DESIGN AND ANALYSIS OF ANALOG FILTERS A Signal ...

18 DESIGN AND ANALYSIS OF ANALOG FILTERS:
Chapter 3, Butterworth Filters, is a presentation of the first specific filter
type presented in the book. It is historically one of the first developed methods, and
is very commonly used in practice. It is designed to yield a maximally-flat magnitude
response in the passband (actually at DC) and is frequently referred to as the
maximally-flat design. The design is based on Butterworth polynomials.
Chapter 4, Chebyshev Type I Filters, is a presentation of the first of two
filter designs based on Chebyshev polynomials. Type I filters have ripple in the
passband of an equal across-the-band magnitude and of a specified amount, with the
response monotonically falling off through the transition band and the stopband.
These filters will usually meet a set of magnitude specifications with a lower order
than will a comparable Butterworth design, but have less desirable phase response and
time-domain characteristics.
Chapter 5, Chebyshev Type II Filters, covers the second filter design based
on Chebyshev polynomials, having a flat magnitude response in the passband, but
having ripple in the stopband of an equal across-the-band magnitude (referred to as
equiripple) and of a specified amount. As with Type I filters, these filters will usually
meet a set of magnitude specifications with a lower order than will a comparable
Butterworth design, in fact, with the identical order as a Chebyshev Type I design.
However, this design requires specified finite-value zeros in the transfer function,
whereas a Chebyshev Type I design has no finite-value zeros for a lowpass filter.
Therefore a Chebyshev Type II design has a somewhat more complex transfer function
than does either a Butterworth or a Chebyshev Type I design. It also has less
desirable phase response and time-domain characteristics than does a Butterworth
design.
Chapter 6, Elliptic Filters, presents filters that have equiripple characteristics
in both the passband and the stopband, but fall off monotonically through the
transition band. This design is based on Chebyshev rational functions, which in turn
are dependent upon Jacobian elliptic functions. Among common filter types, elliptic
filters will meet given magnitude specifications with the lowest order. However, they
have very poor phase response and time-domain characteristics. As will be seen in
Part II (more specifically, Chapter 12), they also can have implementation
components with large sensitivities (very critical component values).
Chapter 7, Bessel Filters, covers filters that are designed for maximally-flat
group delay, and are closely related to Bessel polynomials. While optimized for flat
group delay, the magnitude response is that of a lowpass filter. Since flat group delay
is analogous to a linear phase response, Bessel filters have very good phase
characteristics. They also have very good time-domain characteristics. However, for
a given set of magnitude specifications, a Bessel filter requires the highest order of any
of the common filter types.
Chapter 8, Other Filters, presents a few of the filter design methods that have
been reported, other than the above classical filters, but are less known. These filters
have certain desirable characteristics, but are generally only marginally superior to the
Chapter 1
Introduction