Analog Audio Tone Controls and Equalizers

Application Note AN-12 by Christopher Moore

Introduction Sweeping this potentiometer from 1k to 100k in eight log steps

In this note I present a versatile topology for implementing high will vary the corner frequencies while maintaining the maximum
quality tone controls and equalizers. While this topology uses boost or cut.
more op amps than the usual Baxandall bass and treble control Treble control
and requires potentiometers with a fourth terminal (center tap to Simply interchanging C1 and R4 and choosing their values
ground), it gives the designer far more options. This technique appropriately leads to a normal treble control. In this example,
will be of interest to designers of high end audio and profes- the lower corner frequency is 1.6kHz.
sional audio equipment.
T 20.00
Bass control
The curves below are from a bass control, with an upper corner
frequency of 325Hz and a maximum boost/cut of 13dB. The 10.00

bass control is swept in 11 steps with linear spacing, calling for a

Gain (dB)

potentiometer with a linear taper. 0.00

T 20.00

-10.00
10.00
Gain (dB)

-20.00
0.00 10 100 1k 10k 100k
Frequency (Hz)

-10.00 By varying R4 we can give the user control over the corner fre-
quencies. In the next figure, the potentiometer is swept from 1k
to 100k in eight log steps.
-20.00
T 20.00
10 100 1k 10k 100k
Frequency (Hz)

We can make a more versatile tone control if we replace R4 with 10.00

another potentiometer wired as a variable resistor.
Gain (dB)

T 20.00 0.00

10.00 -10.00
Gain (dB)

0.00 -20.00
10 100 1k 10k 100k
Frequency (Hz)
-10.00
Peaking control
Moving beyond simple bass and treble controls, this versatile
-20.00
architecture allows us to create boost or cut bell curves. To re-
10 100 1k 10k 100k
Frequency (Hz)
alize these curves, we add a multiple-feedback second order
bandpass filter with design criteria for center frequency, gain at
the center frequency (set to 1 for our purposes), and Q (width of A parametric section can be dropped right into this architecture
the skirts). Since the MFB bandpass is inverting, we precede it in place of a peaking control. A preferred parametric realization
with a unity gain inverter (which can be shared by other peaking would use the state variable technique (three op amps, a potenti-
circuits). In the curves below, the center frequency is 80Hz and ometer for Q, and a dual potentiometer for center frequency).
Q equals 2. Note that the family of curves is symmetrical and Graphic equalizer
that the Q is constant as boost/cut is varied.
This architecture is also good for implementing a graphic
T 20.00 equalizer. A graphic equalizer is a bank of from 5 to 31 peaking
sections with frequencies evenly distributed on a log basis.
Design the peaking filters for the required frequencies, all with
10.00
the appropriate Q (all filters in a graphic equalizer have the same
Q).
Gain (dB)

0.00 The overall structure

The overall structure consists of a cascaded pair of inverting op
amp stages. The source is applied at the left side and the output
-10.00
is presented by the second op amp at the right side. The
frequency sensitive stages are driven by the first op amp and
-20.00 have a maximum gain of one in their pass band:
10 100 1k 10k 100k • The high pass filter develops its maximum gain at higher
Frequency (Hz) frequencies and is used for the treble control.
• The low pass filter develops its maximum gain at lower
Interaction between bass and peaking control
frequencies and is used for the bass control.
In this topology, there is essentially no interaction between con- • The bandpass filter develops its maximum gain at its center
trols as long as their regions of influence are sufficiently re- frequency and is used for the peaking control.
moved from each other. But even when the controls overlap, the To provide boost, the filter output is passed through the
curves are still “reasonable” and remain monotonic. In the figure potentiometer to the output op amp, where it combines in phase
below, the boost and cut of the peaking control is varied while with the source signal coming through the input op amp and
the bass control is held at maximum boost and cut. In the cases adds to the source level.
where the peaking control is bucking the bass control, the To provide cut, the filter output is passed through the
peak/notch depth is greater than the cases where the peaking potentiometer to the input op amp, where it combines out of
control is aiding the bass control. Despite the asymmetry, the phase with the source signal also coming into the input op amp
controls would still be useful. and reduces the source level.
T 20.00 This structure delivers symmetrical boost and cut curves.
When a control is not in use (when it is defeated by setting its
potentiometer to the center), it contributes no noise to the
10.00
output.
For any value of boost or cut, the circuit can deliver its
Gain (dB)

0.00 maximum output swing at any frequency: neither the input op

amp nor the filter will overload before the output does so.
This is not the case if a state variable bandpass filter has been
-10.00 incorporated as a filter in this circuit to achieve a fully
adjustable parametric section. For these filters, internal nodes
operate at a gain greater than one, especially at the center
-20.00
10 100 1k 10k 100k
frequency and for cases of higher values of Q. Careful design
Frequency (Hz) and gain scaling are required to minimize overload and noise
issues when using the state variable filter in this structure.
Parametric equalizer
The parametric equalizer is arguably the most useful and versa- Design flow for overall structure
tile audio equalizer. This equalizer gives the user three controls–
center frequency, boost/cut, and Q. When the equalizer has a Choose a value for R0 (feedback/feedforward resistors);
number of parametric sections, the designer or user can con- 28.0K here.
struct complex EQ curves suitable for correcting loudspeaker or
room deficiencies. Curves of a parametric section would resem-
ble those shown above for the peaking control, except that two
more figures would be needed to illustrate sweeping frequency
with boost and Q fixed and varying Q while holding boost and
frequency fixed.
Bass control and more moderate capacitor values, while high frequency
For the bass control, we design for the upper corner frequency, sections can use small to moderate capacitors and resistors.
the frequency below which the bass control begins to boost or
cut. The lower frequency (the frequency at which the shelf has Design flow for peaking section with fixed center fre-
essentially leveled off) tags along and is easily found by consid- quency and Q >0.707
ering the boost amount in volts/volts. In the example here, the Choose values for frequency (Fc, in Hz), Q (from 0.7 to 5 or
maximum boost is 13dB, or 4.5 volts/volt. The lower frequency so), maximum boost/cut (Av, in dB), and C (in farads).
is the upper frequency divided by 4.5. Fc = 80Hz; Q = 2; Av = 13dB, C = 47nF here.
Solve for:
Design flow for bass control K1 = 4*Q^2 – 2; 14 here.
Choose Av, the maximum boost/cut. While all sections usually R2 = 1 / 2*pi* Fc*C*(1 / (K1 + 2) )^0.5; 169K here
have the same maximum boost/ cut amount, each section can R1A = R2 / K1; 12.1K here.
have its own value; 13dB here. R1B = R2 / 2; 84.5K here.
Solve for R3: R3 = R0 / ( 10 ^ ( Av/20 )-1 ); 8.06K here.
R3 = R0 / ( 10 ^ ( Av/20 ) -1 ); 8.06K here.
Pick f1, the upper corner frequency, the frequency below
which the bass control begins to boost or cut; 325Hz here. In conclusion
Pick a convenient value for R4; 10K here. This topology gives you a lot of freedom. You can mix all types
Solve for C1: of equalizers, including user adjustable bass, treble, and
C1 = 1 / 2*pi*f1*(R0 + R3) / (R3*R4); 220nF here. parametric controls, and fixed peaking equalizers. The design
process is straightforward and the performance is good.
Treble control Bibliography
For the treble control, we design for the lower corner frequency, Bohn, Dennis A., Constant-Q Graphic Equalizers, Audio
the frequency above which the treble control begins to boost or Engineering Society Preprint 2265, 1985 October 12-16, Audio
cut. The upper frequency (the frequency at which the shelf has Engineering Society, NYC
essentially leveled off) tags along and is easily found by consid-
ering the boost amount in volts/volts. In the example here, the
maximum boost is 13dB, or 4.5 volts/volt. The upper frequency
is the lower frequency multiplied by 4.5.

Design flow for treble control

Choose Av, the maximum boost/cut. While all sections usually
have the same maximum boost/ cut amount, each section can
have its own value; 13dB here.
Solve for R3:
R3 = R0 / ( 10 ^ ( Av/20 ) -1 ); 8.06K here.
Pick f1, the lower corner frequency, the frequency above which
the treble control begins to boost or cut; 1.6kHz here.
Pick a convenient value for R4; 10K here.
Solve for C1:
C1 = 1 / 2*pi*f1*R4*(R0 + R3) / R3; 2.2nF here.

Peaking filter
The peaking sections use a multiple feedback inverting bandpass
filter. The design flow below is appropriate for moderate to high
Q filters (from 0.707 to any reasonable value). For lower Q’s, a
more complex procedure, one where the two capacitors assume
different values, is available, but space doesn’t permit including
this procedure.
One advantage of this circuit is that each section can be tailored
with respect to capacitor size and resistance values. Generally,
we like to keep capacitor values small to keep their size down,
but at low frequencies this leads to higher resistor values.
Generally, we like to keep resistor values down to reduce noise,
DC offset effects, and variation due to PCB contamination.
Sections operating at low bass frequencies can use large resistors
 R0 28K R0 28K R0 28K
Treble
R0 28K
Input Boost
R3 8.06K 20K Output

C1
2.2nF R4
Cut
10K

Bass
Boost
R4 10K
R3 8.06K 20K
C4
R0 220nF
Cut
Cut
10K
C
R0 10K 47nF
R2 80Hz Peak
169K Boost
R1B
84.5K R3 8.06K
20K
C
R1A 47nF Cut
12.1K

Schematic showing bass, treble, and peaking tone controls

Mission statement of Seven Woods Audio

I am an electrical engineering consultant specializing in the con-
ception and design of products and circuits used in audio appli-
cations. My company, Seven Woods Audio, is committed to
helping manufacturers quickly create digital or analog audio
products that generate a good return on investment, work right
the first time, sound excellent, and please the end user. Seven
Woods Audio works with manufacturers of professional audio,
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equipment.
rev: February 21, 2002 Copyright 2002. All rights reserved.

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moore@SevenWoodsAudio.com
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