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Accelerated Slope Tone Control Equalizers Accelerated Slope Tone Control Equalizers*
DENNIS A. BOHN,
AES Member
Rane Corporation, Mukilteo, WA, USA
A tone-control shelving equalizer providing low shelf (bass) boost and cut, as well
as high shelf (treble) boost and cut is described. The active filter stages provide sharpened
(accelerated) amplitude versus frequency response characteristics at the band transitions,
thus leaving-the center frequencies uncorrupted by out-of-band effect of the tone controls.
0 INTRODUCTION
The opportunity to pursue this subject did not appear
again until 1987. While designing a 16-channel matrix
mixer, the author investigated, using computer circuit
analysis, the possibility of creating steeper slopes for
conventional bass and treble tone-control circuits. The
project was canceled before the circuit could be fin-
alized. In 1989 the author resurrected the circuit for a
new microphone input module. The circuit was finally
completed in 1990 and steeper slope tone controls were
a reality. The new circuit, dubbed Accelerated Slope
Tone Controls , was awarded a patent in 1991 [2].¹
The need for bass and treble tone-control circuits
with steeper slopes has been obvious to the author since
his 1976 writings [l] on the subject of designing tone-
control circuits. It became clear that it did not matter
if the tone-control circuits were passive or active, tube,
transistor, or integrated circuits; they all suffered from
the same malady of too much interaction with the mid-
band frequencies.
1 BACKGROUND
Tone-control equalizers, as the term is used here,
refer to relatively uncomplex bass and treble tone con-
trols found on most high-fidelity systems and on certain
professional audio recording consoles and mixers. Most
of these circuits use some variation of Baxandalls
negative-feedback circuit done in 1952 [3]. The Bax-
andall tone-control circuit is commonly referred to as
a shelving control because of the shape created by
* Presented at the 92nd Convention of the Audio Engi-
neering Society, Vienna, Austria, 1992 March 24-27.
Almost universally, these shelving tone controls use
one-pole filter circuits. The steepest response slope
that can ever by achieved by a one-pole filter is, of
course, 6 dB/octave (or 20 dB/decade, equivalent
terms). This would be for an ideal filter circuit. In
practice, the overall shelving tone-control transfer
function results in a response slope that rarely exceeds
about 3 dB/octave. (Due to the close proximity of the
pole and zero of the transfer function, there is near
cancellation; a 2.7-dB/octave slope is typical for ±12
dB designs.) This gentle slope causes the control to
influence the midband frequencies because of overlap-
ping effects from the adjacent high and low frequencies.
Such corruption causes disturbing effects on the critical
midband frequencies. This is an unwanted situation.
If you want to add bass or treble, you want to do so
without disturbing the midband frequencies. What is
needed are tone-control circuits with steeper (or ac-
celerated) slopes.
Ideally the boost and cut tone controls should change
the slope of the transition frequencies into the high
and low end but should not alter the response charac-
the amplitude versus frequency response when boosting
or cutting the low and high end frequencies. The shape
of the response curves when using such a shelving circuit
is that of a shelf, contrasted with peak or dip-type
(bandpass) response shapes, and further contrasted with
total boosting or cutting of the response. Shelving tone
controls cause amplification (boost) or attenuation (cut)
at a substantially constant slope or rate, then level off
to a flat response. The magnitude of this constant slope
is the issue.
¹ Royalty-free licenses are available from the author and
Rane Corporation.
J. Audio Eng. Soc., Vol 40, No. 12, 1992 December ENGINEERING REPORTS
TONE CONTROL EQUALIZERS
teristics of the center or midband frequencies. Practical,
existing filter designs so far have not effectively isolated
the high and low band tone controls from the center or
midband frequencies.
Although it is conceivable that filters having addi-
tional poles with sharper response characteristics could
be incorporated into the tone-control circuitry, such
multiple-pole filters create a different problem. That
problem is the creation of excessive phase shift, ap-
proaching 180°, which produces cancellations and
dropouts due to frequencies that are out of phase with
the input signal. Stability problems also appear because
of the tendency of oscillations at or near the 180° phase
shift region. Rather than accent such problems of drop-
outs, or cancellations and other instabilities, most tone-
control circuits use the single-pole filter. Such single-
two-pole, one-offset zero filter.
Thus, in general, the accelerated slope circuit pro-
vides a tone-control equalizer having a low and/or high
end controllable gain filter stage with n poles and n
1 offset zeros, where n is any integer value of 2 or
more. While the principles of the circuit may be adopted
in a variety of controllable equalizer circuits, the pre-
ferred application is in a relatively simple bass and
treble tone-control equalizer configured in a shelving-
type filter using active filter components. These and
other advantages and features of Accelerated Slope
Tone Controls will be better understood after reading
the detailed description of the figures in the next section.
3 DESCRlPTlON OF FIGURES
pole filters have a maximum phase shift of 90° and,
Fig. 1 is a schematic diagram of an Accelerated Slope
therefore, are inherently stable and preclude cancel-
Tone Control using the phase-compensating offset zero
lations since the frequency shift never approaches the
180° region.
in a two-pole, one-zero equalizer filter circuit adapting
the authors equalizer topology [4] for tone-control
use.
2 ACCELERATED SLOPE TONE CONTROLS
Fig. 2 is a plot of relative amplitude versus frequency
showing, for comparison, the two- and three-pole. one-
This engineering report offers a solution to the fore-
and two-zero phase-compensated tone-control circuits
going problem of unwanted corruption of the midband
superimposed on a corresponding plot of the response
frequencies due to variations in the tone controls, by
characteristics of a conventional one-pole tone-control
incorporating in the equalizer, filters that have two,
filter. Note the comparisons between the steepness of
three, or more poles to achieve the desired steepness
the slopes, and that it takes a three-pole phase-com-
of the frequency response and then compensating for
pensated circuit to approach the theoretical 6 dB/octave
the otherwise excessive phase shift that would result
expected from the conventional one-pole design. It is
by incorporating one or more zeros offset from the
very interesting to note that the actual slope of the full
poles so as to lie outside the high or low band frequencies
theoretical +12 dB boosted response, using the three-
of interest. One such offset zero is being provided for
pole circuit, is only about 5.2 dB/octave. So three poles
each additional pole that is added to the filter. This
want to be 18 dB/octave, but only yield about 5 dB/
offset zero is to be distinguished from a zero occurring
octave. Very roughly each pole improves the slope by
in the overall transfer function of the shelving-type
about 1 dB/octave. However, the sonic benefit is im-
tone control that is caused by the interaction of the
mense since the total area under the curve now unaf-
filters pole with the broad-band signal, and which
fected is quite large.
causes the response curve to flatten out as a shelf. The
Fig 3 shows the amplitude versus frequency and re-
zero due to pole interaction appears away from the
lated phase shift versus frequency plots of the two-
midband and is directly within the high (or low) band
pole phase-compensated filter of Fig. 1 (large solid
of interest.
squares) and, for comparison, the corresponding plots
Thus a two-pole shelving filter is used, with one,
of a conventional one-pole filter (small solid squares),
additional offset zero being located away from the two
a two-pole filter without phase compensation (small
poles and toward the midband. The two poles provide
open squares), and the three-pole filter phase-compen-
the desired steep rise or fall into the low (or high) end
sated circuitry of Fig. 5 (large open squares).
frequencies, and yet as the frequency moves back into
It is observed from Fig. 3(a) that the two-pole phase
the midband, the otherwise excessive phase shif