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

Band-Rejection Filter Design
16-36
|A| — Gain — dB
5
0
–5
–10
–15
–20
–25
–30
A1
A2
Q = 1
–35
100 1 k 10 k 100 k
f — Frequency — Hz
Q = 10
Figure 16–35. Gain Responses of a Fourth-Order Butterworth Band-Pass and its Partial Filters
16.6 Band-Rejection Filter Design
A band-rejection filter is used to suppress a certain frequency rather than a range of frequencies.
Two of the most popular band-rejection filters are the active twin-T and the active Wien-
Robinson circuit, both of which are second-order filters.
To generate the transfer function of a second-order band-rejection filter, replace the S
term of a first-order low-pass response with the transformation in 16–18:
which gives:
s 1 s
A(s) A 0 1 s 2
1 ·s s 2
1 M
(16–18)
(16–19)
Thus the passband characteristic of the low-pass filter is transformed into the lower passband
of the band-rejection filter. The lower passband is then mirrored at the mid frequency,
f m (Ω=1), into the upper passband half (Figure 16–36).