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368 Other Direct Filter Design Methods
Equating slopes (9.55) and (9.57), the trap susceptance must be
(9.59)
This shows the converse limitation. Therefore, two elements cannot replace
one.
Three elements can .replace two elements using a first-order approximation.
Figure 9.33 illustrates the replacement of two elements by three, introducing a
notch in the process. The relationship among element values may be obtained
by writing relationships for the susceptance and its frequency slope, as
follows:
(9.60)
L-r=
I
",'C'("'I"'o -"'01",)2
(9.61 )
(9.62)
•
Three elements can replace four elements using a first-order approximation.
Figure 9.34 illustrates the replacement of four elements by three, removing a
notch in the process. The relationship among element values may be obtained
by writing relationships for the susceptance and its frequency slope, as
L,
Co
L,
L, C,
Figure 9.34. First·order equivalence of a four~element branch to a three-element branch.