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

16.5.1 Second-Order Band-Pass Filter
Active Filter Design Techniques
Band-Pass Filter Design
To develop the frequency response of a second-order band-pass filter, apply the transformation
in Equation 16–7 to a first-order low-pass transfer function:
A(s) A0 1 s
1
s 1 s Replacing s with
yields the general transfer function for a second-order band-pass filter:
A(s)
A0 ··s
1 ·s s2 (16–9)
When designing band-pass filters, the parameters of interest are the gain at the mid frequency
(A m) and the quality factor (Q), which represents the selectivity of a band-pass
filter.
Therefore, replace A 0 with A m and ∆Ω with 1/Q (Equation 16–7) and obtain:
A(s)
Am
Q ·s
1 1
·s s2
Q
(16–10)
Figure 16–32 shows the normalized gain response of a second-order band-pass filter for
different Qs.
|A| — Gain — dB
0
–5
–10
–15
–20
–25
–30
–35
Q = 1
Q = 10
–45
0.1 1
Frequency — Ω
10
Figure 16–32. Gain Response of a Second-Order Band-Pass Filter
16-29