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362 Other Direct Filter Design Methods
ANTIMET
ELLIP FLTR~CT12/78,1008
REJECTION,RIPPLE(DS),1/2-DEG(2-15l ~TYPE(A,B,OR C):
83.3068 .17728767 4 C
u- .392699067 AO~ .253168244 EP= .414213539
E= .383100151
E= .293985074
E= .159524088
RE=-.0941605422 SE= .447245616
RE=-.232749695 SE= .187680214
RF=-.0417918631 SF= 1.01712478
RF=-.138269216 SF= .902058076
RF=-.260576346 SF= .637014303
RF=-.390335577 SF= .21738535
LD RESIS= 1 (1 )
L(C) C(L) PEAK
1 1.20340853
2 1.09152826 1.37701951 2.47036986
3 1.35005027 1.5232667 1.68577457
4 1.58486991 1.32003532 1.47480406
5 1.39727972 STPED ED8E=.1.45323639
TESTS 1.2381468E-(15 1.28149986E-06
Figure 9.25.
Sample run for an antimetric type-c filter.
9.3.6. Summary of Doubly Tenninated Elliptic Filters. The effect of trap
resonance on elliptic filter input impedance is such that it is easy to determine
the first lumped-element and the next trap-branch-element values. All that is
required is the input impedance and its time delay at that trap's frequency;
both are available from the poles and zeros of the elliptic transfer function.
The computation is made easier by the fact that the input reflection coefficient
is necessarily unity at any trap frequency. The poles and zeros are Jacobian
elliptic functions that are easy to compute. Improved accuracy is obtained by
using the infinite-product formulation of Amstutz.
Amstutz's remarkable permutation algorithm determines all element values
without the round-off error typical of all other realization methods. It is based
on the fact that two-port networks having the same geometry may have the
same response even when the three-element sets responsible for the notches
are permuted. This fact was developed by writing continued fraction expansions
for two such equivalent networks, each having a different trap subsection
at their input port. By equating expressions for their impedances and for
their time delays at all frequencies, and at the second trap frequency in
particular, a method was determined for finding the element values of the trap
subsection that is once removed from the input port.
The development for permuting just two trap subsections enabled the
construction of a table and its generating algorithm to determine all element
values in a network. Once again, the only required data are the input
impedance and time delay at each trap frequency.
Two Amstutz (1978) FORTRAN programs were translated into BASIC
and included for use on personal computers. Reasonably sized elliptic filters