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Band-Pass Filter Design
16.5.1 Second-Order Band-Pass Filter
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:
Replacing s with
A(s) A 0
1 s
1 s 1
s
yields the general transfer function for a second-order band-pass filter:
A(s)
A0··s
1 ·s s 2
(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)
A m
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.
0
–5
–10
Q = 1
|A| — Gain — dB
–15
–20
–25
Q = 10
–30
–35
–45
0.1 1 10
Frequency — Ω
Figure 16–32.
Gain Response of a Second-Order Band-Pass Filter
Active Filter Design Techniques
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