"Chapter 1 - The Op Amp's Place in the World" - HTL Wien 10

Band-Rejection Filter Design
16-38
V IN
Figure 16–38. Active Twin-T Filter
C
R
R/2
The transfer function of the active twin-T filter is:
2C
k1 s
A(s)
2
1 2(2 k)·s s2 C
R
R 1
R 2
V OUT
(16–21)
Comparing the variables of Equation 16–21 with Equation 16–20 provides the equations
that determine the filter parameters:
mid-frequency:
inner gain:
passband gain:
fm 1
2RC
G 1 R 2
R 1
A 0 G
Q
1
rejection quality:
2(2 G)
The twin-T circuit has the advantage that the quality factor (Q) can be varied via the inner
gain (G) without modifying the mid frequency (f m). However, Q and A m cannot be adjusted
independently.
To set the mid frequency of the band-pass, specify fm and C, and then solve for R:
R 1
2fmC
Because of the dependency between Q and A m, there are two options to solve for R 2: either
to set the gain at mid frequency:
R 2 A 0 1R 1