DESIGN AND ANALYSIS OF ANALOG FILTERS A Signal ...

6. 1 INTRODUCTION
CHAPTER 6
ELLIPTIC FILTERS
Elliptic filters, also known as Cauer filters in recognition of the contributions
of Wilhelm Cauer to elliptic, as well as other filters, are noted for having
an equiripple passband magnitude response similar to Chebyshev Type I
filters, and an equiripple stopband magnitude response similar to Chebyshev Type II
filters. They require the lowest order of all the classical filters to meet given design
specifications. As was noted at the opening to Chapter 4, although a logical
presentation of classical analog filters frequently follows the order of Butterworth,
Chebyshev Type I, Chebyshev Type II, and elliptic, such as is done in this book, this
is not the chronological order, as was shown in Section 1. 4.
In this chapter the elliptic filter magnitude response is defined, and it will be
observed that it satisfies the Analog Filter Design Theorem. Explicit formulas for the
design and analysis of elliptic 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 elliptic filters, the phase response, phase delay, group delay, and timedomain
response characteristics are investigated.
The magnitude-squared frequency response of an elliptic filter is defined
below.
Definition of the magnitude-squared elliptic response: