The Need for Equalisation
Equalisation to attain a desired flat frequency response may be applied to correct problems in the loudspeaker itself, or, moving along the audio chain, to modify the interaction of the loudspeaker with the room it is operating in. Moving along the audio chain still further, equalisation can also be used to modify the response of the room itself, by cancelling resonances with dips or notches in the overall amplitude response. However, it is not normally considered a good idea to try to combine an active crossover with a room equaliser, not least because they are doing quite different jobs. Moving the loudspeakers from one listening space to another will not require adjustment of the crossover, except insofar as the loudspeaker placement with regard to walls and corners has changed, but would almost certainly require a room equaliser to be re-adjusted unless the room dimensions, which determine its resonances, happen to be the same.
At low audio frequencies, normal rooms (i.e., not anechoic chambers with enormous sound absorption) have resonances at a series of frequencies where one dimension of the space corresponds to a multiple number of half-wavelengths of the sound being radiated. The half-wavelength is the basic unit because there must be a node, that is a point of zero amplitude, at each end. Sound travels at about 345 metres/second, so a room with a maximum dimension of 5 metres will have resonances from 34.5 Hz upwards. This is simply calculated from velocity/frequency = wavelength, bearing in mind that it is the half-wavelength that we are interested in. We might therefore expect a resonance at 34.5 Hz, and another at about 69 Hz; this is twice the frequency because we now need to fit in two half-wavelengths between the two reflecting surfaces. This continues for three and four times the lowest frequency, and so on. These “resonant modes” cause large peaks and dips in response, the height of which depends on the amount of absorbing material. A room with big soft sofas, thick carpeting, and heavy curtains will be acoustically fairly “dead,” and the peaks and dips of the frequency response will typically vary by something like 5–10 dB. A bare room with hard walls and an uncarpeted floor will be much more acoustically “live,” and the peaks and dips are more likely to be in the range of 10 to 20 dB, though larger excursions are possible. Resonant modes at low frequencies cause the greatest problems, because they cannot be effectively damped by convenient absorption material such as curtains or wall hangings. Room equalisation that attempts to deal with this situation is a very different subject from active crossover design and is not dealt with further here.
What Equalisation Can and Can’t Do
When the word “equalisation” is used without qualification, it almost always refers to correcting the amplitude/frequency response, without attempting to simultaneously correct the phase/frequency response. Correcting both is much more difficult, but it can be done. It is important to realise that if you use the right sort of equaliser, you can put a peak into the frequency response, and then cancel it out completely by using another equaliser with the reciprocal characteristic. The high-Q peak/dip equaliser described later in this chapter can perform this, as it is reciprocal—in other words, its boost and cut curves are exact mirror images of each other about the 0 dB line. Figure 11.18 below shows the symmetrical 6 dB peak and dip at 1 kHz that this circuit creates. If one equaliser is set to maximum boost, and it is then followed by an otherwise identical equaliser set to maximum cut, the final frequency response is exactly flat, as one might hope. What is much less obvious, but equally true, is that the phase shifts introduced by the first equaliser are also cancelled out by the second equaliser, so a square-wave input will emerge as a square-wave output. This process is demonstrated in Figure 11.1, where the square-wave with added ringing is the output from the first (peaking) equaliser.
The visually perfect square-wave is not the input waveform; it is the output from the second (dip) equaliser. The rise and fall times of the input square-wave were deliberately slowed down to 10 usec to avoid distracting effects due to the finite bandwidth of the opamps used. You will note that the height of the ringing takes a little while to settle down after the start at 0 msec. When applying square-waves and the like to filters and other circuits with energy-storage elements, you need to allow enough cycles for the circuit to reach equilibrium, otherwise you may draw some wildly false conclusions.
Having reassured ourselves on this point, things are generally very much otherwise in crossover equalisation. If a drive unit has, say, a 2 dB peak or hump in its amplitude/frequency response, this will probably be due to some under-damped mechanical resonance or other electro-acoustic phenomenon, and while it is, in principle at least, straightforward to cancel this out, it is very unlikely that the associated phase-shifts will also cancel, because the physics behind the drive unit peak and the equaliser dip are completely different.
Excerpt from The Design of Active Crossovers by Douglas Self © 2011 Taylor & Francis Group. All Rights Reserved.