402  Equalisation

This variable-frequency circuit is relatively complex compared with fixed equalisers and is noisier because of the extra Johnson noise from the high-value frequency-determining resistors. In production it would probably be replaced by a fixed equaliser like that in the previous section, with component values set to give the desired response.

Adjustable Peak/Dip Equalisers With High Q

The two peak/dip equalisers we have just examined have low Qs and are not suitable for dealing with relatively narrow response irregularities; obtaining higher Qs requires more complex circuitry. There are several different approaches that might be taken; for example a state-variable filter would give the most flexibility, with control over centre frequency and Q as well as the amount of peak or dip. While it could be very useful for optimisation, it would however be excessively complex and costly for permanent inclusion in a crossover design. The approach I have chosen here is based on using a gyrator to simulate a series LC resonant circuit.

The essence of the scheme is shown in Figure 14.15, which the alert reader will spot as the basic concept behind graphic equalisers. [6] L1, C1 and R3 make up an LCR series-resonant circuit; this has a high impedance except around its resonant frequency; at this frequency the reactances of L1, C1 cancel each other out, and the impedance to ground is that of R3 alone (a parallel LC circuit works in the opposite way, having a low impedance at all frequencies except at resonance).At the resonant frequency, when the wiper of RV1 is at the R1 end of its track, the LCR circuit forms the lower leg of an attenuator of which R1 is the upper arm; this attenuates the input signal, and a dip in the frequency response is therefore produced. When the RV1 wiper is at the R2 end, an attenuator is formed with R2 that reduces the amount of negative feedback at resonance and so creates a peak in the response. It is not exactly intuitively obvious, but this process does give absolutely symmetrical cut/boost curves. At frequencies away from resonance the impedance of the RLC circuit is high and the gain of the circuit is unity.

Figure 14.15: The basic idea behind the peak/dip equaliser; gain is unity with the wiper central.

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Inductors are always to be avoided if possible, They are relatively expensive, often because they need to be custom-made. Unless they are air-cored (which limits their inductance to low values), the ferromagnetic core material will cause non-linearity. They can crosstalk to each other if placed close together and can be subject to the induction of interference from external magnetic fields. In general they deviate from being an ideal circuit element much more than resistors or capacitors do.

Gyrator circuits are therefore extremely useful, as they take a capacitance and “gyrate” it, so it acts in some respects like an inductor. This is simple to do if one end of the wanted inductor is grounded— which fortunately is the case here. Gyrators that can emulate floating inductors do exist but are far more complex.

Figure 14.16 shows how it works; C1 is the normal capacitor, as in the series LCR circuit, while C2 is made to act like the inductor L1. As the applied frequency rises, the attenuation of the highpass network C2, R1 falls, so that a greater signal is applied to unity-gain buffer A1 and it more effectively bootstraps the point X, making the impedance from X to ground increase. Therefore we have a part of the circuit where the impedance rises proportionally to frequency—which is just how an inductor

behaves. There are limits to the Q values that can be obtained with this circuit because of the inevitable presence of R1 and R2. The remarkably simple equation for the inductor value is shown; note that this includes R2 as well as R1.

The gyrator example in Figure 14.16 has values chosen to synthesise a grounded inductor of 100 mH in series with a resistance of 2 kΩ; that would be quite a hefty component if it was a real coil, but it would have a much lower series resistance than the synthesised version.

Figure 14.17 shows a gyrator-based high-Q peak/dip equaliser, with a centre frequency of 1 kHz. The

Q at the maximum boost or cut of 6.3 dB is 2.2, considerably higher than that of the previous peak/dip equaliser we looked at and much more suitable for correcting localised response errors. The maximal cut and boost curves and some intermediate boost values are seen in Figure 14.18. The +4 dB peak results from the values R2 = 9 kΩ and R3 = 1 kΩ. The +1.5 dB peak results from the values R2 = 7 kΩ and R3 = 3 kΩ. For development work R2 and R3 can be replaced by a 10 kΩ pot RV1. To obtain different centre frequencies scale C1 and C2, keeping the ratio between them the same.

Figure 14.16: Synthesising a grounded inductor in series with a resistance using a gyrator.

Figure 14.17: Gyrator-based high-Q peak/dip equaliser, with centre frequency fixed at 1 kHz. For development work R2 and R3 can be replaced by a 10 kΩ linear pot RV1.

Figure 14.18: Frequency response of gyrator high-Q equaliser with various boost/cut settings.

Equalisation  405

The beauty of this arrangement is that two, three, or more LCR circuits, with associated cut/boost resistors or pots, can be connected between the two opamp inputs, giving us an equaliser with pretty much as many bands as we want. It is, after all, based on a classic graphic equaliser configuration.

This configuration can produce a response dip with well-controlled gain at the deepest point, but it is not capable of generating very deep and narrow notches of the sort required for notch crossovers (see Chapter5).

However, notches for equalisation purposes are not normally required to be particularly deep or narrow. The implementation of filters that do have deep and narrow notches is thoroughly dealt with in Chapter12.

Parametric Equalisers

The most complicated equalisers that are likely to be of use in crossover design are parametric equalisers. Since a standard 2nd-order resonance curve is completely defined by the three parameters of amplitude, centre frequency, and Q, they are called parametric equalisers. They are most commonly encountered in mixing console input channels, where four equalisers covering LF, LOW-MID, HIMID and HF are fitted to high-end models. The LF and HF equaliser are usually switchable to give shelving responses like the Baxandall tone control.

Given their flexibility, parametric equalisers are relatively complex, and it is not likely that anyone would want to build them permanently into a crossover. However, even more so than other variable equalisers, they can be extremely useful during the development period for determining exactly what correction gives the best results, and this can then be implemented in simpler and cheaper fixed circuitry.

Parametric equalisers are almost always based around state-variable filters because of their ability to alter centre frequency and Q independently. State-variable filters are described in Chapter 10; for equalisers the constant-amplitude version is used so that the gain at the peak or dip does not vary with the Q setting. In Figure 14.19, the state-variable filterA1,A2,A3 only provides a bandpass boost resonance curve, and for equalisation is combined with the cut/boost stage A1.

Figure 14.19: Low-noise parametric equaliser giving ±15 dB of boost or cut at 70 Hz–1.2 kHz, with Q 0.7–5.