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56 Some Tools and Examples of Filter Synthesis
1 1 1
~?- ~
',,~ 12
Y=r~J
Figure 3.6.
of Yll'
(a)
Network realizations for Example 3-14 using (a) zit (Of z22) and (b) the reciprocal
Using the even and odd parts of Hand K in (3.70) and assuming that
R, = R 2 = 1, the chain matrix is found to be:
Therefore, (3.85) yields
[~
B]=[1+2s 2
D 2s
(b)
2S+2S'].
I +2s 2 (3.90)
(3.91)
and (3.86) yields
_'_ = 1!. = 2s'+ 2s
YII D 2s 2 +1
(3.92)
A network for this example is shown in Figure 3.6, as found by continued
fraction Program B3-5. There must be three elements according to the degree
of (3.89). Figure 3.6a uses Zll to find only the first two elements. (Why?)
Figure 3.6b uses I/YII to find all three elements, because y is a short-circuit
parameter, and the last element is in series. Note that both ZII and z22 could
have been used to find all three elements, two at a time, including the shunt C
in the middle twice. That would have shown whether or not R, = R 2
(Why?)
and could provide greater numerical accuracy. Mellor (\975) has estimated
that computer decimal-digit word length (Nd) and filter synthesis degree (N)
are compatible if N