VCA610
12
To visualize the circuit’s operation, consider a circuit condi-
tion and an approximation that permit replacing the VCA610
and R
with short circuits. First consider the case where the
VCA610 produces G = 1. Then, replacing this amplifier with
short circuit leaves the operation unchanged. In this shorted
state, the circuit is simply a voltage amplifier with an R–C
bypass around R
. The resistance of this bypass, R
, serves
only to phase compensate the circuit and practical factors
make R
<< R
. Neglecting R
for the moment, the circuit
becomes just a voltage amplifier with capacitive bypass of
R
1
. This circuit produces a response zero at f
Z
= 1/2
π
R
1
C.
Adding the VCA610 as shown permits amplification of the
signal applied to capacitor C and produces voltage control
of the frequency f
Z
. Amplified signal voltage on C in-
creases the signal current conducted by the capacitor to the
op amp feedback network. The result is the same as if C
had been increased in value to GC. Replacing C with this
effective capacitance value produces the circuit’s control
expression f
Z
= 1/2
π
R
1
GC.
Two factors limit the high-frequency performance of the
resulting high-pass filter. The finite bandwidth of the op
amp and the circuit’s phase compensation produce response
poles. These limit the frequency duration of the high-pass
response. Selecting the R
phase compensation with the
equation R
=
√
(R1/2
π
f
C) assures stability for all values of
G and sets the circuit’s bandwidth at BW =
√
(f
/2
π
R
C).
Here, f
is the unity-gain crossover frequency of the op amp
used. With the components shown, BW = 100kHz. This
bandwidth provides a high-pass response duration of five
decades of frequency for f
Z
= 1Hz, dropping to one decade
for f
Z
= 10kHz.
The output voltage limit of the VCA610 imposes an input
voltage limit for the filter. The expression V
= GV
relates
these two voltages. Thus, an output voltage limit V
OAL
constrains the input voltage to V
I
≤
V
OAL
/G.
FIGURE 13. Adding the VCA610 to a State-Variable Filter Produces a Voltage-Controlled BandPass Filter With a Center
Frequency Variable Over a 100:1 Range.
VOLTAGE-CONTROLLED BAND-PASS FILTER
The VCA610’s variable gain also provides voltage control
over the center frequency of a band-pass filter. Shown in
Figure 13, this filter follows from the state-variable configu-
ration with the VCA610 replacing the inverter common to
that configuration. Variation of the VCA610 gain moves the
filter’s center frequency through a 100:1 range following the
relationship f
O
= [10
–(V
C
+ 1)
]/2
π
RC.
As before, variable gain controls a circuit time constant to
vary the filter response. The gain of the VCA610 amplifies
or attenuates the signal driving the lower integrator of the
circuit. This alters the effective resistance of the integrator
time constant producing the response
Evaluation of this response equation reveals a passband gain
of A
= –1, a bandwidth of BW = 1/2
π
nRC and a selectivity
of Q = n10
–(V
C
+ 1)
. Note that variation of control voltage V
C
alters Q but not bandwidth.
The gain provided by the VCA610 restricts the output swing
of the filter. Output signal V
must be constrained to a level
that does not drive the VCA610 output, V
, into its satura-
tion limit. Note that these two outputs have voltage swings
related by V
= GV
. Thus, a swing limit V
OAL
imposes a
circuit output limit of V
OL
≤
V
OAL
/G.
–s/nRC
s
2
+ s/nRC + G/R
2
C
2
V
O
V
I
=
VCA610
OPA620
OPA620
5k
R
330
nR
5k
nR
0.047μF
C
V
C
R
330
V
OA
0.047μF
C
V
I
V
O
V
O
V
I
–s/nRC
s
2
+ s/nRC + G/R
2
C
2
f
O
=10
–(VC + 1)
2
π
RC
BW =
1
2
π
nRC
Q = n10
–(VC + 1)
A
O
= –1
=