
PRODUCT SPECIFICATION
RC4156/RC4157
10
These equations suggest a tuning sequence where
w
is first
trimmed via R1 or R2, then Q is trimmed by varying R7
and/or R3. An important advantage of the state-variable
bandpass filter is that Q can be varied without affecting
center frequency
w
0
.
This analysis has assumed ideal op amps operating within
their linear range, which is a valid design approach for a
reasonable range of
w
0
and Q. At extremes of
w
0
and at high
values of Q, the op amp parameters become significant. A
rigorous analysis is very complex, but some factors are par-
ticularly important in designing active filters.
1.
The passive component values should be chosen such
that all op amps are operating within their linear region
for the anticipated range of input signals. Slew rate, out-
put current rating, and common-mode input range must
be considered. For the integrators, the current through
the feedback capacitor (I = C dV/dt) should be included
in the output current computations.
2.
From the equation for Q, it should seem that infinite Q
could be obtained by making R7 zero. But as R7 is made
small, the Q becomes limited by the op amp gain at the
frequency of interest. The effective closed-loop gain is
being increased directly as R7 is made smaller, and the
ratio of open-loop gain to closed-loop gain is becoming
less. The gain and phase error of the filter at high Q is
very dependent on the op amp open-loop gain at w
0
.
3.
The attenuation at extremes of frequency is limited by
the op amp gain and unity-gain bandwidth. For integra-
tors, the finite open-loop op amp gain limits the accu-
racy at the low-end. The open-loop roll-off of gain limits
the filter attenuation at high frequency.
The RC4156 quad operational amplifier has much better fre-
quency response than a conventional 741 circuit and is ideal
for active filter use. Natural frequencies of up to 10 kHz are
readily achieved and up to 20 kHz is practical for some con-
figurations. Q can range up to 50 with very good accuracy
and up to 500 with reasonable response. The extra gain of the
RC4156 at high frequencies gives the quad op amp an extra
margin of performance in active-filter circuits.
Schematic Diagram
(1/4 shown)
65-0735
(11)
-V
D1
F1
(4)
+V
(1,7,8,14)
Outputs
Q1
To
Next
Amplifier
Q6
R2
10K
(2,6,9,13)
- Input
(3,5,10,12)
+ Input
R1
4900
Q2
Q4
Q5
Q8
R3
18K
Q9
R4
22K
Q10
Q7
Q3
R9
30
Q13
Q12
R5
30K
D2
C1
Q11
Q17
Q14
R7
20
R6
20
Q16
Q15
R8
150