Download Digitally-Controllable Audio Filters and Equalizers

Digitally-Controllable
Audio Filters and Equalizers
Gary K. Hebert
and Fred Floru
THATCorporation,Marlborough,MA01752, USA
Filters arecommonplace elements in audiosignal processing. Most well-known filter topologies generate fixed responses with fLxedelement values, or use variableresistors to altertheir responses under user control.This paper explores solutions to varying the response of filters and equalizersusing digital control techniques suitable for computer-controlled systems. High-pass, low-pass, band-pass, and parametric topologies are covered using VCAs, resistor ladders, and
multiplying DACs as control elements.
1. INTRODUCTION
tems offer the promise of infinite flexibility with regard to
computer-controlled
filtering, the cost of professionalWhile Digital-Signal-Processing
(DSP) -based audio sys(D/A) converters and digital signal processors is currently
quality analog-to-digital (A/D) and digital-to-analog
prohibitive in many applications. There are also many applications where computer control over a well defined set
of filtering and/or equalization functions is desirable. For
these applications, digitally-controlled analog filters can
be a high-performance, cost-effective alternative,
This paper describes several approaches for implementing
familiar audio filtering and equalization functions under
digital control. It is hoped that these examples will serve
to illustrate the important issues and offer a starting point
for the engineer seeking to design computer-controlled
audio filters for a wide range of specific applications,
2. DIGITAL CONTROL OF ANALOG
2.1 Resistor-Switch
FILTERS
Arrays
Historically, the characteristics of analog audio filters
have been varied using potentiometers, either as variable
resistances or variable voltage dividers. The most obvious
approach to digital control of these components is to provide a string of resistors and electronic switches that can
be selected via a digital code (Figure 1). Integrated devices such as this exist [11, and, when appropriate, they
can be substituted directly for potentiometers in analog
circuits. However, currently available devices are somewhat limited in their application to professional audio
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]i.................
,_,"_
D'_--_
.....
DE_
]
y__-......::]
l
Figure 1 - Digitally Controlled
"Pot"
products in that they are restricted to operation on maximum power supply voltages of +/-5 V. Limiting signal
levels to within these extremes entails sacrificing approximately 10 dB of dynamic range with respect to systems using traditional +/-15 V (or greater) power supply voltages.
Available "tapers" are either linear (equal resistance steps)
or two-slope piecewise-linear approximations to a logarithmic taper. An additional limitation of this approach
shows up when a system requires filter parameters to be
varied while the circuit is processing program material.
(Sometimes the circuit is varied in response to the program material.) In such cases, tile discrete nature of tile
changes in position along the resistor string of the "wiper"
can lead to zipper noise.
Other commercially available resistor-switch array integrated circuits (ICs) are intended specifically for implementing graphic equalizer functions [2, 3]. These devices
are aimed at replacing the potentiometers that control
boost and cut in a traditional analog graphic equalizer.
The resistor segments are chosen to implement exponential steps in boost or cut at the filter center frequency, typically one or two dB per step over a +/-12 dB range. These
195
HEBE RT AND FLORU
devices have seen application in professional audio equalizers as well as in the consumer market where they were
originally targeted. Zipper noise is less a concern with
graphic equalizers since they are usually set once and not
varied (or at least not varied much) while program material is present. The best of these graphic equalizer ICs
will accept +/-7.5 V power supply voltages, which gains
about 3 dB in dynamic range over +/5 V devices. The
main objection to their wider use in professional audio
graphic equalizers is that 1 dB resolution in boost and cut
is considered inadequate for the most demanding
applications.
2.2 Multiplying
D/A Converters
Another approach to digital control of analog filters involves the use of multiplying D/A converters (MDACs).
An MDAC is a specific type of D/A converter (DAC) with
an externally accessible reference input that will accept bipolar signals (Figure 2). Its output is the product of the
reference input and the digital input code according to the
equation:
tion of the range and resolution of parameter variation desired. The steps are typically linear, yet many filter
parameters that must be adjusted in audio applications are
more suitably adjusted in exponential fashion. For exampie, frequency is most naturally varied in octaves, or fractions thereof, and amplitude is most often adjusted in dB.
Implementing exponential control with a linear DAC inevitably wastes bits at one end of the scale, thus requiring
a higher resolution DAC than the desired number of control steps would indicate.
There are MDACswith logarithmicallyspacedsteps intended for use as audio attenuators. While many of these
have non-uniform dB-step-size, at least one implements
3/8 dB steps over an 88.5 dB range [4]. As an illustration,
this device provides 8 bits of exponential control resolution but requires an internal 17-bit MDAC to implement
it. Additionally, because the control steps are discrete, the
possibility of zipper noise exists in dynamic control applications where parameters are varied during the processing
of program material.
2.3 Voltage-Controlled
Vout _ -r
rej_. _-_ _ _ _]
(I)
where Vt,r is the reference input voltage, Vo,t is the DAC
output voltage, CODE is the decimal value of the digital
input, and N is the number of input bits.
An MDAC can thus implement two-quadrant multiplication in discrete steps. As shown in Figure 2, most
MDACs are intended to be used as current output devices
fed to the virtual ground of an opamp current-to-voltage
converter.
Often a feedback resistor which will track with
the resistors internal to the converter is integrated into the
device. In other devices, the entire current-to-voltage convener is included on the same substrate. Note that the
Amplifiers
with DACs
Another form of two quadrant multiplier, the voltagecontrolled amplifier (VCA), has been used to provide electronic control over analog circuits for many years now.
As implied by the name, the gain or attenuation of this
device is a function of an externally applied control voltage. The VCAs used most often in audio applications
have control port characteristics of the form:
Vc°n_°/
G = e v,c,/e
(2)
where G is the VCA current gain, Vcon_o_
is the gain control voltage and V_,_ is a constant that depends on the device type.
current output is non-inverting with respect to the
reference-voltage input, but that the voltage output is
Equation (2) may be rearranged as follows:
inverted.
Vcontrol= V_c_i_ln(G).
A wide range of integrated MDACs is currently available
in resolutions from 8 to 16 bits, with devices up to 12 bits
available in multiple device-per-package
configurations.
The number of bits required for any application is a func._
v_,
,,,_
[-_
....
(3)
The control voltage, V,o,t_o_ , exponentially controls the
VCA gain. This produces the desirable result that the
control voltage linearly affects gain in decibels. Using a
conventional linear DAC to generate this control voltage
(Figure 3) provides digital control of gain or attenuation
stant step size in decibels per step, or dB/bit. As shown in
in equal,3, exponentially-spaced
Figure
a typical VCA has a virtual-ground
steps. This produces
current ainput
conand a current output intended for connection to the virtual
ground of an opamp current-to-voltage
converter. In contrast to the MDAC, this VCA inverts the current output
with respect to the input, but the eventual voltage output is
in phase with respect to the input.
Figure 2 - Typical MDAC
196
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DIGITALLY-CONTROLLABLE
AUDIO FILTERS
R
)in
C
/
/
lout
R
AND EQUALIZERS
_
'
/
Vref
_ DIGcIoT
DAC
VDAC
Y_
!
Figure 3 - VGA with Linear Control DAO
The combination of a VCA and DAC offers some unique
advantages to the audio designer in addition to the exponential control mentioned above. As shown in Figure 3,
the output of the controlling DAC may be lowpass filtered
(R2 and C) before application to the VCA control port.
This serves to attenuate any glitch energy that the DAC
may generate during transitions, and also serves to make
the transitions between discrete gain steps continuous,
thus eliminating the source of zipper noise. A further
practical advantage is that the DAC may be physically distant from the VCA (and close to the controlling processot), easing the task of keeping digitally generated noise
out of the audio signal path.
Figure 3 also illustrates a typical method of scaling and
offsetting the DAC output to suit the desired range and
resolution of VCA gain. The control voltage V¢ may be
expressed as:
]- (CODE_ R2
Vc =-VreJg_.'_'_'j_ll
R2 1
R3 J '
2.4 l'radeoffs
Applying the resistor-switch array devices in audio circuits typically involves simply replacing potentiometers
with their digitally-controlled equivalents in existing circuits. If their performance in the areas of dynamic range,
resolution, zipper noise, and distortion are adequate for
the application, their use is a relatively straightforward
exercise.
The following sections concentrate on the use of twoquadrant multipliers (MDACs or VCA-DAC combinations) as building blocks to implement digitally controlled
filter and equalization functions. As will be shown, using
these building blocks requires some revision of familiar
circuits. It is hoped that these examples will serve to illustrate the general approach to adapting existing analog circults to digital control.
(4)
The choice of which of these two building blocks to use is
very application dependent. The MDAC will typically
(though not in ail cases) offer very low distortion and
where CODE is the decimal value of the digital input code
and N is the number DAC input bits.
noise. As mentioned above, the discrete steps can lead to
audible zipper noise if parameters are adjusted while program material is being processed. If exponential control is
The voltage V_¢_,referred to in equations (2) and (3) is
usually temperature dependent, most commonly proportional to absolute temperature (PTAT). This causes the
gain of the VCA to vary with temperature at gains other
than unity. While this temperature dependence is relatively mild and may be ignored in many applications, for
the most demanding designs a convenient method of compensating is to make the DAC reference voltage Vrcf vary
in a similar manner. (For a PTAT control port characteristic, V,f must vary .33%/degree Celsius around 27 degreesCelsius.)
desired, extra cost will be incurred both in the requirement
for a DAC with higher resolution than the number of control steps would imply, as well as in the means to calculate
the correct codes to implement exponentially-spaced steps.
This typically takes the form of a ROM-based lookup table
used by the controlling processor.
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The use of a VCA-DAC combination will typically result
in slightly higher noise and distortion levels, though the
best currently available devices offer distortion levels below.03%,and dynamicrange ofover 115dB [5]. As
mentioned above, reai-time variation of filter parameters
while processing program material can be implemented
without zipper noise problems. Controlling software (and
197
HEBERTAND
FLORU
_VV_
R1
---11
C
R1
.; ,; _
yea
N
R
_
/
LOWPASS
x'_
HIGH PASS
Vc
Figure 4 - VGA-Gontrollecl
hardware) is often simplified by the exponential control
characteristic of the VCA.
First-Order
State-Variable
Filter
3.2 First Order Shelving
Though the VCA-DAC combination is used in most of the
examples below, it is generally possible to substitute an
MDAC for each instance ofa VCA and control DAC.
The designer will need to adjust the circuit for the inverted
input-to-output
of the MDAC
relative totothe
that of
the VCA, and totransfer
add additional
gain external
The circuit shown in Figures 5 is a first-order highfrequency equalizer. This circuit operates somewhat differently from its more familiar potenfiometer-based counterpart. The tnfnsfer function of the circuit of Figure 5 is:
Vout
--
MDAC
in instances where the VCA provides gain as well
as
attenuation,
Filters
_ + [G(R,+-_'2)+R2I
G+I
c')[G(Ri+R2)+R2]
(s
Vm
G+ii )R2]C '_[gl
-.I.-[Ri+(G+
J
+(G+
(7)
1)R2]
3. FIRST ORDER FILTERS AND EQUALIZERS
where G is, again, the VCA current gain.
3.1 Highpass
While this at first looks uninsightful, inspection reveals
that, at low frequencies (as s approaches 0), the transfer
function approaches -1. At high frequencies (as s approaches infinity), the transfer function approaches:
and Lowpass
Filters
The circuit shown in Figure 4 is a first-order state variable
filter offering both highpass and lowpass outputs [61. The
transfer functions at the two outputs are:
o
Vout
V_p
R_
V,---7
- s+_
(5)
and
Vhp
k R2 2 + 1
: -
V,, s--->oo
(8)
G + R_+R2
R2
To gain further insight, examine a few cases of values of
G. When G=I, the transfer function reduces to -1. Thus,
_
$'
G
(6)
where G is the VCA current gain, Vmis the input voltage,
V¥ is the lowpass output voltage, and Vhpis the highpass
output voltage. With the resistor ratios shown, the passband gain at both outputs is unity, and the cutoff frequency of each filter is controlled by the VCA gain.
Using a VCA with a control characteristic as described by
equations (2) and (3) along with a linear control DAC
causes each bit of the DAC input word to change the cutoff frequency by a constant fraction of an octave.
when the VCA gain is set to unity, the circuit's response is
flat. For the case where:
G ¢> Ri + R2
R2
'
equation (8), the expression for high-frequency gain
approaches:
Vout
Vin s-.o_
_
Ri__+ R2 for G >> R1 + R2
R2
R2
(9)
Similarly, for the case where:
198
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CONFERENCE
DIGITALLY-CONTROLLABLE AUDIO FILTERS AND EQUALIZERS
5
RI
T
Comp
yin
_
k--+
°_/_/_
!
A
+--q:<7.,
- ?
vou,
7
Ve
Figure 5 - VGA-Controlled
G <<
High Frequency
-- R2
R ] + R2 '
?----3--2for G <<
R._____g2
R2 + Ri
R2 + R1 '
(10)
example in Figure 6 illustrates· The individual frequency
response curves are for VCA gain stepped from -30 dB to
+30 dB in 3 dB.steps. The component values (referring to
Figure 5) are R,=45.3 kC2, R2=I0 kC2, R3= 45.3 kc2, and
C=2.2 nF. The curves asymptotically approach limits set
by the passive preemphasis and deemphasis networks.
However, for boost and cut commands substantially less
than these asymptotic limits (to about +/-10 dB in Figure
6), the boost and cut are nearly proportional to the VCA
gain. This suggests that the designer should choose preemphasis and deemphasis networks for more ultimate
boost and cut than is desired for the application to yield
th e most useful control characteristic.
An intuitive understanding of the circuit can be gained by
noting that when the VCA gain is much less than 1, the
VCA and A_ are effectively out Of the circuit and the circuit performance is governed entirely by the resistor from
the input to the summing junction of A 2 and the feedback
components around A 2. These components make up a familiar high-frequency deemphasis network. Conversely,
when the VCA gain is very large, the VCA, along with At
and A 2 form a block of high open loop gain. Under this
condition, the circuit behavior is governed by the components between the input and the summing junction of the
VCA (a high-frequency pre-emphasis network) and the
feedback resistor from the circuit output to the VCA sum-
The low-frequency shelving circuit shown in Figure 7 has
a transfer function:
ming
junction.
S+
].5.aaei'""i'"'i i_
i''"'i'"'"'
ii'i' ')_........ i""'T'""ii
, !,
!I,E,,
I
'A'_'
I ,
_
,
:
_G+(R_____)
_
rout
(G+I)R2c
_-
-
ta.am .......{--'t-' '-'t+. 't ........ !--.-.--i
....... [...... '!"ii...........i'" "'i"' i-¢-___
[
J [ i i
:
i
[
_i
;ii
i
'[i
;
! _ m_iimm_
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i i . _. __
_.,
Filter
The use of the VCA as a variable open-loop gain block resuits in a control characteristic that is not directly proportional to VCA gain, and thus this circuit does not offer
direct exponential (dB)control over boost and cut. The
control characteristic is nevertheless quite useful, as the
equation(8) approaches:
Vout
_
Vin s_oo
Shelving
i i t i iii i
_
I
I
J
I
'i '_':',,,,_/_"_.i
_
_ i ....
_..-*___i
! i '___d!
'
_ , _ _-_gE_--_-4- __L
i i iii
(J
S-I-
(11)
+1
(G+I)R2G
*
!
J
i
It may be analyzed in a similar fashion. FigureSshowsa
family of Curvestaken from a circuit with the following
,
!
_--_q..___.__
_-_...
_'"_ .....................
i.................................................
'__"_"'___"'_
' '-' '
component values (referring to Figure 7): R_ = 19.6 k_-2,
P_ = 84.5 k_2, R3 =40.2 kC2, C=22 nF. VCA gain is
_!,,_ ...............
_ _
I _I____
-xem ....._,
_......i..4.4.--[
i..1...
_ _
stepped from-30
_s_
I !
{
_ _ _"_*'
2.
la.
i
......
_
, _ _ __,_i_
_
___:._.-___
i____ {i _
_ i , ,_,,_1
i
_k m,
Figure 6 - High-Frequency Shelving Responses
(VCA Gain Varied 3 dB/Step)
AES 13th INTERNATIONAL CONFERENCE
dB to +30 dB in 3 dB steps.
Both of these shelving circuits exhibit TI-ID less than .01%
throughout the audio band and 20kHz-bandwidth noise
floors below -95 dBV.
A few practical notes are in order. The capacitor C_om_
(typically 10 pF to 47pF) shown with dotted connections
around A_ in both Figure 5 and Figure 7 is typically required to mitigate phase shift caused by the combination
199
HEBE RTAND FLORU
WX/_
v,,)_
yea
7
!
)ye,,
Ye
Figure 7 - VCA-Controlled
Low-Frequency Shelving Filter
of A_'s feedback resistor and the VCA's (or MDAC's) out-
[/hp
S2
=
put capacitance. In the case of high VCA gain the
Since thepole
VCAbecomes
has a finite
gain-bandwidth
R3/Ccomp
the dominant
pole in product,
the loop. it begills to contribute excess phase shift at high frequencies as
gain is increased. Depending on the device used and the
maximum boost required, the lead network Cq,adR_eaa
may
Vin
S2
Vbp
be required to maintain stability.
4. HIGHER ORDER FILTERS
4.1 State-Variable
2'
G, S
( G_'-_-_
R7
"l- _. R2 C j
Gl
R2CS
=
Vi.
Filters
Jr
se
(12)
(13)
G_ . ( .c,_-7_'_ 2'
+R-7+
[, R--C-.
)
and
GiG2
One of the most versatile filter building blocks is the familiarstate-variable
filter. Figure9 showsthiscircuit
.tpF'
=
adaptedof for
each
the VCA
three outputs
control [61.
(highpass,
The transfer
bandpass,
functions
and lowfor
15.ii/iii
i)
t)
ii i! ii iiii
!!!)
Y_!_iii
i
i
!_. _4-4__'h_ i
_:_ _
i__'_-....""x_i
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i
t
ii i
lt.8
ii i i ii
i_
i ! !!iii!
i
) i i i _iii
i
i i ) )_iii
i
) ! i i iiii
i
i I ) i iiii
)
i i i i ilil
i
i i i i iiii
,
_'_
I
i
i i i iiii
i
)
!
C..__--._------_)
........
ii
ii
i i i!i!il
i
ii ii
_ _1_1_
_iii
i
I
i iiil
i
i I i iiili
_
i_{i]_i
ilic__
i[ ii iil
i _iiii
i
i
i i i iiii
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;
;
;
i
i
i
i
i , _)_
i
;
;
'i ............,
i iI i
'z:lpii
· · .
......
;__=-.J_-"-<'_"--._d
_____,
_
ii ii ii iiil
iiti
, _ ) ) ,_
; ; 11;1
_
(14)
G1
( c;_-_- '_ 2'
s2 + R-_ s + (R_)
Vm
,
ii
tn
)'_2c'2
where:
vd
t_
_/1
_
e Vscale
= thecurrent gainofVCA_ and
%2
G2
e V.ca_ = the current gain of VCA 2.
TM
w-i_i
'
The resistor ratios around the circuit were chosen for unity
i i i i _ i __
_i iiii
i i .i i i iiii
i
_
_ i i ___
_
_
passband gain at all three outputsto simplifythe equai? i i iiiiii_-_--_
i i i _i;
ii,iii_i
i
-5.e_8
'-'
"_"=:¢'j._::'"-_P'rr_'_'"'_
........................
i--"i
i'i'i
...........
P''--i"
i-'i-'ii
{ "i--"--{--'i'--i
i i i iiii...............
ii
-_-+--_-_../_./-/r
.....
__ i :.
i _iNi
_ _ } {{ _{_{
{
dons, but this is not required. It should also be noted that
_ii/iii
'
_..__
..............
'_
i
':_..:t._d..!.ii
i
i
i
i
ii
ii
i
a bandreject output can be created by summing the low- ' i ' '
i ................
t""'""V'"'U"V'V7
TT'i
T""""T""'K'T"V7
TTT
i
'___
'_ [_'i_ '!!
i I t i i it ii
i
pass and highpass outputs.
i
i
i i i iiii
__.iiiil
i i ii iiii
_ii
i
i
i
i i iiifil
i i i iiil
t_
t
i i I i i_iI
I
i
i i iiiiil
1
_
tii_ _
By inspection,the naturalfrequencyand Q for all three
outputs are:
Vcl+Vc2
Figure 8 - Low-Frequency
Shelving
Responses
(VGA Gain Varied 3 dB/Step)
pass)
are:
_-_G2
(0. -
R2C
-
R2C
(15)
and
Q=
G2 = e
_1-1
200
e 2Vscale
2Vscal¢
(16)
Vt2- Vc 1
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DIGITALLY-CONTROLLABLE AUDIO FILTERS AND EQUALIZERS
m
R!
'XAA,
Vin
{t2
x_7 mI2
Vip
\Vhpi
v_2
Vbp
Figure 9 - VCA-Controlled State Variable Filter
^t stlani appe s at,. p n n co. olo r
natural frequency and Q (one of the main attractions of
the state-variable topology) will be rather awkward with
this circuit. However, this is another instance where the
exponential control characteristic of the VCA is very
handy. Adding sum and difference amplifiers to process
the control voltages to the VCAs as shown in Figure 10
_33 - _
Vcl= -A Vfreq+BVQ
(19)
yields the following:
Vo2 = -A Vpeq-BVQ.
(20)
Vcl
:
-
R33
Vfreq q-
Substituting these expressions into equations (15) and (16)
yields:
and
-A V qe q
COnVc2:-
'
yields:
_g3 R33
L'
q-R4') 'j VQ (17)
R;TR6'
- A and _77
_o' °
Vfreq-
VQ
4 01(32
e rs,at,
- --
(21)
(18)
and
Choosing resistor values such that:
Q =
G2 = e _s*_*.
'(_1
AAA
RI
T v:vs
v,.)
(22)
-BVQ
Vhp
C-tc
_
?
-
,,/
vip
Vbp
Figure 10 - VCA-Controlled State Variable Filter With Control-Voltage Conditioning Circuitry
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201
HEBERT AND FLORU
The
and Q are now
funcfions natural
of V_q frequency
and Vq, respectively.
Theindependent
natural frequency
Vout-boost
_ 1+
_ UR7::S
(G3
,, c,_
Gl,
(G_'_
s2 + s--_.'s + _. RT
will
manner
againwith
be V_eq.
conveniently
Varying varied
the Q in
in athis
"volts-per-octave"
fashion is less familiar, but not difficult. For example, setting Vq to 0 volts
Vin
(0 dB)sets Q=I, setting Vq to the voltage corresponding to
6 dB VCA gain sets Q=2, etc.
( Gl )
( Gd--__2
s 2 + G3 ,.R'-_.., s + _. R_)
2
)
=
(24)
The values of P_ and C should be chosen so that the VCAs
are used primarily in attenuation mode, rather than requiring high VCA gain. This will maximize the bandwidth of
the VCAs and minimize "Q-enhancement" problems. A
useful approach is to choose P_ and C such that:
s2
G1 , ( od---_-_
_ 2
+ R'-_._ + [, R----_--J
where G3= the current gain of VCA 3.
With switch Si in the cut position, the transfer function
I----L-- --fmax
2rcR 2 C
(23)
where fro= is the maximum natural frequency desired.
becomes:
Vout-cut
Figure 11 shows the state-variable filter adapted for
MDAC control. Note that the feedback paths have been
changed to reflect the fact that the integrators are now inverting rather than non-inverting.
Independent control of
Vi-----'_-
Evaluating
_.R2CjS q-
_
R---'-_)
f G, '_
( od---__- -_2'
s 2 + G3 _.R-'7) S + [, RT)
(25)
the magnitude of both of these expressions at
natural frequency and Q is performed in the same manner,
though exponential control is more computationally
the natural frequency of the filter, s =jo)n, 'yields:
complex.
4.2 Parametric
I r
Vout-Ooost
Equalizers
Figure 12 shows a parametric equalizer circtdt utilizing
the state-variable filter described above. Noting equation'
=
G3 = e
vsca_e
(26)
_?*n
Vi.
and
(13) (the transfer function to the bandpass output of the
filter), the transfer function of the parametric equalizer
with switch S l in the "boost" position is:
1
-_3
_j_o. = G---3-= e %_te.
Vout-cut
Vin
(27)
R1
, w
I
C
RI
+//
RI
C
+//
-+//
RI
H]GHPASS
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Figure 11 - MDAC-Controlled
202
--t',
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State Variable Filter
AES 13th INTERNATIONAL CONFERENCE
DIGITALLY-CONTROLLABLE AUDIO FILTERS AND EQUALIZERS
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Thus, the boost and cut at the center frequency are directly
proportional to the gain of VCA 3 and can be controlled in
a "volts-per-dB" manner via its control voltage. The gain
of VCA 3 is always varied between 0 dB and the gain corresponding to the desired maximum boost -- even for cut
operation. Switch S, would typically be implemented with
a solid state switch, and the controller would be programmed to change the switch setting while the gain of
VCA 3is set to unity (G3=I). Under these conditions there
is no signal present at the output of A, due to the cancellation of signal currents at the summing junction of A6.
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gain, the characteristics revert to those of what are cornmonly known as asymmetric parametric equalizers. This
type is preferred by some users. Figure 16 shows measurements from the same prototype illustrating tiffs mode of
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AES 13th INTERNATIONAL CONFERENCE
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with the following values (referring to Figure 12):
R_=I0 k£-l, R_=4.99 1_, R3=I0 1_1, R4=20 1_-2,and
C=1.5 nF. The measured 20kHz-bandwidth noise floor of
this circuit was typically below -96 dBV when set for flat
response, below -88 dBV when set for -15 dB cut, and below -85 dBV when set for +15 dB boost. Distortion was
below .05% in the audio band under all modes.
This type of parametric equalizer seems to be the most
prevalent, and produces symmetrical boost/cut characteristics as illustrated in Figures 13, 14, and 15. These
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203
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From this we derive the natural frequency (COn)
and Q to
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of the FCA, the transfer function of this circuit is:
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204
AES
13th
INTERNATIONAL
CONFERENCE
DIGITALLY-CONTROLLABLE AUDIO FILTERS AND EQUALIZERS
5. SUMMARY AND CONCLUSIONS
,,.
T
c
....
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R2
the
of two-quadrant
multipliers
implement
digital
The use
authors
have presented
several to
examples
illustrating
controlofanalogaudiofilters. It has beenshownthat,
tion and
filtermodifications,
circuits that have
a standard
part of
with
minor
many become
of the familiar
equalizathe audio engineer's toolbox can be adapted to digital
_7
_:__
Two common versions of the two-quadrant multiplier
were discussed. The MDAC, which performs its multiplicontrol.
cation in discrete steps, yields mi_fimalperformance degradation due to its essentially passive nature. This comes
v_
Figure 18 - Variable-Q Sallen
and Key Highpass
at the cost of the potential for zipper noise, and, in applications requiring fine exponential control of amplitude or
frequency parameters, higher cost for high-resolution
DACs and more complex control firmware.
For G=I, this reduces to the familiar expression for the Q
of a Sallen and Key highpass filter:
1 IR2
Q = _/,_
'_--- .
V_i
(31)
The curves in Figure 19 illustrate how Q varies with VCA
gain. For these curves R_ and P_ were chosen to be
3.32 k_Qand 53.6 k_Qrespectively, setting the initial Q (at
0 dB VCA gain) to 2. The VCA gain is stepped from
0 dB to -4 dB is I dB steps. Q can also, of course, be increased by increasing VCA gain. Caution
should be ob2Ri
served, however, since if G exceeds _
becomesan oscillator.
The combination of VCAs and inexpensive control DACs
offers continuous transitions between discrete parameter
settings, thus avoiding zipper noise. VCAs with an exponential gain-control characteristic offer direct decibel control, yielding high resolution control of filter parameters
over a wide range. This also simplifies controller firmware for frequency and amplitude parameters that are traditionally dealt with in exponential fashion. The
performance available with today's VCAs rivals or exceeds
current DSP-based systems at much lower cost.
+ 1 the circuit
It is hoped that these exampleswill serveas a starting
point for engineers wishing to enhance the functionality
A corresponding lowpass version is, of course, also
possible,
of
their designs by adding the flexibility that digital control
brings.
6. REFERENCES
[1] Dallas Semiconductor Corporation, "Digital Potentiometer Family Overview", Dallas, Texas 75244.
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[2] National Semiconductor Corporation, "Linear Appli!
i[.............
ii.......L.....!......L..i..A...t......._.._-_---_-_,
i ! _i/_ "---4_ i
'r _,!
..e i..........................
cation Specific IC's Databook", pp. 1-172 through 1-186,
i
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i
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i i i i i ii
-6'e_i ..........................
[..............
i" -"T'"'"'i.....
i' '"_.....................
i...............
t"-"t'"'"t"'"Vr"'i'"i'"i Clara, California 95052 (1993).
i
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i i i i iii[
--12.mi
_i..........
i _i, i...i,
{...i
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__i.............
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"LMC835Digital ControlledGraphicEqualizer" Santa
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[3] NJR Corporation, "CMOS ICDatabook", pp. ll-I
I
[
-24..e!
! _ t _ !_
{
I [ I I I i I!
through11-23, NJU7305, NJU7306, andNJU7307Da!......f_...__....L.
...............!....!_!_
!........
tasheets, Mountain View, California 94043 (1992).
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_i..............
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[4] Analog Devices, Incorporated,, "Data Converter Refer[
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_............._.........._.......i......_....._....._..._..;
.........................
_...............
3...........g...._.._......_....._....;....i...!
ence Manual",
pp. 2-247 through
2-252, AD7111
Data
i
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i i i i _ iii
i
i i i i i iii
Sheet, Norwood, Massachusetts 02062(1992).
1_
lk
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Figure 19 - Variable-O Highpass Responses
(FCA gain varied from 0 dB to -4 dB in I dB steps)
[5] THAT Corporation, "2150-Series IC VoltageControlled Amplifiers Datasheet", Marlborough, Massachusetts 01752 (1993).
[6] Allen, William A., "Applications of Voltage
Controlled Amplifiers", presented at the 70 thConvention
of the Audio Engineering Society, preprint 1846.
AES 13th INTERNATIONAL CONFERENCE
205