Chapter 10

Tone Controls and Equalizers

Facilities that alter the shape of the frequency response are called tone controls when they are incorporated in hi-fi systems, and equalization (or EQ) in mixing consoles.

Tone controls have suffered at the hands of fashion for some years now. It has been claimed that tone controls cause an audible deterioration even when set to the flat position. This is usually blamed on ‘phase-shift’. For a long time tone controls on a preamp damaged its chances of street (or rather sitting room) credibility, for no good reason. A tone control set to ‘flat’ – assuming it really is flat – cannot possibly contribute any extra phase-shift unless you have accidentally built in an all-pass filter, which would require truly surreal levels of incompetence, and so the control really must be inaudible. My view is that hi-fi tone controls are absolutely indispensable for correcting room acoustics, loudspeaker shortcomings, or the tonal balance of the source material, and that a lot of people are suffering suboptimal sound as a result of this fashion. It is commonplace for audio critics to suggest that frequency-response inadequacies should be corrected by changing loudspeakers; this is an extraordinarily expensive way of avoiding tone controls.

The equalization sections of mixers have a rather different function, being creative rather than corrective (from now on I am going to just call it EQ). The aim is to produce a particular sound, and to this end mixer EQ is much more sophisticated than that found on most hi-fi preamplifiers. There will be middle controls as well as bass and treble (which in the mixing world are more often called LF and HF) and these introduce a peak or dip into the middle range of the audio band. On more complex consoles the middle frequencies are infinitely variable, and the most advanced examples have variable Q as well, to control the width of the peak or dip introduced. No one has so far suggested that mixing consoles should be built without EQ.

It is not necessary to litter these pages with equations to determine center frequencies and so on. In each case, altering the range of frequency controlled can be done very simply by scaling the capacitor values given. If a stage gives a peaking cut/boost at 1 kHz, but you want 2.5 kHz, then simply reduce the values of all the capacitors by a factor of 2.5 times.

Scaling the associated resistors instead would give the same frequency response, but may also affect noise performance, because if the resistor values are raised, Johnson noise will increase. Distortion will increase if reducing the resistor values places excessive loading on the op-amps used. Another consideration is that potentiometers come in a very limited number of values, usually multiples of 1, 2, and 5. Changing the capacitors is simpler and more likely to be trouble free.

Passive Tone Controls

For many years all tone controls were passive, simply providing frequency-selective attenuation. These came in a bewildering variety of forms; take a look at the chapter on ‘Tone compensation and tone control’ in the famous Radio Designer’s Handbook [1]. This is 42 pages long with 90 references. The final edition was published in 1953, and interestingly does not include the Baxandall configuration. Some of the circuits are incredibly complex, requiring multi-section switches and tapped inductors to give quite limited tone-control possibilities. Figure 10.1 shows one of the simpler arrangements [2], which is probably the best-known passive tone control configuration. It was described by Sterling [3], though I have no idea if he originally invented it.

Figure 10.1: A pre-Baxandall passive tone control, with severe limitations

The arrangement gives about ±18 dB of treble and bass boost and cut, the curves looking something like those of a Baxandall control but with less symmetry.

Such circuitry has several disadvantages. When set to flat it gives a loss in each network of 20.8 dB, which means a serious compromise in either noise (if the make-up gain is after the tone-control network) or headroom (if the make-up gain is before the tone-control network). In the days of valves, when these networks were popular, headroom may have been less of a problem, but given the generally poor linearity of valve circuitry, the increased level probably gave rise to significantly more distortion.

Another problem is that if linear pots are used the flat position corresponds to one-tenth of the rotation. It is therefore necessary to use log pots to get the flat setting to somewhere near the center of control travel, and their large tolerances in law and value mean that the flat position is actually rather variable, and is unlikely to be the same for the two channels of stereo.

This circuit counts as a passive tone control because the valve in the middle of it is simply providing make-up gain for the treble network and is not in a frequency-dependent feedback loop. In the published circuit there was another identical valve stage immediately after the bass network to make up those losses. There are some other interesting points about this valve-based circuit: it runs at a much higher impedance than solid-state versions, using 2 MΩ pots rather than 10 kΩ, and it uses a single supply rail, and that is at an intimidating 300 V. Circuitry running at such high impedances is susceptible to capacitative hum pickup.

Baxandall Tone Controls

The Baxandall bass-and-treble tone control swept all other versions before it. The original Baxandall tone control, as famously published in Wireless World in 1952 [4], was in fact rather more complex than the simplified version which has become universal. The original circuit required a center-tapped treble pot to give minimum interaction between the two controls, but such specialized components are almost as unwelcome to manufacturers as they are to home constructors, and the form of the circuit that became popular is shown in Figure 10.2, some control interaction being regarded as acceptable. The advantages of this circuit are its simplicity and its feedback operation, the latter meaning that there are no awkward compromises between noise and headroom, as there are in the passive circuit above. It also gives symmetrical cut and boost curves and is easily controlled.

Figure 10.2: The one-capacitor Baxandall tone control

It is not commonly realized that the Baxandall tone control comes in two versions. Either one or two capacitors can be used to define the bass time-constants, and the two arrangements give rather different results at the bass end. The original Baxandall design was the two-capacitor version.

In the descriptions that follow, I have used the term ‘break frequency’ to indicate where the tone control begins to take action. This is defined as the frequency where the response is ±1 dB away from flat with maximum cut or boost applied.

The Baxandall Two-Capacitor LF Control

This is probably the most common form of the Baxandall tone control, simply because it saves a capacitor. The circuit is shown in Figure 10.2. At high frequencies the impedance of C1 is small and the bass control RV1 is effectively shorted out and R1, R2 give unity gain. At low frequencies RV1 is active and controls the gain, ultimately over a ±15 dB range at very low frequencies. R1, R2 are then end-stop resistors that set the maximum boost or cut.

At high frequencies again, C2 has a low impedance and treble control RV2 is active, with maximum boost or cut set by end-stop resistor R4; at low frequencies C2 has a high impedance and so RV2 has no effect. Resistor R3 is chosen to minimize interaction between the controls.

The one-capacitor version is distinguished by its fixed LF break frequency, as shown by the bass control response in Figure 10.3. The treble control response in Figure 10.4 is similar.

Figure 10.3: Bass control frequency responses. The effect of the LF control above the ‘hinge point’ at 1 kHz is very small

Figure 10.4: Treble control frequency responses

In these figures the control travel is in 11 equal steps of a linear pot (central plus five steps on each side). The bass curves are ±1.0 dB at 845 Hz, while the treble curves are ±1.0 dB at 294 kHz. This sort of overlap is normal with the Baxandall configuration. Phase spikes are shown at input and output to underline that this stage phase-inverts, which can be inconvenient; phase spikes will be seen in most of the diagrams that follow in this chapter.

An HF-stabilizing capacitor C3 is shown connected around A1. This is often required to ensure HF stability at all control settings, depending on how much stray capacitance to introduce extra phase-shifts there is in the physical layout. The value required is best determined by experiment. This capacitor is not shown in most of the diagrams that follow, to keep them as uncluttered as possible, but the likely need for it should not be forgotten.

It is important to remember that the input impedance of this circuit varies both with frequency and control settings, and it can fall to rather low values.

Taking the circuit values shown in Figure 10.2, the input impedance varies with frequency as shown in Figure 10.5, for treble (HF) control settings, and as in Figure 10.6 for bass (LF) control settings. With both controls central the input impedance below 100 Hz is 2.9 kΩ. At low frequencies C1, C2 have no effect and the input impedance is therefore half the LF pot resistance plus the 1k8 end-stop resistor, adding up to 6.8 kΩ. In parallel is 5 kΩ, half the impedance of the HF pot, as although this has no direct connection to the summing point (C2 being effectively open circuit), its other end is connected to the output, which is the input inverted. Hence the center of the pot is approximately at virtual earth. The parallel combination of 6.8 and 5 kΩ is 2.9 kΩ.

Figure 10.5: Input impedance variation with frequency, for 11 treble control settings

Figure 10.6: Input impedance variation with frequency, for 11 bass control settings

At frequencies above 100 Hz (still with both controls central) the input impedance falls because C1 is now low impedance, and the LF pot is shorted out. The input impedance is now 1.8 kΩ in parallel with 5 kΩ, which is 1.3 kΩ. This is already about as much loading as you would want to put on a TL072, and we haven’t applied boost or cut yet.

When the HF control is moved from its central position, the HF impedance is higher at full cut at 2.2 kΩ. It is, however, much lower at 350 Ω at full boost. There are very few op-amps that can give full output into such a low impedance, but this is not quite as serious a problem as it first appears. The input impedances are only low when the circuit is boosting; therefore driving the input at the full rail capability is not relevant, for if you do the output will clip long before the stage driving it. Nonetheless, op-amps such as the 5532 will show increased distortion driving too heavy a load, even if the level is a long way below clipping, so it is a point to watch.

The input impedances can of course be raised by scaling the impedance of the whole circuit. For example, multiply all resistor values by 4, and quarter the capacitor values to keep the frequency response the same. The downside to this is that you have doubled the Johnson noise from the resistors, and so made the stage noisier.

When the LF control is moved from its central position, the input impedance variations are similar, as shown in Figure 10.6. At full cut the input impedance is increased to 5.0 kΩ; at full boost it falls to 770 Ω. This variation begins below 1 kHz, but is only fully established below 100 Hz.

The Baxandall Two-Capacitor Tone Control

The two-capacitor version of the Baxandall tone control is shown in Figure 10.7, and while it looks very similar there is a big difference in the LF end response curves, as seen in Figure 10.8. The LF break frequency rises as the amount of cut or boost is increased. It is my view that this works much better in a hi-fi system, as it allows small amounts of bass boost to be used to correct loudspeaker deficiencies without affecting the whole of the bass region. In contrast, the one-capacitor version seems to be more popular in mixing consoles.

Figure 10.7: The two-capacitor Baxandall tone control

Figure 10.8: Bass control frequency responses for the two-capacitor circuit. Compare

Note that the treble control here has been configured slightly differently, and there are now two end-stop resistors, at each end of the pot, rather than one attached to the wiper; the frequency response is identical, and this variation is only shown to make that point. An extra resistor is required without any corresponding benefit.

The input impedance of this version shows variations similar to those of the one-capacitor version. With controls central, at LF the input impedance is 3.2 kΩ; from 100 Hz to 1 kHz it slowly falls to 1.4 kΩ. The changes with HF and LF control settings are similar to those of the one-capacitor version, and at HF the impedance falls to 370 Ω.

The Baxandall Two-Capacitor HF Control

The treble control can also be implemented with two capacitors, as in Figure 10.9.

Figure 10.9: Circuit of the two-HF-capacitor version

In this case the frequency response results are identical to those of the one-capacitor version, but there are interesting differences in the loading presented to the preceding stage. With controls central, at LF the input impedance is 6.8 kΩ, which is usefully higher; from 100 Hz to 1 kHz it slowly falls to the previous value of 1.4 kΩ.

When the LF control is varied, at full cut the input impedance is increased to 11.7 kΩ, and at full boost it falls to 1.9 kΩ (see Figure 10.10). On varying the HF control, at full cut the input impedance is increased to 2.3 kΩ; at full boost it falls to 420 Ω. These values are higher because with this configuration C3, C4 effectively disconnect the HF pot from the circuit at low frequencies. In some cases the higher input impedance may justify the cost of an extra capacitor.

Figure 10.10: Input impedance variation with frequency, for 11 bass control settings; two-HF-capacitor version

One disadvantage of the Baxandall tone control is that it inherently phase-inverts. This is decidedly awkward, because relatively recently the hi-fi world has decided that absolute phase is important; in the recording world keeping the phase correct has always been a rigid requirement.

An important point about all of the circuits shown so far is that they assume an FET-input op-amp (such as the TL072, or a more sophisticated FET part) will be used to minimize the bias currents flowing. Therefore all the pots and switches are directly connected to the op-amp without any explicit provision for preventing DC flowing through the pots. Excessive DC would make the pots scratchy and crackly when they are moved; this does not sound nice. It is, however, long established that typical FET bias currents are low enough to prevent such effects in circuits like these. Substituting a bipolar op-amp such as the 5532 will improve the noise and distortion performance markedly, at the expense of the need to make provision for the much greater bias currents by adding DC-blocking capacitors.

Switched-Frequency Baxandall Controls

While the Baxandall approach gives about as much flexibility as one could hope for from two controls, there is often a need for more. The most obvious elaboration is to make the break frequencies variable.

This is straightforward if a small number of switched break frequencies meets the case.

The frequency response of the Baxandall configuration is set by its RC time-constants, and one obvious way to make a variable-frequency version is to make the capacitors switchable. Changing the R part of the RC is far less practical as it would require changing the potentiometer values as well. Figure 10.11 shows a typical tone control with three switched treble frequencies, as used in a preamplifier design I did in 1976 [5]. The break frequencies are 1, 3, and 5 kHz. I found break frequencies higher than that to be a bit too subtle. Note that the circuit impedances are much higher than I would use nowadays.

Figure 10.11: A Baxandall tone control with three switched treble turnover frequencies

A parameter switchable in steps is inconvenient, compared with having it infinitely variable. Also, multi-way switches are more expensive than variable resistors, and so there is a strong incentive to make the operating frequencies variable without switches and banks of capacitors. To do this requires a different configuration, as described in the next section.

Variable-Frequency LF and HF EQs

Since we are now moving more into the world of mixing consoles rather than preamplifiers, I shall stop using ‘bass’ and ‘treble’ and switch to ‘LF’ and ‘HF’, which of course means the same thing. The circuit shown in Figure 10.12 gives HF equalization only, but with a continuously variable break frequency, and is used in many mixer designs. It is similar to the Baxandall concept in that it uses op-amp A1 in a shunt-feedback mode so that it can provide either cut or boost, but the resemblance ends there.

Figure 10.12: A variable-frequency HF shelving circuit. The break frequency range is 1−15 kHz

R1 and R2 set the basic gain of the circuit to –1, and ensure that there is feedback at DC to establish the operating conditions; there is no DC feedback path to the non-inverting input of A1. When the wiper of RV1 is at the input end, extra input signal is fed forward and gain increases. When the wiper of RV1 is at the output end, more output is fed back, the total amount of NFB increases, and gain is reduced.

The signal tapped off is scaled by divider R3, R4, which set the maximum cut/boost. The signal is then buffered by voltage-follower A2, and fed to the frequency-sensitive part of the circuit, a high-pass RC network made up of C1 and (R5 + RV2). The frequency-setting control RV2 has a relatively high value at 100 kΩ. This is because the range of variation is usually at least 10:1, and a lower value would give excessive loading on A2 at the high-frequency end.

A2 prevents interaction between the amount of cut/boost and the break frequency. Without it cut/boost would be less at high frequencies because R5 would load the divider R1, R2. In cheaper products this interaction may be acceptable, and A2 could be omitted. In EQ circuitry it is the general rule that the price of complete freedom from control interaction is more op-amps. The frequency range can be scaled simply by altering the value of C1, as shown in Figure 10.13. The range of frequency variation is controlled by the value of end-stop resistor R5, subject to restrictions on loading A2 if distortion is to be kept low. The corresponding LF EQ is made by swapping the positions of C1 and R5, RV2 in Figure 10.12.

Figure 10.13: The response of the shelving circuit with C1 increased to 100 nF. Maximum cut/ boost is slightly greater than ±15 dB

The component values given are the E24 values that give the closest approach to ±15 dB cut/boost at the control extremes. When TL072 op-amps are used this circuit is stable as shown, assuming the usual supply-rail decoupling. If other types are used a small capacitor (say 33 pF) across R2 may be required.

In Chapter 11 a tone control with variable HF and LF frequencies is examined as part of a complete preamplifier design. 5532 op-amps are used and the resulting need for DC-blocking capacitors is looked at in detail.

Tone-Balance Controls

A tone-balance or tilt circuit is operated by a single control, and affects not just part of the audio spectrum, but most or all of it. Typically the high frequencies are boosted as the low frequencies are cut, and vice versa. It has to be said that the name is unfortunate as it implies it has something to do with interchannel amplitude balance, which it has not. A ‘stereo tone-balance control’ alters the frequency response of both channels equally and does not introduce amplitude differences between them, whereas a ‘stereo balance control’ is something quite different. It is clearer to call a tone-balance control a tilt control.

Tone-balance controls are (or were) supposedly useful in correcting the overall tonal balance of recordings in a smoother way than a Baxandall configuration, which concentrates on the ends of the audio spectrum. An excellent (and very clever) approach to this was published by Ambler in 1970 [6] (see Figure 10.14). The configuration is very similar to the Baxandall’s – the ingenious difference here is that the boost/cut pot effectively swaps its ends over as the frequency goes up. At low frequencies C1, C2 do nothing, and the gain is set by the pot, with maximum cut and boost set by R1, R2. At high frequencies, where the capacitors are effectively short-circuit, R3, R4 overpower R1, R2 and the control works in reverse. The range available with the circuit shown is ±8 dB at LF and ±6.5 dB at HF. This may seem ungenerous, but because of the way the control works, 8 dB of boost in the bass is accompanied by 6.5 dB of cut in the treble, and a total change of 14.5 dB in the relative level of the two parts of the spectrum should be enough for anyone. The measured frequency response at the control limits is shown in Figure 10.15; the response is not quite flat with the control central due to component tolerances.

Figure 10.14: Tone-balance control of the Ambler type

Figure 10.15: Frequency response of tone-balance control

The need for one set of end-stop resistors to take over from the other puts limits on the cut/boost that can be obtained without the input impedance becoming too low; there is of course also the equivalent need to consider the impedance the op-amp sees when driving the feedback side of the network.

The input impedance at LF, with the control set to flat, is approximately 12 kΩ, which is the sum of R3 and half of the pot resistance. At HF, however, the impedance falls to 2.0 kΩ. Please note that this is not a reflection of the values of the HF end-stop resistors R3, R4, but just a coincidence. When the control is set to full treble boost, the input impedance at HF falls as low as 620 Ω. The impedance at LF holds up rather better at full bass boost, as it cannot fall below the value of R1, i.e. 6.8 kΩ.

The impedances of the circuit shown here have been reduced by a factor of 10 from the original values published by Ambler, to make them more suitable for use with op-amps. The original (1970) gain element was a two-transistor inverting amplifier with limited linearity and load-driving capability. Here a stabilizing capacitor C3 is shown explicitly, just to remind you that you might need one.

A famous example of the use of a tilt control is the Quad 44 preamplifier. The tilt facility is combined with a bass cut/boost control in one quite complicated stage, and it is not at all obvious if the design is based on the Ambler concept. Tilt controls have never really caught on and remain rare.

Middle Controls

A middle control affects the center of the audio band rather than the bass and treble extremes. It must be said at once that middle controls, while useful in mixers, are of very little value in a preamplifier. If the middle frequency is fixed, then the chances that this frequency and its associated Q correspond with room shortcomings or loudspeaker problems are remote in the extreme. Occasionally middle controls appeared on preamps in the 1970s, but only rarely and without much evidence of success in the marketplace. One example is the Metrosound ST60 (1972), which combined a three-band Baxandall tone control (more on this below) with slider controls in one package. The middle control had a very wide bandwidth centered on 1 kHz, and it was suggested that it could be used to depress the whole middle of the audio band to give the effect of a loudness control.

Middle controls come into their own in mixers and other sound-control equipment, where they are found in widely varying degrees of sophistication. In recording applications middle controls play a vital part in ‘voicing’ or adjusting the timbres of particular instruments, and the flexibility of the equalizer, and its number of controls defines the possibilities open to the operator.

The obvious first step is to add a fixed middle control to the standard HF and LF controls. Unfortunately, this is not much more useful in a mixer than in a preamplifier. In the past this was addressed by adding more fixed middles, so a line-up with a high middle and a low middle would be HF–HMF–LMF–LF, but this takes up more front panel space (which is a very precious resource in advanced and complex mixers, and ultimately defined by the length of the human arm) without greatly improving the EQ versatility.

The minimum facilities in a mixer input channel for proper control are the usual HF and LF controls plus a sweep middle with a useful range of center frequency. This also requires four knobs but is much more useful.

Fixed-Frequency Baxandall Middle Controls

Figure 10.16 shows a middle version of a Baxandall configuration. The single control RV1 now has around it both the time-constants that were before assigned to the separate bass and treble controls. R4 and R5 maintain unity gain at DC, and keep the stage biased correctly.

Figure 10.16: Fixed middle control of the Baxandall type. Center frequency 1.26 kHz

As the input frequency increases from the bottom of the audio band, the impedance of C2 falls and the position of the pot wiper begins to take effect. At a higher frequency, the impedance of C1 becomes low enough to effectively tie the two ends of the pot together, so that the wiper position no longer has effect, and the circuit reverts to having a fixed gain of unity. The component values shown give a mid frequency of 1.26 kHz, at a Q of 0.8, with a maximum boost/cut of ±15 dB. The Q value is only valid at maximum boost/cut; with less the curve is flatter and the effective Q lower. It is not possible to obtain high values of Q with this approach.

This circuit gives the pleasingly symmetrical curves shown in Figure 10.17, though it has to be said that the benefits of exact symmetry are visual rather than audible.

Figure 10.17: The frequency response of the Baxandall middle control in

As mentioned above, in the simpler mixer input channels it is not uncommon to have two fixed mid controls; this is not the ideal arrangement, but it can be implemented very neatly and cheaply, as in Figure 10.18. There are two stages, each of which has two fixed bands of EQ. It has the great advantage that there are two inverting stages so the output signal ends up back in phase. The first stage needs the extra resistors R5, R6 to maintain DC feedback.

Figure 10.18: A four-band Baxandall EQ using two stages only

There will inevitably be some control interaction with this scheme. It could be avoided by using four separate stages, but this is most unlikely to be economical for mixers with this relatively simple sort of EQ. To minimize interaction, the control bands are allocated between the stages to keep the frequencies controlled in a stage as far apart as possible, combining HF with LO MID, and LF with HI MID, as shown here.

Three-Band Baxandall EQ in One Stage

The standard Baxandall tone control allows adjustment of two bands with one stage. When a three-band EQ is required, it is common practice to use one such stage for HF and LF, and a following one to implement the middle control, as in Figure 10.16. This has the advantage that the two cascaded inverting stages will leave the signal in the correct phase.

When this is not a benefit, because a phase inversion is present at some other point in the signal path, it is economical to combine HF, MID, and LF in one quasi-Baxandall stage. This not only reduces component count, but reduces power consumption by saving an op-amp.

The drawback is that cramming all this functionality into one stage requires some compromises on control interaction and maximum boost/cut. The circuit shown in Figure 10.19 gives boost/cut limited to ±12 dB in each band.

Figure 10.19: The circuit of a Baxandall three-band EQ using one stage only

The frequency responses for each band are given in Figures 10.2010.22.

Figure 10.20: The frequency response of a Baxandall three-band EQ. Bass control

Figure 10.22: The frequency response of the Baxandall three-band EQ. Treble control

Wien Fixed Middle EQ

An alternative way to implement a fixed middle control is shown in Figure 10.23. Here the signal tapped off from RV1 is fed to a Wien bandpass network R1, C1, R2, C2, and returned to the op-amp non-inverting input. This is the same Wien network as used in audio oscillators.

Figure 10.23: The Wien fixed-middle circuit. Center frequency is 2.26 kHz. The Q at max cut/boost is 1.4

With the values shown the center frequency is 2.26 kHz and the Q at max cut/boost is 1.4; it gives beautifully symmetrical response curves like those in Figure 10.17, with a maximal cut/ boost of 15.5 dB.

Sweep Middles

A fully variable-frequency middle control is much more useful and versatile than any combination of fixed or switch middles. In professional audio this is usually called a ‘sweep middle’ EQ. It can be implemented very nicely by putting variable resistances in the Wien network of the stage previously described, and the resulting circuit is shown in Figure 10.24.

Figure 10.24: A Wien sweep circuit. The center frequency range is 150 Hz – 2.4 kHz (a 16:1 ratio)

The variable load that the Wien network puts on the cut/boost pot RV1 causes a small amount of control interaction, which is normally considered acceptable. It could be eliminated by putting a unity-gain buffer stage between the RV1 wiper and the Wien network, but in the middle-range mixers where this circuit is commonly used, this is not normally economical.

The Wien network is carefully arranged so that the two variable resistors RV2, RV3 can have common terminals, reducing the number required from six to three. This is sometimes taken advantage of by pot manufacturers making ganged parts specifically for this EQ application. R1, C1 are sometimes seen swapped in position but this naturally makes no difference.

The combination of a 100k pot and a 6k8 end-stop resistor gives a theoretical ratio of 15.7:1, which is about as much as can be obtained using reverse-log law C pots, without excessive cramping at the high-frequency end of the scale. This will be marked on the control calibrations as a 16:1 range.

The measured frequency responses at the control limits are shown in Figure 10.25. The frequency range is from 150 Hz to 2.3 kHz; the ratio is slightly adrift due to component tolerances.

Figure 10.25: The measured response of the sweep middle circuit at control extremes. The cut/boost is slightly short of ±15 dB

The Single-Gang Sweep Middle

The usual type of sweep middle requires a dual-gang reverse-log pot to set the frequency. These are not hard to obtain in production quantities, but can be difficult to get in small numbers. They are always significantly more expensive than a single pot.

The problem becomes more difficult when the design requires a stereo sweep middle – if implemented in the usual way, this demands a four-gang reverse-log pot. Once again, such components are available, but only to special order, which means long lead-times and significant minimum order quantities. Four-gang pots are not possible in flat-format mixer construction where the pots are mounted on their backs, so to speak, on a single big horizontal PCB. The incentive to use a standard component is strong, and if a single-gang sweep middle circuit can be devised, a stereo EQ only requires a dual-gang pot.

This is why many people have tried to design single-gang sweep middle circuits, with varying degrees of success. It can be done, so long as you don’t mind some variation of Q with center frequency; the big problem is to minimize this interaction. I too have attacked this problem, and here is my best shot so far, in Figure 10.26.

Figure 10.26: My single-gang sweep middle circuit. The center frequency range is 100 Hz – 1 kHz

This circuit is a variation of the Wien middle EQ, the quasi-Wien network being tuned by a single control RV2, which not only varies the total resistance of the R5, R7 arm, but also the amount of bootstrapping applied to C2, effectively altering its value. This time a unity-gain buffer stage A2 has been inserted between the RV1 wiper and the Wien network; this helps to minimize variation of Q with frequency.

The response is shown in Figure 10.27; note that the frequency range has been restricted to 10:1 to minimize Q variation. The graph shows only maximum cut/boost; at intermediate settings the Q variations are much less obvious.

Figure 10.27: The response of the single-gang sweep middle circuit of . Boost/cut is ±15 dB, and the frequency range is 100 Hz – 1 kHz The Q varies somewhat with center frequency

It is possible to make a more economical version of this, if one accepts somewhat greater interaction between boost/cut, and Q and frequency. The version shown in Figure 10.28 omits the unity-gain buffer and uses unequal capacitor values to raise the Q of the quasi-Wien network, saving an op-amp section. The frequency range is still 10:1.

Figure 10.28: My economical single-gang sweep middle circuit. The center frequency range has been changed to 220 Hz – 2.2 kHz

The response in Figure 10.29 shows the drawback – a higher Q at the center of the frequency range. Once again the Q variations will be much less obvious at intermediate cut/boost settings.

Figure 10.29: The response of the economical single-gang sweep middle circuit of . The response is ±15 dB as before, but the frequency range has now been set to 220 Hz – 2 kHz. Only the boost curves are shown

The question naturally arises as to whether it is possible to design a single-gang sweep middle circuit where there is absolutely no variation of Q with frequency. Is there an ‘existence theorem’, i.e. a mathematical proof that it can’t be done? At the present time, I just don’t know.

Switched-Q Variable-Frequency Wien Middle EQs

The next step in increasing EQ sophistication is to provide control over the Q of the middle resonance. This is often accomplished by using a full state-variable filter solution, which gives fully variable Q that does not interact with the other control settings, but if two or more switched values of Q are sufficient, there are much simpler circuits available.

One of them is shown in Figure 10.30; here the Wien bandpass network is implemented around A2, which is essentially a shunt-feedback stage, with added positive feedback via R1, R2 to raise the Q of the resonance. When the Q switch is in the LO position, the output from A2 is fed directly back to the non-inverting input of A1, because R7 is short-circuited. When the Q switch is in the HI position, R9 is switched into circuit and increases the positive feedback to A2, raising the Q of the resonance. This also increases the gain at the center frequency, and this is compensated for by the attenuation now introduced by R7 and R8.

Figure 10.30: Variable-frequency switched-Q middle control of the Wien type

With the values shown the two Q values are 0.5 and 1.5. Note the cunning way that the Q switch is made to do two jobs at once – changing the Q and also introducing the compensating attenuation. If the other half of a two-pole switch is already dedicated to an LED indicator, this saves having to go to a four-pole switch. On a large mixing console with many EQ sections this sort of economy is important.

Switchable Peak/Shelving LF/HF EQs

It is frequently desirable to have the highest and lowest frequency EQ sections switchable between a peaking (resonance) mode and shelving operation. The peaking mode allows relatively large amounts of boost to be applied near the edges of the audio band without having a large and undesirable amount occurring outside it.

Figure 10.31 shows one way of accomplishing this. It is essentially a switchable combination of the variable-frequency HF shelving circuit of Figure 10.12 and the sweep middle circuit of Figure 10.24; when the switches are in the PEAK position the signal tapped off RV1 is fed via the buffer A2 to a Wien bandpass network C2, RV2, R5, C3, R6, RV3, and the circuit has a peak/dip characteristic. When the switches are in the SHLV (shelving) position, the first half of the Wien network is disconnected and C1 is switched in, and in conjunction with R6 and RV3 forms a first-order high-pass network, fed by an attenuated signal because R2 is now grounded. This switched attenuation factor is required to give equal amounts of cut/boost in the two modes because the high-pass network has less loss than the Wien network. R7 allows fine-tuning of the maximum cut/boost; reducing it increases the range.

Figure 10.31: Variable-frequency peak/shelving HF EQ circuit

As always we want our switches to work as hard as possible, and the lower switch can be seen to vary the attenuation brought about by R1, R2 with one contact and switch in C3 with the other. Unfortunately, in this case two poles of switching are required. The response of the circuit at one frequency setting can be seen in Figure 10.32.

Figure 10.32: The response of the variable-frequency peak/shelving with R7 = 220k; the cut/ boost range is thus set to ±15 dB

When the peaking is near the edges of the audio band, this is sometimes called return-to-zero (RTZ) operation as the gain returns to unity (0 dB) outside the band.

Parametric Middle EQs

A normal second-order resonance is completely defined by specifying its center frequency, its bandwidth or Q, and the gain at the peak. In mathematical language, these are the parameters of the resonance. Hence an equalizer that allows all three to be changed independently (proviso on that coming up soon) is called a parametric equalizer. Upscale mixing consoles typically have two fully parametric middle sections, and usually the LF and HF can also be switched from shelving to peaking mode, when they become two more fully parametric sections.

The parametric middle EQ shown in Figure 10.33 is included partly for its historical interest, showing how op-amps and discrete transistor circuitry were combined in the days before completely acceptable op-amps became affordable. I designed it in 1979 for a now long-gone company called Progressive Electronics, which worked in a niche market for low-noise mixing consoles. The circuitry I developed was a quite subtle mix of discrete transistor and op-amp circuitry, which gave a significantly better noise performance than designs based entirely on the less-than-perfect op-amps of the day; in time, of course, this niche disappeared. This parametric middle EQ was used, in conjunction with the usual HF and LF controls, in a channel module called the CM4.

Figure 10.33: An historical parametric middle EQ dating back to 1979

The boost/cut section used an op-amp because of the need for both inverting and non-inverting inputs. I used a 741S, which was a completely different animal from the humble 741, with a much better distortion performance and slew rate; it was, however, markedly more expensive, and only used where its superior performance was really necessary. The unity-gain buffer Q1, Q2 that ensured a low-impedance drive to the state-variable bandpass filter was a discrete circuit block, as its function is simple to implement. Q1 and Q2 form a CFP emitter-follower. R13 was a ‘base-stopper’ resistor to make sure that the Q1, Q2 local feedback loop did not exhibit VHF parasitic oscillation. With the wisdom of hindsight, putting a 2k2 resistor directly in the signal path can only degrade the noise performance, and if I was doing it again I would try to solve the problem in a more elegant fashion. The high input impedance of the buffer stage (set by R14) means that C6 can be a small non-electrolytic component.

The wholly conventional state-variable bandpass filter requires a differential stage U2, which once again is best implemented with an op-amp, and another expensive 741S was pressed into service. The two integrators U3, U4 presented an interesting problem. Since only an inverting input is required, discrete amplifiers could have been used without excessive circuit complexity; a two-or possibly three-transistor circuit (see Chapter 3) would have been adequate. However, the PCB area for this approach just wasn’t there, and so op-amps had to be used. To put in two more 741S op-amps would have been too costly, and so it pretty much had to be a couple of the much-despised 741 op-amps. In fact, they worked entirely satisfactorily, because they were in integrator stages. The poor HF distortion and slew rate were not really an issue because of the large amount of NFB at HF, and the fact that integrator outputs by definition do not slew quickly. The indifferent noise performance was also not an issue because the falling frequency response of the integrators filtered out most of the noise. In my designs the common-or-garden 741 was only used in this particular application. Looking at the circuit again, I have reservations about the not inconsiderable 741 bias currents flowing through the two sections of the frequency-control pot RV2, which could make them noisy, but it seemed to work alright at the time.

The filter Q was set by the resistance of R6, R7 to ground. It does not interact with filter gain or center frequency. The Q control could easily have been made fully variable by using a potentiometer here, but there was only room on the channel front panel for a small toggle switch. Note the necessity for the DC-blocking capacitor C3, because all the circuitry is biased at V/2 above ground.

The filtered signal is fed back to the boost/cut section through R17, and I have to say that at this distance of time I am unsure why that resistor was present. It could only impair the noise performance. Grounding it would give an EQ-cancel that would also stop noise from the state variable filter.

It is worth noting that the design dates back to when the use of single supply rails was customary. In part this was due to grave and widely held doubts about the reliability of electrolytic coupling capacitors with no DC voltage across them, which would be the case if dual rails were used. As it happened, there proved to be no real problem with this, and things would have progressed much faster if capacitor manufacturers had not been so very wary of committing themselves to approving non-polarized operation. The use of a single supply rail naturally requires that the circuitry is biased to V/2, and this voltage was generated in the design shown by R15, R16, and C5; it was then distributed to wherever it was required in the channel signal path. The single rail was at +24 V, because 24 V IC regulators were the highest voltage versions available, and nobody wants to get involved with designing discrete power supply regulators if they can avoid it. This is obviously equivalent to a ±12 V dual rail supply, compared with the ±15 or ±17 V that was adopted when dual-rail powering became universal, and so gave a headroom that was lower by 1.9 and 3.0 dB respectively.

This design is included here because it is a good example of making use of diverse circuit techniques to obtain the best possible performance/cost ratio at a given point in time. It could be brought up to date quite quickly by replacing all the antique op-amps and the discrete unity-gain buffer with 5532s or other modern types.

Modern parametric equalizers naturally use all op-amp circuitry. Figure 10.34 shows a parametric EQ stage I designed back in 1991; it is relatively conventional, with a three-stage state-variable filter composed of A2, A3, and A4. There is, however, one improvement on the standard circuit topology. Most of the noise in a parametric equalizer comes from the filter path. In this version the filter path signal level is set to be 6 dB higher than usual, with the desired return level being restored by the attenuator R6, R7. This attenuates the filter noise as well, and the result is a parametric section approximately 6 dB quieter than the industry standard. The circuit is configured so that, despite this raised level, clipping cannot occur in the filter with any combination of control settings. If excess boost is applied, clipping can only happen at the output of A1, as usual.

Figure 10.34: Variable-frequency variable-Q middle control. State-variable type

Other features are the Q control RV4, which is configured to give a wide parameter range without affecting the gain. Note the relatively low values for the DC feedback resistors R1 and R2, chosen to minimize Johnson noise without causing excessive op-amp loading.

This equalizer section has component values for typical low-mid use, with center frequency variable over a wide range from 70 Hz to 1.2 kHz, and Q variable from 0.7 to 5. The cut and boost range is the usual ±15 dB.

Graphic Equalizers

Graphic equalizers are so called because their cut/boost controls are vertical sliders, the assumption being that a graph of the frequency response will pass through the slider knob positions. Graphic equalizers can have any number of bands from three to 31, the latter having bands one-third of an octave wide. This is the most popular choice for serious room equalization work as bands one-third-octave wide relate to the perceptual critical bands of human hearing.

Graphic equalizers are not normally fitted to large mixing consoles, but are often found on smaller powered mixers, usually in the path between the stereo mix and the power amplifiers. The number of bands provided is limited by the space on the mixer control surface, and is usually in the range of seven to 10.

There is more than one way to make a graphic equalizer, but the most common version is shown in its basic concept in Figure 10.35, with some typical values. L1, C1, and R3 make up an LCR series resonant circuit that 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 simply that of R3. At resonance, when the wiper of RV1 is at the R1 end, 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 created. When the RV1 wiper is at the R2 end, an attenuator is formed with R2 that reduces the feedback factor at resonance and so creates a peak in the response. It is not exactly intuitively obvious, but this process does give symmetrical cut/boost curves. At frequencies away from resonance the impedance of the LRC circuit is high and the gain of the circuit is unity.

Figure 10.35: The basic idea behind graphic equalizers; gain is unity with the wiper central

The beauty of this arrangement is that two, or three or more LRC circuits, with associated cut/ boost pots, can be connected between the two op-amp inputs, giving us an equalizer with pretty much as many bands as we want. Obviously, the more bands we have, the narrower they must be to fit together properly.

As described in Chapter 2, inductors are in general thoroughly unwelcome in a modern design, and the great breakthrough in graphic equalizers came when the LRC circuits were replaced by gyrator circuits that emulated them but used only resistors, capacitors, and a gain element. It is not too clear just when this idea spread, but I can testify that by 1975 gyrators were the standard approach, and the use of inductors would have been thought risible.

The basic notion is shown in Figure 10.36; C1 works as a normal capacitor as in the LCR circuit, while C2 pretends to be the inductor L1. As the applied frequency rises, the attenuation of the high-pass network C2–R1 reduces, so that a greater signal is applied to unity-gain buffer A1 and it more effectively bootstraps the point X, making the impedance from it to ground increase. Therefore we have a circuit fragment 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.

Figure 10.36: Using a gyrator to synthesize a grounded inductor in series with a resistance

The sample values in Figure 10.36 synthesize a grounded inductor of 100 mH (which would be quite a hefty component if it was real) in series with a resistance of 2 kΩ. Note the surprisingly simple equation for the inductor value. Another important point is that the op-amp is used as a unity-gain buffer, which means that the early gyrator graphic equalizers could use a simple emitter-follower in this role. The linearity was naturally not so good, but it worked and made graphic equalizers affordable.

A simple seven-band gyrator-based graphic equalizer is shown in Figure 10.37. The maximal cut/boost is ±8 dB. The band center frequencies are 63, 160 and 410 Hz, and 1, 2.5, 7.7 and 16 kHz. The Q of each band at maximum cut or boost is 0.9.

Figure 10.37: A seven-band graphic equalizer

The response of each band is similar to that shown in Figure 10.21. The maximum Q value is only obtained at maximum cut or boost. For all intermediate settings the Q is lower. This behavior is typical of the straightforward equalizer design shown here, and is usually referred to as ‘proportional-Q’ operation, and results in a frequency response that is very different from what might be expected on looking at the slider positions.

Figure 10.21: The frequency response of a Baxandall three-band EQ. Mid control

There is, however, another mode of operation called ‘constant-Q’ in which the Q of each band does not decrease as the cut/boost is reduced [7]. This gives a frequency response that more closely resembles the slider positions.

The graphic equalizer described here has a symmetrical response, also known as a reciprocal response; the curves are the same for cut and for boost operations. It is also possible to design an equalizer for an asymmetric or non-reciprocal response, in which the boost curves are as shown above, but the cut response is a narrow notch. This is often considered to be more effective when the equalizer is being used to combat feedback in a sound reinforcement system.

References

[1]  F. Langford-Smith (Ed.), The Radio Designer’s Handbook, fourth ed. Newnes, 1953, pp. 635–677. reprinted 1999, Chapter 15.

[2]  F. Langford-Smith (Ed.), The Radio Designer’s Handbook, fourth ed. Newnes, 1953, p. 668. reprinted 1999, Chapter 15.

[3]  H.T. Sterling, Flexible dual control system, Audio Engineering (February 1949).

[4]  P. Baxandall, Negative-feedback tone control, Wireless World (October 1952) p. 402.

[5]  D. Self, Self On Audio, second ed. Newnes, 2006, p. 5.

[6]  R. Ambler, Tone-balance control, Wireless World (March 1970) p. 124.

[7]  D.A. Bohn, Constant-Q graphic equalizers, JAES (September 1986) p. 611.

Small Signal Audio Design; ISBN: 9780240521770

Copyright © 2010 Elsevier Ltd; All rights of reproduction, in any form, reserved.

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