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SBOS275C JUNE 2003 REVISED OCTOBER 2004
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17
Adding the VCA810 as shown in Figure 13 permits
amplification of the signal applied to capacitor C, and
produces voltage control of the frequency f
Z
. Amplified
signal voltage on C increases 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 control expression
f
Z
1
R
1
GC
.
2
Another factor limits the high-frequency performance of
the resulting high-pass filter: the finite bandwidth of the op
amp. This limits the frequency duration of the equalizer
response. Limitations such as bandwidth and stability are
clearly shown in Figure 14.
OPA846
VCA810
V
C
50
50
OPA820
V
OA
C
2
μ
F
R
3
3
V
O
R
2
750
R
1
750
V
I
F
Z
1
2
π
x
(
GR
1
+ R
3
C
withG= 10
≈
2(V
C
+1)
Figure 13. Tunable Equalizer
Other limitations of this circuit are stability versus VCA810
gain and input signal level for the circuit. Figure 14 also
illustrates these two factors. As the VCA810 gain
increases, the crossover slope between the A
OL
curve of
the OPA846 and noise gain will be greater than
20dB/decade, rendering the circuit unstable. The signal
level for high gain of the VCA810 will meet two limitations:
the output voltage swings of both the VCA810 and the
OPA846. The expression V
OA
= GV
I
relates these two
voltages. Thus, an output voltage limit V
OAL
constrains the
input voltage to V
I
≤
V
OAL
/G.
With the components shown, BW = 50kHz. This
bandwidth provides an integrator response duration of four
decades of frequency for f
Z
= 1Hz, dropping to one decade
for f
Z
= 10kHz.
100
90
80
70
60
50
40
30
20
10
0
Frequency (Hz)
1
10
100
1k
10k
100k
1M
10M
100M
G
G = +40dB
G = +15dB
G =
15dB
G =
40dB
A
OL
Figure 14. Amplifier Noise Gain and A
OL
for
Different Gain
VOLTAGE-CONTROLLED BAND-PASS
FILTER
The variable gain of the VCA810 also provides voltage
control over the center frequency of a band-pass filter. As
shown in Figure 15, this filter follows from the
state-variable configuration with the VCA810 replacing the
inverter common to that configuration. Variation of the
VCA810 gain moves the filter’s center frequency through
a 100:1 range following the relationship of Equation (5):
f
O
10
2
VC
RC
1
As before, variable gain controls a circuit time constant to
vary the filter response. The gain of the VCA810 amplifies
or attenuates the signal driving the lower integrator of the
circuit. This amplification alters the effective resistance of
the integrator time constant, producing the response of
Equation (6):
V
O
V
I
s
nRC
s
2
s
nRC
G
R
2
C
2
(5)
(6)