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Doubly Terminated Elliptic Filters 357
Table 9.1.
Input Impedance and Its Time
Delay at the Three Trap
Frequencies for the Elliptic
Filter in Figure 9.18
W Zin Z;n
W, j2.69645206 1.329461
W3 j 1.58927603 1.553162
W4 j 1.24311958 1.753632
B 44
= 0.748384, which produces C, = I/B 44 = 1.3362. The last value is comparable
to the 1.3200 value shown in Figure 9.18, the difference being attributable
to the approximate derivatives utilized in this example. (In practice, the
derivatives are known exactly from the pole/zero factors.)
9.3.3. The Complete Permutation Algorithm. The algorithm in Table 9.2
generates the elements for M traps. Then the actual element values are L j = L ii •
K i = I/B ii , and Mi=BiJwf for i= 1,2,...,M. The new element values L ii and
Table 9.2.
Array of Permutation Algorithm Coefficients for M =4 Traps
Input:
Trap k i=l i=3 i=4
For i = 1 (first column):
For k= 1,2, ... , M:
L
LK,=X,,(WK)/WK, where
M K1 =[Z (WK) - L K1 J;2
BK1=MK1W~
For i=2,3, ... ,M:
For j=i, i+ 1.... ,M:
U = L j _ J • i _ J - Lj,i_J
I/V=U/[ (wJ-'-wi~'I)Bi_l.i_I]-1
Lji=UV
L----'========B ji = V 2 B j ,i_l- (V + 1)2 Bi_l,i_1