07-07-2012, 02:05 PM
Active Filter Design Techniques
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Introduction
A filter is a device that passes electric signals at certain frequencies or
frequency ranges while preventing the passage of others. — Webster.
Filter circuits are used in a wide variety of applications. In the field of telecommunication,
band-pass filters are used in the audio frequency range (0 kHz to 20 kHz) for modems
and speech processing. High-frequency band-pass filters (several hundred MHz) are
used for channel selection in telephone central offices. Data acquisition systems usually
require anti-aliasing low-pass filters as well as low-pass noise filters in their preceding signal
conditioning stages. System power supplies often use band-rejection filters to suppress
the 60-Hz line frequency and high frequency transients.
In addition, there are filters that do not filter any frequencies of a complex input signal, but
just add a linear phase shift to each frequency component, thus contributing to a constant
time delay. These are called all-pass filters.
Fundamentals of Low-Pass Filters
where the complex frequency variable, s = jω+σ , allows for any time variable signals. For
pure sine waves, the damping constant, σ, becomes zero and s = jω .
For a normalized presentation of the transfer function, s is referred to the filter’s corner
frequency, or –3 dB frequency, ωC, and has these relationships:
Butterworth Low-Pass FIlters
The Butterworth low-pass filter provides maximum passband flatness. Therefore, a Butterworth
low-pass is often used as anti-aliasing filter in data converter applications where
precise signal levels are required across the entire passband.
Figure 16–5 plots the gain response of different orders of Butterworth low-pass filters versus
the normalized frequency axis, Ω (Ω = f / fC); the higher the filter order, the longer the
passband flatness.
Bessel Low-Pass Filters
The Bessel low-pass filters have a linear phase response (Figure 16–7) over a wide frequency
range, which results in a constant group delay (Figure 16–8) in that frequency
range. Bessel low-pass filters, therefore, provide an optimum square-wave transmission
behavior. However, the passband gain of a Bessel low-pass filter is not as flat as that of
the Butterworth low-pass, and the transition from passband to stopband is by far not as
sharp as that of a Tschebyscheff low-pass filter (Figure 16–9).