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358 Other Direct Filter Design Methods
B ij require four parameters, computed in the previous i-1st step; only
Lj_l,i_l and Bi_l,i_1 are actual element values. The other two parameters,
L j i-I and Hi i-I' can be considered element values when Wi_I is interchanged
with W; in the trap sequence. Of course, this process may be accomplished
from either end of the doubly terminated filter, especially to test accuracy.
It is well known that not every sequence of traps frequencies will yield
positive elements. Lin and Tokad (1968) describe the minor tests to be added
to the preceding algorithm so that all elements are positive.
9.3.4. Symmetric Type-s Filter Program. Symmetric filters have odd-degree
N, and the number of traps is M = (N - I)/2. Figure 9.19 shows the lowpass
and highpass midshunt and midseries topologies, respectively, that Program
B9-2 (Appendix B) designs. The program is a translation of Amstutz' (1978)
FORTRAN into BASIC. The original program utilized double precision,
although most eight-bit-microprocessor personal computers should be able to
design elliptic filters with as many as seven traps without difficulty.
Two typical runs are illustrated by the computer output in Figures 9.20 and
9.21 for lowpass and highpass networks, respectively. The program discrimi-
L,
L,
F,
F,
F, F,
L 1 L 3
L 4 L 2
Figure 9.19. Lowpass, midshunt and highpass, midseries topologies computed by Program B9~2
for symmetric type-s filters. [From Amstutz, P., IEEE Trans. Circuits Syst., Vol. CAS-25, No. 12,
p. 1011, December 1978. © 1978 IEEE.]