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

|A| [dB]
0
–3
|A| [dB]
0
–3
0 1 Ω
0
Figure 16–36. Low-Pass to Band-Rejection Transition
Ω 1
∆Ω
1
Band-Rejection Filter Design
The corner frequency of the low-pass transforms to the lower and upper –3-dB frequencies
of the band-rejection filter Ω 1 and Ω 2. The difference between both frequencies is the
normalized bandwidth ∆Ω:
max min
Identical to the selectivity of a band-pass filter, the quality of the filter rejection is defined
as:
Q fm
1
B
Therefore, replacing ∆Ω in Equation 16–19 with 1/Q yields:
16.6.1 Active Twin-T Filter
A(s) A0 1 s2 1 1
·s s2
Q
Ω 2
Active Filter Design Techniques
Ω
(16–20)
The original twin-T filter, shown in Figure 16–37, is a passive RC-network with a quality
factor of Q = 0.25. To increase Q, the passive filter is implemented into the feedback loop
of an amplifier, thus turning into an active band-rejection filter, shown in Figure 16–38.
V IN
Figure 16–37. Passive Twin-T Filter
C
R/2
2C
C
R R
V OUT
16-37