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Op Amps27

This document describes the transformation of a low-pass filter into a band-pass filter and defines key terms such as the lower and upper -3 dB frequencies, normalized bandwidth, normalized mid frequency, and quality factor. It also explains that the simplest design of a band-pass filter consists of connecting a high-pass and low-pass filter in series and that higher order narrow-band filters are made of cascaded second-order band-pass filters.

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27 views1 page

Op Amps27

This document describes the transformation of a low-pass filter into a band-pass filter and defines key terms such as the lower and upper -3 dB frequencies, normalized bandwidth, normalized mid frequency, and quality factor. It also explains that the simplest design of a band-pass filter consists of connecting a high-pass and low-pass filter in series and that higher order narrow-band filters are made of cascaded second-order band-pass filters.

Uploaded by

lecuellarq85gmailcom
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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|A| [dB] |A| [dB]

0 0
–3 –3

∆Ω

0 1 Ω 0 Ω1 1 Ω2 Ω

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 fre-
quencies of the band-pass, Ω1 and Ω2. The difference between both frequencies is de-
fined as the normalized bandwidth ∆Ω:

DW + W 2 * W 1

The normalized mid frequency, where Q = 1, is:

W m + 1 + W 2·W 1

In analogy to the resonant circuits, the quality factor Q is defined as the ratio of the mid
frequency (fm) to the bandwidth (B):

fm fm 1
Q+ + + + 1 (16–8)
B f2 * f1 W2 * W1 DW

The simplest design of a band-pass filter is the connection of a high-pass filter and a low-
pass filter in series, which is commonly done in wide-band filter applications. Thus, a first-
order 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.

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