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PRODUCT SPECIFICATION
RC4156/RC4157
8
characteristics. The values shown for C1, C2, R4, R5 and R6
are arbitrary. Pre-selecting their values will simplify the filter
tuning procedures, but other values can be used if necessary.
The generalized transfer function for the state-variable active
filter is:
Filter response is conventionally described in terms of a nat-
ural frequency
w
0
in radians/sec, and Q, the quality of the
complex pole pair. The filter parameters
w
0
and Q relate to
the coefficients in T(s) as:
and
T s
( )
a
s
2
s
a
s
b
1
s
a
0
+
+
b
0
+
+
-----------------------------------
=
w
0
b
0
=
Q
0
b
0
------
=
The input configuration determines the polarity (inverting or
non-inverting), and the output selection determines the type
of filter response (lowpass, bandpass, or highpass).
Notch and all-pass configurations can be implemented by
adding another summing amplifier.
Bandpass filters are of particular importance in audio and
telecommunication equipment. A design approach to band-
pass filters will be shown as an example of the state-variable
configuration.
Design Example Bandpass Filter
For the bandpass active filter (Figure 16) the input signal is
applied through R3 to the inverting input of the summing
amplifier and the output is taken from the first integrator
(V
BP
). The summing amplifier will maintain equal voltage at
the inverting and non-inverting inputs (see Equation 1).
Figure 15. 2-Pole State-Variable Active Filter
65-0751
C2
1000 pF
V
Lowpass
Output
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C
R2**
C1
1000 pF
R5
100K
R4
10K
R1**
R6
100K
V
Highpass
Ouput
V
Bandpass
Output
V1
V
N
R3*
R8*
R7*
* Input connections are chosen for inverting or non-inverting response. Values of
R3,R7,R8 determine gain and Q.
** Values of R1 and R2 determine natural frequency.
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B
4156/57
A
10
9
8
5
6
7
3
2
1
Equation 1.
-------R3
HP
s
( )
R5
---R+
R4
+
R5
R3
+
-------R3
LP
s
( )
R4
---R+
R5
+
R4
R3
+
-------R4
IN
s
( )
R5
---R+
R3
+
R5
R4
+
R7
R6
BP
s
( )
+
+
+