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

Band-Pass Filter Design
16-28
|A| [dB]
0
–3
|A| [dB]
0
–3
0 1 Ω
0
Figure 16–31. Low-Pass to Band-Pass Transition
The corner frequency of the low-pass filter transforms to the lower and upper –3 dB frequencies
of the band-pass, Ω 1 and Ω 2. The difference between both frequencies is defined
as the normalized bandwidth ∆Ω:
2 1
The normalized mid frequency, where Q = 1, is:
m 1 2 · 1
In analogy to the resonant circuits, the quality factor Q is defined as the ratio of the mid
frequency (f m) to the bandwidth (B):
Q fm fm
B f2 f1 1
2 1 1
Ω 1
∆Ω
1
Ω 2
Ω
(16–8)
The simplest design of a band-pass filter is the connection of a high-pass filter and a lowpass
filter in series, which is commonly done in wide-band filter applications. Thus, a firstorder
high-pass and a first-order low-pass provide a second-order band-pass, while a
second-order high-pass and a second-order low-pass result in a fourth-order band-pass
response.
In comparison to wide-band filters, narrow-band filters of higher order consist of cascaded
second-order band-pass filters that use the Sallen-Key or the Multiple Feedback (MFB)
topology.