the walls and the reflector is practically as good as the sound going directly to the audience. Real sound sources such as people and instruments do not have axes and sweet spots, so the concept of on-axis sound is meaningless. The reflections are correctly identified as delayed versions of the direct sound and the Haas effect (the ability of our ears to localize sounds) simply allows them to make the listening experience louder and richer. If the reflections in a concert hall are taken away, everyone rightly complains.

Why deaden control room walls?

So why, then is critical loudspeaker monitoring carried out in control rooms that are deliberately deadened, at great cost, to prevent reflections? Why do the engineers complain that the imaging is diminished if the sound absorbing is removed? How can the same human auditory system and the same laws of acoustics result in two diametrically opposed approaches to listening? What is wrong here?

Figure 1.  At a) the sound on axis may have a prefect frequency response, but that is not enough. Typically, the sound off axis (b) is highly coloured because of directivity problems. Real sound sources do not have axes, so loudspeakers like this cannot sound like real sound sources.  (Click to enlarge).

Figure 1. At a) the sound on axis may have a prefect frequency response, but that is not enough. Typically, the sound off axis (b) is highly coloured because of directivity problems. Real sound sources do not have axes, so loudspeakers like this cannot sound like real sound sources. (Click to enlarge).

If we replace a real sound source with a legacy loudspeaker having poor directivity, no matter how good the recording we reproduce, there will be problems. Figure1 shows that the on-axis sound may be fine, but the off-axis sound will not. If the directivity becomes narrower as frequency rises and then jumps wider at some crossover to a smaller driver, the off-axis frequency response may resemble a dog’s hind leg, complicated by the fact that we need a different breed of dog for each direction.

The result is that the HAS does not recognise the coloured sound as reverberation because it does not resemble the direct sound modified by the room. Instead, it is treated as a new sound that distracts from the original. The fact that the frequency response is different in every direction means that no equalisation of the input signal can possibly work, because if the response is corrected in any one direction it will simply be wrong in the others.

Figure 2 illustrates that the on-axis sound only forms a small part of the total sound power radiated. If the majority of the power radiated is inaccurate, it is not accepted by the HAS as a reflection and so has to be absorbed.

Replacing concert musicians with a legacy loudspeaker results in a sound quite inferior to that of the orchestra. Yet, if a loudspeaker designed using modern quality criteria and adequate directivity performance is used, it sounds great in a concert hall. Moreover, in a control room, the need for the heavy absorption goes away. The additional cost of constructing a loudspeaker that meets modern performance criteria is less than what it might cost in the hall’s acoustic treatment. 

Figure 2.  In a real listening environment, most of the sound received by the listener comes from reflected surfaces. With legacy speakers that are inaccurate off-axis, most of the sound is coloured. Instead of fixing the speakers, the sound has to be absorbed by walls at great cost.  (Click to enlarge).

Figure 2. In a real listening environment, most of the sound received by the listener comes from reflected surfaces. With legacy speakers that are inaccurate off-axis, most of the sound is coloured. Instead of fixing the speakers, the sound has to be absorbed by walls at great cost. (Click to enlarge).

Speaker colorization

A very simple test for loudspeaker directivity problems is to walk out of the room where the speakers are playing and to determine how the sound changes. Unless the loudspeakers are pointing directly at the door, the sound coming out the door will be mostly reverberant. If the off-axis performance of the speakers is poor, the sound coming out the door will be poor. This saves a lot of time at trade shows, where if the sound at the door of a demonstration room is coloured, do not bother to go in.

The corollary is that a loudspeaker of modern directivity characteristics can produce sound coming out of the door of a room that is indistinguishable from the real thing. In fact, it is one of the criteria for an accurate loudspeaker that it should be able to do that.

The criterion for a realistic loudspeaker is that the frequency response should be the same in all of the directions in which it radiates. Drive units of finite size naturally tend to radiate a narrower beam of sound as frequency rises, so the search for realism must include considering all of the techniques that could oppose that.

Speaker directivity

Whilst the frequency response should be the same in all directions, that does not determine what range of directions is optimal. That is a completely different issue and is affected by the nature of the sound to be reproduced and by the environment. For example, because woofers are always smaller than the sound’s wavelength and are therefore always omni-directional, in free space, a realistic full range loudspeaker can be obtained by making the rest of the frequency range omni-directional as well. This helps ensure the frequency response is essentially independent of direction, at least in the horizontal plane. For home listening, the omni-directional loudspeaker has much to recommend.

In the case of wall-mounting speakers, the woofers will have a directivity of 180 degrees, so again it makes sense to arrange the rest of the spectrum to have the same characteristic. In public address applications, where the acoustics may be unfriendly, the only significant acoustic absorbent may be the audience’s clothing. In this case, it makes sense to direct the sound only at the audience and nowhere else in order to avoid echoes. In environments where only speech will be reproduced, the low frequencies can be filtered out so that the speaker can be directional at all frequencies.

In horn loudspeakers, the diaphragm can be quite large compared to the sound wavelength, but it does not radiate directly. Instead, a waveguide arrangement channels the sound coherently to a central small area from which it excites the mouth of a horn. In a multi-cellular horn, the waveguide is designed to channel exactly the same sound waveform having the same timing to a large number of horn mouths, each of which curves off in a different direction. Such speakers can produce an approximation to spherically expanding waves, but the use of horns introduces other problems such as resonances due to standing waves.

Rear view of a multi-cellular horn speaker.

Rear view of a multi-cellular horn speaker.

In a woofer, the diaphragm must be rigid so that all parts of it move together. Any unwanted flexing of the cone is called cone breakup. Breakup is also deliberately used in the small speakers of low-cost portable equipment because it results in higher efficiency, with the trade-off of a sound that no longer bears much relation to the input.

However, moving different parts of the diaphragm in a controlled manner can have useful results. Instead of a single radiating element, the drive unit becomes an array of elements. A rigid diaphragm has a rectangular window, but if the amplitude of the outer parts of the diaphragm can be reduced with respect to the centre, it is the equivalent of applying a window function. The window will get smaller and the directivity will widen.

Another approach is to carefully corrugate or soften the diaphragm. In that way the mass of the outer parts of the diaphragm receives a reduced driving force because of the flexing of the cone. Done properly, the compliance and the mass of the cone act as a filter. As can be seen in Figure 3, the outer parts of the diaphragm decouple as frequency rises, reducing the effective diameter and improving the directivity pattern.

Figure 3.  With a lossy diaphragm, the effective diameter is reduced as frequency rises. At low frequency, top, vibrations reach the perimeter of the cone and are terminated. At high frequencies, bottom, the vibrations are absorbed before they reach the perimeter.  (Click to enlarge).

Figure 3. With a lossy diaphragm, the effective diameter is reduced as frequency rises. At low frequency, top, vibrations reach the perimeter of the cone and are terminated. At high frequencies, bottom, the vibrations are absorbed before they reach the perimeter. (Click to enlarge).

Another possibility is to construct the diaphragm in the form of a radial transmission line. In this scenario, vibrations from the central coil travel outwards at a known speed. If the forward component of that speed is less than the speed of the sound, the vibrations travelling outward from the coil do so gradually and the diaphragm does not act like a piston. Both of these approaches effectively apply a window function to the rectangular aperture.

If directivity cannot be fixed with signal processing, then we have to fix it another way. In this case, we can purposefully introduce problems that can be corrected electronically. For many years, a minority of passive speakers have been designed using drive units mounted with their axes vertical to illuminate a more or less conical reflector. These designs mostly failed because such an approach, whilst having excellent directivity, also displayed serious loss of HF response because the same energy radiates into a larger solid angle. Either electronic compensation was not applied, or if it was, the conventional tweeter ended up working much harder than in a legacy configuration and was driven into distortion.

A successful omni-directional loudspeaker must be an active system. This permits appropriate equalisation matched to the characteristics of the HF driver to be employed. This is no penalty because, as has been seen, passive crossovers are inadequate by design. The HF unit needs to be designed with sufficient power handling to deliver adequate level into such a large solid angle.

John Watkinson Consultant, publisher, London (UK).

John Watkinson Consultant, publisher, London (UK).

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