Chapter 15 Tone Controls and Equalisers – Small Signal Audio Design, 3rd Edition

CHAPTER 15

Tone Controls and Equalisers

Introduction

Facilities that alter the shape of the frequency response are called tone controls when they are incorporated in hi-fi systems, and equalisation (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. Even if you managed to do it, it would still be inaudible except possibly on artificial test signals such as isolated clicks. This is well known; most loudspeaker crossovers have an all-pass phase response, and this is considered entirely acceptable. A tone control set to flat really is 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 sub-optimal 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 equalisation 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 centre 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 is a bit more complex; if you reduce the resistors too much, distortion will increase due to excessive loading on the opamps used. If you increase the resistors, this may degrade the noise performance, as Johnson noise and the effects of current noise will increase. Another consideration is that potentiometers come in a very limited number of values, either multiples of 1, 2, and 5, or multiples of 1, 2.2, and 4.7.(The E3 series) Changing the capacitors is simpler and much more likely to be trouble free.

Passive Tone Controls

For many years, all tone controls were passive, simply providing frequency-selective attenuation. The famous Radio Designer’s Handbook [1] shows that they came in a bewildering variety of forms; take a look at the chapter on “Tone compensation and tone control”, which is 42 pages long with 90 references but does not include the Baxandall tone control; that is hidden away in an appendix at the back of the book. (The final edition was published in 1953, but modern reprints are available.) Some of the circuits are incredibly complex, requiring multi-section switches and tapped inductors to give quite limited tone-control possibilities. Figure 15.1 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. 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.

Figure 15.1 A pre-Baxandall passive tone control, with severe limitations.

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 levels 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 centre 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 the losses therein. 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 at an intimidating +300 volts. Circuitry running at such high impedances is very susceptible to capacitive hum pickup. There will also be a lot of Johnson noise from the high-value resistors.

Baxandall Tone Controls

The Baxandall bass-and-treble tone control swept all other versions before it. The original design, famously published in Wireless World in 1952 [4], was in fact rather more complex than the simplified version, which has become universal. Naturally at that date, it used a valve as the active component. The original schematic is rarely if ever displayed, so there it is in Figure 15.2. THD was quoted as less than 0.1% at 4 Vrms out up to 5 kHz.

The 1952 circuit specified a centre-tapped treble pot to give minimum interaction between the two controls, but such specialised 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 15.3, 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. It also gives symmetrical cut and boost curves and is easily controlled.

It is not commonly realised that the Baxandall tone control comes in several 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 same applies to the treble control. The original Baxandall design used two capacitors for bass and one for treble.

In the descriptions that follow, I have used the term “break frequency” to indicate where the tone control begins to take action. I have defined this as the frequency where the response is +/-1 dB away from flat with maximum cut or boost applied.

The Baxandall One-LF-Capacitor Tone Control

This is probably the most common form of the Baxandall tone control used today, simply because it saves a capacitor or two. The circuit is shown in Figure 15.3. 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 +/-16 dB range at very low frequencies. R1, R2 are end stop resistors which set the maximum boost or cut.

Figure 15.2 The original Baxandall tone control of 1952. The series output resistor R7 is to give stability with capacitive loads.

Figure 15.3 The one-capacitor Baxandall tone control.

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 minimise interaction between the controls. The HF network can also be configured with two capacitors, with some advantages; more on that later.

The one-LF-capacitor version is distinguished by its fixed LF break frequency, as shown by the bass control response in Figure 15.4. The treble control response in Figure 15.5 is similar.

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 Hz. 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.

Figure 15.4 Bass control frequency responses. The effect of the LF control above the “hinge-point” at 1 kHz is very small.

Figure 15.5 Treble control frequency responses.

An HF stabilising capacitor C3 is shown connected around A1. This is sometimes required to ensure HF stability at all control settings, depending on how much stray capacitance there is in the physical layout to introduce extra phase shifts. 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 with both frequency and control settings, and it can fall to rather low values.

Taking the circuit values shown in Figure 15.3, the input impedance varies with frequency as shown in Figure 15.6, for treble (HF) control settings, and as Figure 15.7 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 centre of the pot is approximately at virtual earth. The parallel combination of 6.8 kΩ and 5 kΩ is 2.9 kΩ, and so this is the input impedance at LF.

Figure 15.6 Input impedance variation with frequency, for 11 treble 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 a significant loading on the previous stage, and we haven’t applied boost or cut yet.

When the HF control is moved from its central position, with the LF control central, 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 opamps that can give full output into such a low impedance, but this is not quite as serious a problem as it at 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, opamps 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 four, 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 quadrupled the effect of opamp current noise and so made the stage noisier.

Figure 15.7 Input impedance variation with frequency for 11 bass control settings.

When the LF control is moved from its central position, with the HF control central, the input impedance variations are similar, as shown in Figure 15.7. At full LF cut, the input impedance is increased to 5.0 kΩ; at full LF boost, it falls to 770 Ω at low frequencies. This variation begins below 1 kHz but is only fully established below 100 Hz.

The figure of 770 Ω requires some explanation. The incoming signal encounters a 1k8 resistor, in parallel with 5 kΩ, which represents half of the HF pot resistance if we assume that its wiper is at virtual earth. The value of this is 1.32 kΩ; so how in the name of reason can the input impedance fall as low as 770 Ω? The answer is that our assumption is wrong. The HF pot wiper is NOT at virtual earth; it has a signal on it only 7 dB less than at the output, and this is in phase with the output, in other words in anti-phase with the input. This causes “reverse bootstrapping” of the 5 kΩ resistance that is half of the HF pot and makes it appear lower in value than it is. A similar “reverse bootstrapping” effect occurs at the cold input of the standard differential amplifier balanced input stage; see Chapter 18.

At low frequencies, more of the input current is actually going into the HF section of the tone-control network than into the LF section. This highlights one of the few disadvantages of the Baxandall type of tone control –the input impedances are reduced by parts of the circuit that are not actually doing anything useful at the frequency of interest. Other versions of the tone-control network have a somewhat better behaviour in this respect, and this is examined further on in this chapter.

These input impedances also appear as loading on the output of the opamp in the tone-control stage, when the control settings are reversed. Thus at full LF boost, there is a 770 Ω load on the preceding stage, but at full LF cut, that 770 Ω loading is on the tone-control opamp.

The Baxandall Two-LF-Capacitor Tone Control

The two-capacitor version of the Baxandall tone control is shown in Figure 15.8, and while it looks very similar, there is a big difference in the LF end response curves, as seen in Figure 15.9. 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, where the emphasis is on creation rather than correction.

The other response difference is the increased amount of “overshoot” in the frequency response (nothing to do with overshoot in the time domain). Figure 15.9 shows how the use of LF boost causes a small amount of cut just above 1 kHz, and LF cut causes a similar boost. The amounts are small, and this is not normally considered to be a problem.

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, but the input impedance at HF is usefully increased.

Figure 15.8 The two-LF-capacitor Baxandall tone control.

The input impedance of this version shows variations similar to 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 the one-C version, and at HF, the impedance falls to 370 Ω.

Figure 15.9 Bass control frequency responses for the two-capacitor circuit. Compare Figure 15.4.

The Baxandall Two-HF-Capacitor Tone Control

The treble control can also be implemented with two capacitors, as in Figure 15.10.

The frequency responses are similar to those of the one-HF-capacitor version, but as for the LF control, some “overshoot” in the curves is introduced. There is a useful reduction in the loading presented to the preceding stage. With controls central, at LF, the input impedance is 6.8 kΩ, which is usefully higher than the 2.9 kΩ given by the 1-HF capacitor circuit; from 100 Hz to 1 kHz, it slowly falls to 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 15.11. 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, C2, C3 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. The capacitors will also be about six times larger to obtain the same ±1 dB HF break frequency as the one-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. The tone-control inversion can, however, be conveniently undone by a Baxandall active volume control, which also phase inverts (see Chapter 13). If a balanced input stage is used, then an unwanted phase inversion can be corrected simply by swapping over the hot and cold inputs.

Figure 15.10 Circuit of the two-HF-cap version.

Figure 15.11 Input impedance variation with frequency, for 11bass control settings; two-HF-capacitor version.

A very important point about all of the circuits shown so far is that they assume a FET-input opamp (such as the TL072 or a more sophisticated FET part) will be used to minimise the bias currents flowing. Therefore, all the pots are directly connected to the opamp without any explicit provision for preventing DC flowing through them. 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; however, there is still the matter of offset voltages to be considered. Substituting a bipolar opamp 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.

The Baxandall Tone Control: Impedance and Noise

A major theme in this book is the use of low-impedance design to reduce Johnson noise from resistors and the effects of opamp input current noise flowing in them. Let’s see how that works with the Baxandall tone control.

Figure 15.12 Equivalent Baxandall controls giving ±10 dB boost and cut, using 10 kΩ, 5 kΩ, 2 kΩ, and 1 kΩ pots.

The Baxandall controls in Figure 15.12 all give ±10 dB boost and cut and are equivalent apart from employing 10 kΩ, 5 kΩ, 2 kΩ, and 1 kΩ pots, with all other components scaled to keep the frequency responses the same. 1 kΩ is the lowest value in which dual-gang pots can be readily obtained.

Table 15.1 demonstrates that drastically reducing the impedance of the circuit by 10 times reduces the noise output by 7.0 dB (controls set flat). Using an LM4562 section instead of a 5532 section shows a similar progression but with somewhat lower noise levels. The improvement on going from 2 kΩ to 1 kΩ pots is small (though reliable), and you may question if it is worth pushing things as far as 1 kΩ, given that as we saw earlier, Baxandall controls can show surprisingly low input impedance when boosting, with corresponding heavy loads on the opamp driving the negative feedback path when cutting. The situation becomes proportionally worse when the impedances are scaled down, as we have just done. The design process here was driven by a desire to use 1 kΩ pots throughout in the very-low-noise Elektor Preamp 2012. [5]

In the 1 kΩ case, a 5532 is only able to drive 6.7 Vms (±17 V rails) into the negative feedback path before clipping occurs. Clearly we need to find some way of either reducing the loading or increasing the drive capability. In the previous section I described how the Baxandall configuration with two HF capacitors is easier to drive than the one-capacitor version. Figure 15.12d is shown converted to two-HF-capacitor operation in Figure 15.13. The 5532 now clips at 8.8 Vrms, which is much better, but the opamp is still overloaded and will not give a good distortion performance. Note that the two HF capacitors are both much larger than the single HF capacitor in Figure 15.12d and will be relatively expensive. On the upside, we get the side benefit of yet lower output noise –see the bottom row of Table 15.1.

Elsewhere in this book, I have described the great advantages of using multiple opamps in parallel to drive heavy loads. In this case, it is not at all clear how the inverting opamp A1 can be multiplied in parallel. My solution is to split the drive to the LF and HF control networks so that the LF section is driven by its own unity-gain buffer A2; see Figure 15.14. It is the LF section that is driven by the buffer, so that the HF section can be fed directly from A1 and will not suffer phase shift in A2 that might imperil stability. The output now clips at a healthy 10.8 Vrms, and THD is reduced to the low levels expected.

This scheme is, to the best of my knowledge, novel; it was used for the first time in the Elektor 2012 preamplifier (using LM4562s) with great success. [5] I call it a split-drive Baxandall stage.

Table 15.1 Noise output versus impedance level using 5532 opamp
Pot value HF capacitor configuration Noise output
10 kΩ 1–C –105.6 dBu
5 kΩ 1–C –108.9 dBu
2 kΩ 1–C –112.2 dBu
1 kΩ 1–C –112.6 dBu
1 kΩ 2–C –113.1 dBu

Figure 15.13 Baxandall control with 1 kΩ pots, converted to 2-HF-capacitor configuration to reduce loading.

Figure 15.14 Split-drive Baxandall control fed by two parallel opamps and with separate feedback drive to the LF and HF control networks.

The input side of the control also needs at least two opamps to drive it with low distortion. The arrangement here was also used in the Elektor preamp; it makes no assumptions about what A3 is up to (it was part of a balanced line input in the preamp) but simply uses A4 as a buffer to give separate drive to the input of the LF control network.

Combining a Baxandall Stage With an Active Balance Control

In 1983, I felt moved to design a new preamplifier. This was published in Wireless World as “A Precision Preamplifier”. It seemed to me that a having a separate balance stage simply to introduce some quite small differences in interchannel gain was not a good idea. I therefore wondered which of the existing stages it could be grafted onto. The line-level part of the preamp consisted of a high-impedance unity-gain buffer, a Baxandall tone control, and a Baxandall active volume control; the buffer was a definite possibility (obviously it would have to be reconfigured so it could give gain), but the tone control seemed more promising and was clearly a bit of a design challenge. Now I like design challenges, though I am aware that not everybody does.

The basic idea is to vary the amount of negative feedback sent to the Baxandall network to change the stage gain without affecting the frequency response. It is only possible to increase the gain from unity, by reducing the feedback proportion, unless you accept the added complication of putting gain in the feedback path; that not only might cause stability problems, but definitely makes a nonsense of combining stages to save on active circuitry. The problem boils down to making the source impedance seen by the feedback side of the Baxandall network as constant as possible with the movement of the balance control RV3, so it can be compensated for by putting the same impedance in series with the input. As shown in Figure 15.15, the value chosen here is 1 kΩ. The three resistors R5, R6, R7 around RV3 make the output impedance of the network near constant, preventing interaction between the balance control and tone controls, and also modify the balance control law to give only +0.8 dB of gain with balance central; it should be possible to fit this into a preamp gain structure somewhere. The gain with balance hard over is 0 dB or +5.2 dB. It could be argued the range should be greater, say 10 dB.

Figure 15.15 Baxandall control combined with active balance control.

The balance network was designed by “manual optimisation”, or in other words trial and error. Its output impedance varies from 990 Ω at the balance control extremes to 1113 Ω at the centre, a range of only 123 Ω; not bad, I feel. This could be reduced by reducing the value of R5, but only at the cost of increasing the loading on the opamp with the balance control fully clockwise. It works rather well as it is; with the treble control set to shelve at −4 dB, the difference in the response is only -0.2 dB as the balance control is moved from either extreme to the centre.

If we set the treble control to Mark -3 (i.e. with the treble wiper at the 2 kΩ–8 kΩ point on the track of the 10 kΩ pot) then the treble cut flattens out at –4.0 dB with balance control central. At either extreme balance setting the amount of cut is increased to –4.3 dB, as the impedance of the control and its associated network are at a minimum, and therefore there is more negative feedback and so more treble cut. Similar results are obtained by setting the treble control back to flat and setting the bass control for +7.5 dB of bass boost. In this case, the variation in boost with balance setting is only 0.2 dB. I suggest the control interaction is negligible in both cases.

This combined stage was used in a preamplifier design published in Wireless World in 1983; it was the MRP-10 in my own numbering system. I can say with absolute certainty that no comments on control interaction, negative or otherwise, were ever received.

A variation on this technique is occasionally useful. If for some reason you have to drive a simple Baxandall tone network (without balance control) from a substantial impedance (like R8 in Figure 15.15), the asymmetry that will produce in the control laws can be cancelled out by putting the same impedance in the feedback path.

Switched-HF-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 in some way.

The frequency response of the Baxandall configuration is set by its RC time-constants, and one obvious way to change the frequencies is to make the capacitors switchable, as in an early preamp design of mine. [6] Changing the R part of the RC is far less practical, as it would require changing the potentiometer values as well. If fully variable frequencies controlled by pots are wanted, then a different configuration must be used, as described later in this chapter.

If a large number of switched frequencies (more than three) is wanted, then a relatively expensive rotary switch is required, but if three will do, a centre-off toggle switch will certainly take up less panel space, and probably be cheaper; you don’t have to pay for a knob. This is illustrated in Figure 15.16, where C1 is always in circuit, and either C2 or C3 can be switched in parallel. This is an HF-only tone control with ±1 dB break frequencies at 1 kHz, 3 kHz, and 5 kHz; most people will find frequencies much higher than that to be a bit too subtle. A similar approach can be used with the two-HF-capacitor Baxandall control, but twice as much switching is required.

A disadvantage of the centre-off switch is that the maximum rather than the middle frequency is obtained at the central toggle position. If this is unacceptable, then C&K make a switch variant (Model 7411) [7] with internal connections that are made in the centre position, so that two switch sections will make up a one-pole three-way switch as in Figure 15.17. A stereo version is physically a four-pole switch. This method is naturally more expensive than the centre-off approach.

Figure 15.16 A Baxandall HF-only tone control with three switched turnover frequencies.

Figure 15.17 Making a one-pole three-way switch with two C&K 7411 switch sections.

Figure 15.18 Frequency response of tone control with three switched HF break frequencies, at 1, 3, and 5 kHz.

The circuit of Figure 15.16 also demonstrates how an HF-only tone control is configured, with R2 and R3 taking the place of the LF control and providing negative feedback at DC and LF. If this is cascaded with an LF-only control, the second phase inversion cancels the first, and both stages can be bypassed by a tone-cancel switch without a phase change. The response is shown in Figure 15.18.

A similar approach can be used to switch the LF capacitor in a Baxandall control. The capacitor values tend to be inconveniently large for low break frequencies, especially if you are using low-value pots. A different tone control configuration gives more modest sizes –see the section “Variable-frequency LF EQ”.

Variable-Frequency HF EQ

Since we are moving now 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 mean the same thing. The circuit shown in Figure 15.19 gives HF equalisation 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 opamp A1 in a shunt feedback mode so that it can provide either cut or boost, but the resemblance ends there.

Figure 15.19 A variable-frequency HF shelving circuit. The ±1 dB break frequency range is 400 Hz–6.4 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. When the wiper of RV1 is at the output end, positive feedback partially cancels the negative feedback through R2 and the gain increases. When the wiper of RV1 is at the input end, the signal fed through A2 causes partial cancellation of the input signal, 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). Since only high frequencies are passed, this circuit has no effect at LF. The response is shown in Figure 15.20. The frequency-setting control RV2 has a relatively high value at 100 kΩ, because this allows for a 16:1 of variation in frequency, and a lower value would give excessive loading on A2 at the high-frequency end. This assumes TL072 or similar opamps are used to avoid the need to deal with opamp input bias currents. If 5532 or LM4562 opamps are used, there is considerable scope for reduction in the circuit impedances, resulting in lower noise.

Figure 15.20 The response of the variable frequency HF shelving circuit at extreme frequency settings. Maximum cut/boost is slightly greater than +/-15 dB.

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 R3, R4. 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 freedom from control interaction is not eternal vigilance but more opamps. The frequency range can be scaled simply by altering the value of C1. The range of frequency variation is controlled by the value of endstop resistor R5, subject to restrictions on loading A2 if distortion is to be kept low.

The component values given are the E24 values that give the closest approach to +/-15 dB cut/boost at the control extremes. When TL072 opamps 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.

Variable-Frequency LF EQ

The corresponding variable LF frequency EQ is obtained by swapping the positions of C1 and R5, RV2 in Figure 15.19 to give Figure 15.21. Now only the low frequencies are passed through, and so only they are controlled by the boost/cut control. The frequency response is shown in Figure 15.22.

Figure 15.21 A variable frequency LF shelving circuit. The ±1 dB break frequency range is 60 Hz–1 kHz. Boost/cut range of +/-15 dB is set by R3 and R4.

Figure 15.22 The response of the variable frequency LF shelving circuit at extreme frequency settings. Maximum cut/boost is slightly greater than +/-15 dB.

A New Type of Switched-Frequency LF EQ

In the circuit of Figure 15.21, R3 and R4 attenuate the signal before it passes through the unity-gain buffer A2. If a very-low-noise stage is required, it may be possible to put the attenuator after the buffer instead, in which case it will attenuate the buffer’s noise by 7.4 dB. This is easier to do for a switched-frequency rather than a fully variable frequency EQ. An example is Figure 15.23, which has switched ±1 dB break frequencies at 100 Hz and 400 Hz and gives ±10 dB maximal cut and boost. With SW1 open, R3 and R4 attenuate the signal by the appropriate amount to give ±10 dB. Their combined impedance (R3 and R4 in parallel) gives the required 100 Hz frequency in combination with C1. When SW1 is closed, R5 is now in parallel with R3 and R6 is in parallel with R4; the attenuation is the same, but the impedance is reduced, so the break frequency increases to 400 Hz.

Figure 15.23 Low-noise switched-frequency LF EQ with the attenuation after buffer A2.

At first sight, it appears that the relatively high values of R3, R4, R5, R6 would make the circuit very noisy. In fact, the large value of C1 means that their noise is largely filtered out. In the first version measured, R1 and R2 were 4.7 kΩ, and the output noise (flat) was -109.2 dBu using LM4562 for both opamp sections. Reducing R1, R2 to 2.2 kΩ as shown reduced this handily to -111.1 dBu, which is rather quiet.

Variable-Frequency HF and LF EQ in One Stage

In this section, I describe how to combine variable-frequency LF and HF shelving EQ in one stage. This gives some component economy because opamp A1 can be shared between the two functions. Despite this, the schematic in Figure 15.24 is a little more complex than you might expect from looking at the two circuits above, because this is intended to be premium EQ with the following extra features:

  • The response returns to unity gain outside the audio band. This is often called return-to-flat (RTF) operation. The fixed RTF time-constants mean that the boost/cut range is necessarily less at the frequency extremes, where the effect of RTF begins to overlap the variable boost/cut frequencies.
  • The frequency control pots all have a linear law for better accuracy. The required logarithmic law is implemented by the electronic circuitry.
  • There is an inbuilt tone-cancel switch that does not cause an interruption in the signal when it is operated.
  • Low-impedance design is used to minimise noise.

The boost/cut range is +/-10 dB, the LF frequency range is 100 Hz–1 kHz, and the HF frequency range is 1 kHz–10 kHz. This design was used in my low-noise preamplifier published in Jan Didden’s Linear Audio in 2012 [8], being developed from an earlier version used in the “Precision Preamplifier 96”. [9] Very few hi-fi manufacturers have ever offered this facility. The only one that comes to mind is the Yamaha C6 preamp (1980–81), which had LF and HF frequency variable by slider over wide ranges (they could even overlap in the 500 Hz–1 kHz range) and Q controls for each band as well. The Cello Sound Palette (1992) had a reputation as a sophisticated tone control, but it used six boost/cut bands at fixed frequencies that gave much less flexibility. [10]

The variable boost/cut and frequencies make the tone control much more useful for correcting speaker deficiencies, allowing any error at the top or bottom end to be corrected to at least a first approximation. It makes a major difference.

This control was developed for hi-fi rather than mixer use, and certain features of the tone control were aimed at making it more acceptable to those who think any sort of tone control is an abomination. The control range is restricted to +/-10dB rather than the +/-15 dB which is standard in mixing consoles. The response is built entirely from simple 6 dB/octave circuitry, with inherently gentle slopes. The stage is naturally minimum phase, and so the amplitude curves uniquely define the phase response. The maximum phase shift does not exceed 40 degrees at full boost, not that it matters, because you can’t hear phase shift anyway; see Chapter 1.

The schematic is shown in Figure 15.23. The tone control gives a unity-gain inversion except when the selective response of the sidechain paths allows signal through. In the treble and bass frequency ranges where the sidechain does pass signal, the boost/cut pots RV1, RV2 can give either gain or attenuation. When a wiper is central, there is a null at the middle of the boost/cut pot, no signal through that sidechain, and the gain is unity.

Figure 15.24 The tone-control schematic, showing the two separate paths for HF and LF control. All pots are 5 kΩ linear.

If the pot is set so the sidechain is fed from the input, then there is a partial cancellation of the forward signal; if the sidechain is fed from the output, then there is a partial negative-feedback cancellation, or to put it another way, positive feedback is introduced to counteract part of the NFB. This apparently ramshackle process actually gives boost/cut curves of perfect symmetry. This is purely cosmetic, because you can’t use both sides of the curve at once, so it hardly matters if they are exact mirror images.

The tone-control stage acts in separate bands for bass and treble, so there are two parallel selective paths in the sidechain. These are simple RC time-constants, the bass path being a variable-frequency first-order low-pass filter and the associated bass control only acting on the frequencies this lets through. Similarly, the treble path is a variable high-pass filter. The filtered signals are summed and returned to the main path via the non-inverting input, and some attenuation must be introduced to limit cut and boost. Assuming a unity-gain sidechain, this loss is 9 dB if cut/boost are to be limited to +/-10 dB. This is implemented by R9, R12, and R4. The sidechain is unity-gain and has no problems with clipping before the main path does, so it is very desirable to put the loss after the sidechain, where it attenuates sidechain noise. The loss attenuator is made up of the lowest-value resistors that can be driven without distortion, to minimise both the Johnson noise thereof and the effects of the current noise of opamp A1.

The Tone Cancel switch disconnects the entire sidechain (five out of six opamps) from any contribution to the main path and usefully reduces the stage output noise by about 4 dB. It leaves only A1 in circuit. Unlike configurations where the entire stage is by-passed, the signal does not briefly disappear as the switch moves between two contacts. This minimises transients due to suddenly chopping the waveform and makes valid tone in/out comparisons much easier.

It is very convenient if all pots are identical. I have used linear 5 kΩ controls, so the tolerances inherent in a two-slope approximation to a logarithmic law can be eliminated. This only presents problems in the tone stage frequency controls, where linear pots require thoughtful circuit design to give the logarithmic action that fits our perceptual processes.

In the HF path, C5, R7 is the high-pass time-constant, driven at low impedance by unity-gain buffer A2. This prevents the frequency from altering with the boost/cut setting. The effective value of R7 is altered over a 10:1 range by varying the amount of bootstrapping it receives from A3, the potential divider effect and the rise in source resistance of RV3 in the centre combining to give a reasonable approximation to a logarithmic frequency/rotation law. R8 is the frequency end stop resistor that limits the maximum effective value of R7. C2 is the treble RTF capacitor – at frequencies above the audio band, it shunts all the sidechain signal to ground, preventing the HF control from having any effect. The HF sidechain degrades the noise performance of the tone control by 2 to 3 dB when connected because it passes the HF end of the audio band. The noise contribution is greatest when the HF freq is set to minimum, and the widest bandwidth from the HF sidechain contributes to the main path. This is true even when the HF boost /cut control is set to flat, as the HF path is still connected to A1.

In the LF path, A4 buffers RV1 to prevent boost/frequency interaction. The low-pass time-constant capacitor is the parallel combination of C11 + C12 +C13; the use of three capacitors increases the accuracy of the total value by 3. The associated resistance is a combination of RV4 and R11, R12. C14 and R13 make up the RTF time-constant for the LF path, blocking very low frequencies and so limiting the lower extent of LF control action. The bass frequency law is made approximately logarithmic by A5; for minimum frequency, RV4 is set fully CCW, so the input of A5 is the same as the C11 end of R12, which is thus bootstrapped and has no effect. When RV4 is fully CW, R11, R12 are effectively in parallel with RV4, and the turnover frequency is at a maximum. R11 gives a roughly logarithmic law; its value is carefully chosen so that the centre of the frequency range is at the centre of the control travel. Sadly, there is some pot dependence here. The LF path uses three opamps rather than two but contributes very little extra noise to the tone stage, because most of its output is rolled off by the low-pass action of C11, C12, C13 at HF, eliminating almost all its noise contribution apart from that of A6.

The measured responses for maximum boost and maximum cut at minimum, middle, and maximum frequency settings are shown in Figures 15.25 and 15.26.

Figure 15.25 LF tone-control frequency response, max cut/boost, at minimum, middle, and maximum frequencies.

An important goal in the design of this tone control was low noise. Once the opamps have been chosen and the architecture made sensible in terms of avoiding attenuation-then-amplification, keeping noise-gain to a minimum, and so on, the remaining way of improving noise performance is by low-impedance design. The resistances are lowered in value, with capacitances scaled up to suit, by a factor that is limited only by opamp drive capability. The 5532 or LM4562 is good for this.

Figure 15.26 HF tone-control frequency response, max cut/boost, at minimum, middle, and maximum frequencies.

A complete evaluation of the noise performance is a lengthy business because of the large number of permutations of the controls. If we just look at extreme and middle positions for each control, we have maximum boost, flat, and maximum cut for both HF and LF, and maximum, middle, and minimum for the two frequency controls, yielding 3 ×3 ×3 ×3 = 81 permutations. The measurements given in Table 15.2 are therefore restricted to those that put the greatest demands on the circuitry, e.g. HF freq at minimum.

Measuring the distortion performance of the tone control is likewise a protracted affair, requiring the exploration of the permutations of the four controls. There were no surprises, so I will not use up valuable space displaying the results; if there is interest, I will put them on my website at douglas-self.com. Suffice it to say that THD at 9 Vrms in/out never gets above 0.001%. General THD levels are in the range 0.0003 to 0.0007%.

Be aware that circuits like this tone control can show unexpected input impedance variations. A standard Baxandall tone control made with 10 kΩ pots can have an input impedance that falls to 1 kΩ or less at high frequencies where the capacitors have a low impedance. It is not obvious, but the alternative tone-control configuration used here also shows significant input impedance variations.

Table 15.2 The noise output of the tone control at various settings
HF level HF freq LF level LF freq Noise out
Flat Min Flat Max –105.1 dBu
Flat Mid Flat Max –106.2 dBu
Flat Max Flat Max –107.2 dBu
Flat Max Flat Mid –106.8 dBu
Flat Max Flat Min –107.1 dBu
Flat Min Flat Min –105.6 dBu
Max boost Min Flat Min –100.5 dBu
Max cut Min Flat Min –107.4 dBu
Max cut Min Flat Max –107.6 dBu
Flat Min Max boost Max –103.8 dBu
Flat Min Max cut Max –105.9 dBu
Flat Min Max cut Min –105.6 dBu
Flat Min Max boost Min –105.0 dBu
Tone–cancel –110.2 dBu

Not corrected for AP noise at -119.2 dBu (difference negligible).

Measurement bandwidth 22 Hz–22 kHz, rms sensing, unweighted.

Look at the circuit in Figure 15.24; the original value for R1 was 4k7, and the argument that follows here is based on that value. You might think that because the input terminal connects only to a 4k7 resistor and two 5 kΩ pots, the input impedance cannot fall below their parallel combination, i.e. 4k7 || 5k || 5k = 1.63 kΩ. You would be wrong; the other end of the 4k7 resistor is connected to virtual ground, but the two 5 kΩ pots are connected to the stage output. When the controls are set flat, or tone-cancel engaged, this carries an inverted version of the input signal. The effective value of the pots is therefore halved, with zero voltage occurring halfway along the pot tracks. The true input impedance when flat is therefore 4k7 || 2.5k || 2.5k = 987 Ω, which is confirmed by simulation.

When the tone control is not set flat, but to boost, then at those frequencies the inverted signal at the output is larger than the input. This makes the input impedance lower than for the flat case; when the circuit is simulated, it can be seen that the input impedance varies with frequency inversely to the amount of boost. Conversely, when the tone control is set to cut, the inverted signal at the output is reduced and the input impedance is higher than in the flat case. This is summarised in Table 15.3, with R1, R2 = 4k7.

Table 15.3 shows that the input impedance falls to the worryingly low figure of 481 Ω at maximum HF and LF boost. In this case, the gain is +10 dB, and so the input voltage into this impedance cannot exceed 3 Vrms without the tone-control output clipping. This limits the current required of the preceding stage, and there are not likely to be problems with increased distortion if this is 5532 or LM4562 based.

Table 15.3 Input impedance of the tone control at various settings
HF level HF freq LF level LF freq Input impedance
Flat Min Flat Mid 987 Ω
Flat Mid Max boost Mid 481 Ω
Flat Mid Max cut Mid 1390 Ω
Max boost Mid Flat Mid 480 Ω
Max cut Mid Flat Mid 1389 Ω

As mentioned earlier, this tone control was developed from an earlier version designed some 16 years before. It is instructive to take a quick look at the improvements that were made:

  • All opamps changed from 5532 to LM4562 to reduce noise and distortion
  • A general impedance reduction to reduce noise including the use 5 kΩ linear pots throughout instead of 10 kΩ
  • Frequency control laws improved so the middle of the frequency range corresponds with the middle position of the control
  • Three expensive 470 nF polypropylene capacitors in the LF path replaced with four of 220 nF, giving a cost reduction. The resulting impedance at C14 is quite high at low frequencies, and the pickup of electrostatic hum must be avoided.
  • DC blocking capacitor C10 added to the LF path frequency control to eliminate rustling noises
  • C3 increased from 220 μF to 470 μF to remove a trace of electrolytic capacitor distortion at 10 Hz and 9 Vrms out (with max LF freq and max boost). Reduced from 0.0014% to less than 0.0007%.

The electrolytic capacitors in the tone control are used for DC blocking only, and have no part at all in determining the frequency response. It would be most undesirable if they did, both because of the wide tolerance on their value and the distortion generated by electrolytics when they have significant signal voltage across them. The design criterion for these capacitors was that they should be large enough to introduce no distortion at 10 Hz, the original values being chosen by the algorithm “looks about right”, though I hasten to add this was followed up by simulations to check the signal voltages across them and THD measurements to confirm all was well.

Tilt or Tone-Balance Controls

A tilt or tone-balance 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 “tone balance” 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, and I shall do so.

Tilt controls are (or were) supposedly useful in correcting the overall tonal balance of recordings in a smoother way than a Baxandall configuration, which concentrates more on the ends of the audio spectrum. An excellent (and very clever) approach to this was published by Ambler in 1970. [11] See Figure 15.27. The configuration is very similar to the Baxandall –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 15.28; the response is not quite flat with the control central due to component tolerances.

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 opamp A1 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.

Figure 15.27 Tilt control of the Ambler type.

Figure 15.28 Frequency response of Ambler tilt control.

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 opamps. The original (1970) gain element was a two-transistor inverting amplifier with limited linearity and load-driving capability. Here a stabilising 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. One current example is the Classé CP-800 D/A preamplifier, reviewed by Stereophile in 2012. [12] This gives a maximum of ±6 dB control at the frequency extremes and is implemented by DSP. In analogue use the signal has to be converted to 24-bit digital data, processed, then converted back to analogue, which to me seems somewhat less than elegant.

Middle Controls

A middle control affects the centre 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 corresponds with room shortcomings or loudspeaker problems is remote in the extreme. Occasionally middle controls appeared on preamps in the seventies, but only rarely and without much evidence of success in the marketplace. One example is the Metrosound ST60 (1972), which had a 3-band Baxandall tone control –more on this in what follows – with slider controls. The middle control had a very wide bandwidth centred 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 equaliser and its number of controls defines the possibilities open to the operator. A “presence” control is centred on the upper-middle audio frequencies, so it tends to accentuate vocals when used; nowadays the term seems to be restricted to tone controls on electric guitars.

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 is 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 centre frequency. This also uses four knobs but is much more useful.

Fixed Frequency Baxandall Middle Controls

Figure 15.29 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. R3 and R4 maintain unity gain at DC and high frequencies and keep the stage biased correctly.

Figure 15.29 Fixed middle control of the Baxandall type. Centre frequency 1.26 kHz.

Figure 15.30 The frequency response of the Baxandall middle control in Figure 15.29.

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 15.30, though it has to be said that the benefits of exact symmetry are visual rather than audible.

As mentioned, 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 15.31. 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 15.31 A 4-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 minimise 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 only. 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 opamp. 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 15.32 gives boost/cut limited to +/-12 dB in each band. The pots are now 20 kΩ to prevent the input and feedback impedances from becoming too low.

The frequency responses for each band are given in Figures 15.33, 15.34, and 15.35.

Figure 15.32 The circuit of a Baxandall three-band EQ using one stage only.

Figure 15.33 The frequency response of a Baxandall three-band EQ. Bass control.

Figure 15.34 The frequency response of a Baxandall three-band EQ. Mid control.

Figure 15.35 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 15.36. Here the signal tapped off from RV1 is fed to a Wien band-pass network R1, C1, R2, C2 and returned to the opamp non-inverting input. This is the same Wien network as used in audio oscillators.

With the values shown, the centre 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 15.34, with a maximal cut/boost of 15.5 dB.

Wien Fixed Middle EQ: Altering the Q

The Q of resonance or peaking is defined as the centre frequency divided by the bandwidth between the two -3 dB points in the response. Strictly speaking Q only applies to a simple resonant circuit, where on either side of the peak the response falls away forever. Thus it is always possible to define the -3 dB bandwidth.

Figure 15.36 The Wien fixed-middle circuit. Centre frequency is 2.26 kHz. The Q at max cut/boost is 1.4.

Mid EQs have a resonant peak (or dip), but on either side of the peak the response goes to unity gain rather than falling forever. Therefore, for small amounts of boost/cut, say ±2 dB, it is impossible to quote a Q value, as there are no -3 dB points. Normal practice is to simply quote the Q at maximum boost/cut, even though the control will rarely if ever be used there.

Conventional types of mid EQ have a Q that reduces as you move away from maximum cut or boost. For example, the mid EQ shown in Figure 15.36 has a Q of 1.4 at +15 dB boost, a Q of 0.82 at +10 dB boost, and a Q of 0.35 at +5 dB boost. The Q figures apply to cut mode, as the response curves are symmetrical.

Figure 15.37 shows another example of a fixed-frequency mid control; this time the nominal centre frequency is 1.6 kHz. The Q of the resonance is set by the ratio of the two capacitors C1 and C2; as C2 gets small, the Q is reduced. To keep the same centre frequency, C1 is increased as C2 is reduced. Sometimes R2 must be adjusted to maintain a ±15 dB boost/cut. There is not, so far as I am aware, a simple design equation for setting the Q, and Table 15.4 was constructed by twiddling simulator values. The procedure is thus:

  1. Alter the value of C2. This will alter the centre frequency.
  2. Increase C1 to return the centre frequency to the original value.
  3. If necessary, adjust R2 to get about ±15 dB boost/cut.
  4. Calculate the Q at max boost/cut and see if it is satisfactory.

If not, try again with a different value for C2.

Figure 15.37 The Wien fixed-middle circuit. Nominal centre frequency is 1.6 kHz, Q at max cut/boost is 1.20.

Table 15.4 Capacitor values for setting the Q of the mid control in Figure 15.37
Max Q R1 C1 R2 C2 C1/C2 ratio
1.63 5k1 33n 5k1 12n 2.75
1.20 5k1 39n 4k3 10n 3.90
0.94 5k1 56n 3k9 8n2 6.83
0.86 5k1 68n 3k9 6n8 10.0
0.79 5k1 82n 3k9 5n6 14.6
0.69 5k1 100n 3k9 4n7 21.3

For Table 15.4, I used single E24 resistors and single E12 capacitors, and this does not allow the boost/cut, centre frequency, or Q to be very closely controlled. The component values therefore give a slightly variable response, as shown in Figure 15.38; the changes in Q are obvious but are accompanied by small shifts in maximum boost/cut and centre frequency. This approach keeps the component count down, but if intermediate Q values between those given prove to be really needed, we can always do a bit of paralleling, as in other cases where something needs to be set with some precision.

There are, of course, limits to how high a Q can be achieved with a simple circuit like this. A Q of 1.63 appears to be the maximum.

Thanks to Alex of Barefaced Audio, highly respected manufacturers of guitar cabinets and bass cabinets, for permission to publish the information in Figure 15.38.

Figure 15.38 The response of the mid circuit Wien fixed-middle circuit at various values of Q.

Variable-Frequency Middle EQ

A fully variable frequency middle control is much more useful and versatile than any combination of fixed or switched middle frequencies. 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 15.39.

The variable load that the Wien network puts on the cut/boost pot RV1 causes a small amount of control interaction, the centre frequency varying slightly with the amount of boost or cut. This is normally considered acceptable in middle-range mixers. 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 here is carefully arranged so that the two variable resistors RV2, RV3 have four common terminals, reducing the number of physical terminals 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 frequency ratio of 15.7 to 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-to-1 range. The measured frequency responses at the control limits is shown in Figure 15.40. The frequency range is from 150 Hz to 2.3 kHz, the ratio being slightly adrift due to component tolerances. The maximum Q possible is 1.4, this only applying at maximum boost or cut.

Figure 15.39 A Wien sweep circuit. The centre-frequency range is 150 Hz–2.4 kHz (A 16:1 ratio).

Figure 15.40 The measured response of the sweep middle circuit at control extremes. The cut/boost is slightly short of +/-15 dB.

Single-Gang Variable-Frequency Middle EQ

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 they 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 centre frequency; the big problem is to minimise this interaction. I too have attacked this problem, and here is my best shot so far, in Figure 15.41.

This circuit is a variation of the Wien middle EQ, the quasi-Wien network being tuned by a single control RV2, which varies not only 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 RV1 wiper and the Wien network; this helps to minimise variation of Q with frequency.

The response is shown in Figure 15.42; note that the frequency range has been restricted to 10:1 to minimise Q variation. The graph shows only maximum cut/boost; at intermediate settings, the Q variations are much less obvious.

It is possible to make a yet more economical version of this, if one accepts somewhat greater interaction between boost/cut, and Q and frequency. The version shown in Figure 15.43 omits the unity-gain buffer and uses unequal capacitor values to raise the Q of the quasi-Wien network, saving an opamp section. R8 increases the gain seen by the Wien network and sets maximum boost/cut. The frequency range is still 10:1.

The response in Figure 15.44 shows the drawback: a higher Q at the centre of the frequency range than for the three-opamp version. Once again, the Q variations will be much less obvious at intermediate cut/boost settings.

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 don’t know…

Figure 15.41 My single-gang sweep middle circuit. The centre frequency range is 100 Hz–1 kHz.

Figure 15.42 The response of the single-gang sweep middle circuit of Figure 15.41. Boost/cut is +/-15 dB, and the frequency range is 100 Hz–1 kHz. The Q varies somewhat with centre frequency.

Figure 15.43 My economical single-gang sweep-middle circuit. The centre frequency range has been changed to 220 Hz–2.2 kHz.

Figure 15.44 The response of the economical single-gang sweep-middle circuit. 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; cut is the mirror image.

Switched-Q Variable-Frequency Wien Middle EQ

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 15.45; here the Wien band-pass 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 centre frequency, and this is compensated for by the attenuation now introduced by R7 and R8.

Figure 15.45 Variable-freq 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 EQ

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 15.46 shows one way of accomplishing this. It is essentially a switchable combination of the variable-frequency HF shelving circuit of Figure 15.19 and the sweep-middle circuit of Figure 15.39; when the switches are in the PEAK position, the signal tapped off RV1 is fed via the buffer A2 to a Wien band-pass 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 15.46 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 15.47.

Figure 15.47 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 called RTF (return-to-flat) operation, or sometimes RTZ (return-to-zero) operation as the gain returns to unity (zero dB) outside the peaking band.

Parametric Middle EQ

A normal second-order resonance is completely defined by specifying its centre frequency, its bandwidth or Q, and the gain at the peak. In mathematical language, these are the parameters of the resonance. Hence an equaliser which allows all three to be changed independently (proviso on that coming up soon) is called a parametric equaliser. 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 15.48 is included partly for its historical interest, showing how opamps and discrete transistor circuitry were combined in the days before completely acceptable opamps 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 opamp circuitry, which gave a significantly better noise performance than designs based entirely on the less-than-perfect opamps of the day; in time, of course, this niche virtually disappeared, as they are wont to do. This parametric middle EQ was used, in conjunction with the usual HF and LF controls, in a channel module called the CM4.

The boost/cut section used an opamp 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 was only used where its superior performance was really necessary. The unity-gain buffer Q1, Q2 which ensured a low-impedance drive to the state-variable band-pass 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 band-pass filter requires a differential stage U2, which once again is best implemented with an opamp, 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 opamps had to be used. To put in two more 741S opamps would have been too costly, and so that left a couple of the much-despised 741 opamps. In fact, they worked entirely satisfactorily in this case, 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 ever 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 all right at the time.

The filter Q was set by the resistance of R6, R7 to ground. It does not interact with filter gain or centre 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; probably it was to cancel the effects of the input bias currents of U1. It could only impair the noise performance, and a DC blocking cap might have been a better solution. Grounding the U1 end of R17 would give an EQ-cancel that also stopped 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-polarised 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 V or ±17 V that was adopted when dual-rail powering became universal and so gave a headroom that was lower by 1.9 dB 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 opamps and the discrete unity-gain buffer with 5532s or other modern types.

Modern parametric equalisers naturally use all-opamp circuitry. Figure 15.49 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, an important improvement on the standard circuit topology. Most of the noise in a parametric equaliser comes from the filter path. In this design, 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 15.48 An historical parametric middle EQ dating back to 1979.

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 minimise Johnson noise without causing excessive opamp loading.

Figure 15.49 Variable-freq variable-Q middle control. State-variable type.

This equaliser section has component values for typical low-mid use, with centre 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 Equalisers

Graphic equalisers 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 equalisers can have any number of bands from 3 to 31, the latter having bands one-third of an octave wide. This is the most popular choice for serious room equalisation work, as bands one-third-octave wide relate to the perceptual critical bands of human hearing.

Graphic equalisers 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 7 to 10.

There is more than one way to make a graphic equaliser, but the most common version is shown in its basic concept in Figure 15.50, with some typical values. L1, C1, and R3 make up an LCR series resonant circuit, which 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 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 RLC circuit is high, and the gain of the circuit is unity.

The beauty of this arrangement is that two, three, or more LCR circuits, with associated cut/boost pots, can be connected between the two opamp inputs, giving us an equaliser with pretty much as many bands as we want. Obviously, the more bands we have, the narrower they must be to fit together properly. A good example of a classic LCR graphic design was published by Reg Williamson in 1973. [13]

As described in Chapter 2, inductors are in general thoroughly unwelcome in a modern design, and the great breakthrough in graphic equalisers came when the LCR 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.

Figure 15.50 The basic idea behind graphic equalisers; gain is unity with the wiper central.

The basic notion is shown in Figure 15.51; 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 15.51 Using a gyrator to synthesise a grounded inductor in series with a resistance.

The sample values in Figure 15.51 synthesise 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 opamp is used as a unity-gain buffer, which means that the early gyrator graphic equalisers could use a simple emitter-follower in this role. The linearity was naturally not so good, but it worked and made graphic equalisers affordable.

A simple seven-band gyrator-based graphic equaliser is shown in Figure 15.52. The maximal cut/boost is +/-8 dB. The band centre-frequencies are 63 Hz, 160 Hz, 410 Hz, 1 kHz, 2.5 kHz, 7.7 kHz, and 16 kHz. The Q of each band at maximum cut or boost is 0.9.

The response of each band is similar to that shown in Figure 15.34. The maximum Q value is only obtained at maximum cut or boost. For all intermediate settings, the Q is lower. This behaviour is typical of the straightforward equaliser design shown here, and is usually referred to as “proportional-Q” operation; it results in a frequency response which is very different from what might be expected on looking at the slider positions.

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. [14] This gives a frequency response that more closely resembles the slider positions.

The graphic equaliser 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 equaliser for an asymmetric or non-reciprocal response, in which the boost curves are as shown, but the cut response is a narrow notch. This is often considered to be more effective when the equaliser is being used to combat feedback in a sound reinforcement system.

Figure 15.52 A 7-band graphic equaliser.

References

[1] Langford-Smith, F., ed The Radio Designers Handbook 4th edition, Chapter 15, 1953, pp 635–677, Newnes, reprint 1999

[2] Langford-Smith, F., ed Ibid, p 668

[3] Sterling, H. T. “Flexible Dual Control System” Audio Engineering, Feb 1949

[4] Baxandall, Peter “Negative-feedback Tone Control” Wireless World, Oct 1952, p 402

[5] Self, Douglas “Preamplifier 2012” Elektor, Apr/May/Jun 2012

[5a] Self, Douglas “A Precision Preamplifier” Wireless World, Sept 1983, p 31

[6] Self, Douglas “An Advanced Preamplifier” Self On Audio 2nd edition. Newnes, p 5

[7] C&K switches www.ck-components.com/7000/toggle,10598,en.html Accessed Aug 2013

[8] Self, Douglas “A Low Noise Preamplifier with Variable-Frequency Tone Controls” Linear Audio, Vol. 5, pub. Jan Didden, pp 141–162

[9] Self, Douglas “Precision Preamplifier 96” Electronics World, Jul/Aug/Sept 1996

[10] Cello www.celloseattle.com/ctdocs/prodserve/peripherals/audiopalette.html Accessed Aug 2013

[11] Ambler, R. “Tone-Balance Control” Wireless World, Mar 1970, p 124

[12] Stereophile www.stereophile.com/content/class233-cp-800-da-preamplifier-page-2 Accessed Jun 2013

[13] Williamson, R. “Octave Equalizer” Hi-Fi News, Aug 1973

[14] Bohn, Dennis A. “Constant-Q Graphic Equalizers” JAES, Sept 1986, p 611