DESIGN AND ANALYSIS OF ANALOG FILTERS A Signal ...

CHAPTER 5
CHEBYSHEV TYPE II FILTERS
Chebyshev Type II filters are closely related to Chebyshev Type I filters, and
are noted for having a flat passband magnitude response, and an equiripple
response in the stopband. As was noted in Chapter 4, the Chebyshev
Type I response is often simply referred to as the Chebyshev response. Similarly, the
Chebyshev Type II response is often referred to as the Inverse Chebyshev response,
for reasons that will become clear as the response is developed below.
In this chapter the Chebyshev Type II response is defined, and it will be
observed that it satisfies the Analog Filter Design Theorem. Explicit formulas for the
design and analysis of Chebyshev Type II filters, such as Filter Selectivity, Shaping
Factor, the minimum required order to meet design specifications, etc., will be
obtained. From the defining the corresponding H(s) will be determined,
and means for determining the filter poles and zeros are found. To complete the study
of lowpass, prototype Chebyshev Type II filters, the phase response, phase delay,
group delay, and time-domain response characteristics are investigated.
5.1 EQUIRIPPLE STOPBAND MAGNITUDE
Suppose that is the magnitude-squared frequency response of a
Chebyshev Type I filter according to (4.1):
Let be obtained from (5.1) as follows:
Finally, the desired magnitude-squared response is obtained by replacing by
in (5.2):