What a Crossover Does

2  Crossover Basics

of loudspeaker construction is inadequate but is also rooted in some basic physics. Ideally the acoustic output of a loudspeaker would come from a single point; with such a source the sound field is uniform, because there can be no interference effects that result from multiple sources or from a source of finite size.

Atweeter has a small physical size, with a dome usually around an inch (2 or 3 cm) in diameter, and approximates fairly well to a point source. This technology works very well for high frequencies, say down to 1 kHz, but is hopelessly inadequate for bass reproduction because such a small area cannot move much air, and to reproduce bass frequencies you need to move a lot of it. Low-frequency drive units are therefore of much greater diameter, up to 12 inches for domestic hi-fi and up to 18 inches or more for sound-reinforcement applications. As cone area is proportional to the square of diameter, a 12-inch drive unit has 144 times the area of a typical tweeter, and an 18-inch unit has 324 times the area.

It is not at present technically possible to make a big low-frequency drive unit that works accurately up to 20 kHz, because as the frequency increases the cone ceases to move as a unit—it is not one of those most desirable “infinitely rigid pistons” that are always cropping up in loudspeaker theory but never in manufacturer’s catalogues. This effect is often called “cone break-up” not because the cone physically falls apart but because, due to its finite stiffness, with rising frequency its surface divides up into separate areas of vibration. This unhappy state of affairs is put to advantage in so-called full-range loudspeakers which have a “parasitic tweeter” in the form of a small cone attached to the voice coil. The idea is that at higher frequencies the main cone does its own thing and is effectively decoupled from the voice coil and the tweeter cone, allowing the latter to radiate high frequencies without being restrained by the much greater mass of the main cone—what you might call a mechanical crossover. As you might imagine, there are many compromises involved in such a simple arrangement, and the response is generally much inferior to a good 2-way loudspeaker with separate bass unit and tweeter.

Nonetheless, the field of audio being what it is, there are a certain number of hi-fi enthusiasts who advocate full-range speakers for various reasons. Eliminating a passive crossover naturally increases power efficiency (as none is lost in the crossover components) and reduces cost.

Beaming and Lobing

Even if it was possible to make a large-diameter drive unit which covered the whole audio spectrum perfectly, there is a powerful reason why it is far from certain that this would be a good idea. If a radiating surface is of finite size, then if you stand to the side of the central axis, sound from one area of the drive unit will arrive at your ear at a slightly different time compared with another area because of the differing path lengths through the air. This will cause interference between the two signals and, given the right amount of path difference, complete cancellation. There will therefore be major irregularities in the frequency response anywhere but on the central axis. This is called “beaming” or “lobing”, and it occurs when the diameter of the radiating object is comparable with the wavelength of the sound. It is obviously to be avoided as much as possible; the variation in response as the angle between the listener and the centre axis changes is called the polar response, and a “uniform polar response” is much sought after in loudspeaker design.

Crossover Basics  3

Table 1.1: Onset of beaming versus drive unit diameter.

The beaming phenomenon is why a tweeter has to be of small diameter if it is to approach having a uniform polar response. Deciding when beaming becomes significant depends on the application, but the figures in Table 1.1 [1] have been put forward as shown above.

These frequencies are approximately those at which the wavelength in air equals the driver diameter. The whole business of beaming, lobing, and polar response generally is obviously much too complex to be summed up in a single table, but it does give some indication of when you need to start worrying about it.

There is of course much more to a crossover than simply splitting the audio signal into separate frequency bands. The vital point to understand is that the splitting has then to be followed by summation. The frequency bands have to be joined together again seamlessly. This requires the acoustic signals be summed to be correct not only in amplitude but in phase. The crossover and speaker system can only create the exactly correct signal at one point in space, which is unfortunate, as we have two ears and each listener therefore needs the signal to be correct at two points in space. Crossover design is always a matter of compromise to some degree.

It is not sufficient to get a perfect response on-axis, even if one interprets this as being capable of summing correctly at both ears. The off-axis output from the loudspeaker will not only be heard by those in the room unfortunate enough to not get the best seat on the sofa, but it also creates the ambient sound environment through room reflections and reverberation. If it has serious response irregularities, then these will detract from the listening experience, even if the direct on-axis sound is beyond reproach.

The term “lobing” is also used to describe the reinforcements and cancellations that occur when two separate drive units are radiating; in this case their size is relatively unimportant because interference would still occur even if both were point sources. When the radiation pattern is shifted at the crossover frequency because the signals to the two drive units are not in phase, this is called “lobing error”. There is much more on this in Chapters 3 and 4.