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will be directly from the loudspeaker, with an accurate frequency response, and will be subjected to less room colouration. Correcting for high-frequency absorption is a job for the preamplifier rather than the active crossover, and this is just one reason why preamplifiers without tone-controls are a daft idea.

Equalisation Circuits

There are a many ways of obtaining a desired equalisation response, and any attempt to examine them all would probably fill up the whole book, so I have had to be very selective in picking those looked at here. I have aimed to provide circuits that are easy to design, predictable in their response, easy to configure for good noise and distortion performance, and well-adapted for dealing with common loudspeaker problems. I have included some where the fixed resistors that set the response can be temporarily replaced with variable controls to speed the optimisation of a crossover design.

HF-Boost and LF-Cut Equaliser

This is also known as a shelving highpass equaliser. It gives a frequency response that at low frequencies is flat but begins to rise when the frequency passes the boost frequency fb. It continues to rise at a basic rate of 6 dB/octave until the shelf frequency fs is reached, at which point it shelves or levels out to a fixed gain. Unless the boost frequency and the shelf frequency are spaced by several octaves, the transition slope between the gain regimes will not have time to develop an actual 6 dB/ octave slope. The Figure 14.5 shows the inverting form of the circuit.Anon-inverting version also exists but is less flexible, because at no frequency can it have a gain of less than unity.

The circuit shown here is essentially a shunt-feedback amplifier with unity gain at low frequencies, because R1 = R3. To make it an HF-boost equaliser, the extra network R2, C1 is added.As the

Figure 14.5: Typical application of HF-boost equaliser for constant directivity horn equalisation; with the values shown, the boost starts around 2 kHz and begins to shelve to + 15 dB above 20 kHz.

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frequency rises the impedance of C1 falls and allows a greater input current to flow into the virtual earth point at the inverting input of A1. As the frequency increases further, this current is limited by

R2, causing the gain at high frequencies to reach a maximum of R3 divided by the value of R1 and R2 in parallel. The stabilisation capacitor C2 across R3 has no effect on the response at audio frequencies and is included only to emphasise that it is always good practice to include such a measure. The shuntfeedback configuration has no common-mode signal voltage; this is handy if you are using an opamp prone to common-mode distortion. The downside is that it introduces a phase inversion which will need to be reversed somewhere else in the crossover system.

The design equations for the circuit are given in Figure 14.5, and the frequency response with the values given is shown in Figure 14.6. The equations for the LF gain and the HF or shelf gain are straightforward, but the expressions for the two frequencies require a little explanation. The boost frequency fb is the frequency at which the gain would have increased by 3 dB, just as the cutoff frequency of a lowpass filter is usually specified as the frequency at which the amplitudes response has fallen by 3 dB. Likewise, the shelf frequency fs is the frequency at which the gain is 3 dB below its final shelving value.As with the response slope, in practice the interaction between the boost and shelving actions is such that the equaliser response will only show these 3 dB figures in its response if the boost frequency and the shelf frequency are a long way apart—much further apart than is likely in any practical crossover design. This needs to be kept in mind when examining simulator outputs and measured frequency responses. It is perfectly possible to use component values that give the same boost and shelving frequencies; this does not mean the equaliser is doing nothing; it means that the LF and shelf gains are 6 dB apart.

Figure 14.6: The frequency response of the HF-boost equaliser for constant directivity horn equalisation shown in Figure 14.5.

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Figure 14.7: The same circuit treated as an LF-cut rather than an HF-boost equaliser.

If a basic gain of unity is not what is required, it can be set to any value above or below by altering the value of R3.As with active filters and other frequency-dependent circuits, it is best to decide on a preferred capacitor value first and derive the resistor values from that, given the much greater variety of resistor values available and the ease with which non-standard values can be obtained by combining two (2xE24 format) or three (3xE24 format) of them.

In choosing component values, the resistors should be kept as low as possible to minimise Johnson noise and the effects of current noise flowing through them, but they must not be so low that opamp distortion is increased, either in A1 or in the preceding stage. Particular care is needed with the latter because the input impedance of the circuit falls to R1 in parallel with R2 at high frequencies, where opamp distortion is most troublesome. The circuit values shown give an HF input impedance of 824 Ω, and if 5532 opamps are being used, you will not want to go much lower than this.

This type of HF-boost equaliser can be used to deal with response irregularities of many kinds.

Acommon application in the sound-reinforcement field is for constant directivity horn equalisation; the requirement for this is explained earlier in this chapter. Siegfried Linkwitz also recommends this configuration to smooth the transition between a floor-mounted woofer and a free-standing midrange/ tweeter assembly. [3]

It is important to understand that while this circuit has so far been described as an HF-boost equaliser, it can also be regarded as an LF-cut equaliser; it is simply a matter of how you look at it. Figure 14.7 shows a circuit that has unity gain across most of the audio spectrum but gives a gentle cut from about 200 Hz down, as in Figure 14.8. The important point is that to set the normal or unequalised gain, where the impedance of C1 is so low it has no effect, to unity you must choose R1 and R2 so their combined value in parallel is equal to that of R3 (other unequalised gains greater or lesser than unity can be chosen).As the frequency falls, the impedance of C1 increases until the current flow through R2 is negligible and the shelving gain of the circuit is set by R1 alone, to −2.5 dB. In this case the boost frequency is higher than the shelving frequency, not lower, as it was with the CD horn example.

HF-Cut and LF-Boost Equaliser

This is also known as a shelving lowpass equaliser. It gives a frequency response that at low frequencies is flat but begins to fall as the frequency rises and approaches the cut frequency fc. It continues to fall at a basic rate of6 dB/octave until the shelf frequency fs is reached, at which point

Figure 14.9: Typical example of HF-cut equaliser set up for diffraction compensation;

with the values shown the response falls from about 200 Hz and shelves to −6 dB around 5 kHz. The middle −3 dB point is at 1 kHz.

Figure 14.10: The frequency response of the HF-cut equaliser in Figure 14.9, showing a typical curve for diffraction correction.