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366 Other Direct Filter <strong>Design</strong> Methods<br />

L"<br />

I<br />

Z, , "<br />

I<br />

1+ jon<br />

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I<br />

I<br />

,f-<br />

: =C, L, =;:: C, ) L, =;:: C, L,<br />

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)<br />

r<br />

L _<br />

g2F Ar<br />

1- glg2-(N g<br />

-l)Fi.r<br />

Figure 9.30.<br />

Three·pole bandpass equivalent network using L I2 and CD'<br />

c"<br />

-<br />

C,<br />

L, : ~c, L, ~;:; C, L, 1<br />

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L,<br />

c,__N",.(,--Nco."-----"l_F",,,<br />

g2<br />

g2FAr/r<br />

Figure 9.31. Three~pole bandpass equivalent network using C l2 and L 23 •<br />

9.4.2. Trap Approximations. Taylor series were described in Section 5.] A. A<br />

first-order approximation <strong>of</strong> susceptance by value and slope at a frequency<br />

was employed for resonators in Section 8.304. The difference here is that the<br />

susceptance at the frequency <strong>of</strong> interest will not be zero. In the following, it<br />

will be assumed that trap notch frequencies are greater than any reference<br />

frequency. Pole-zero branches having two, three, or four elements, similar to<br />

those discussed earlier in Section 904.1, will be considered.<br />

It is informative to note that two elements cannot replace one in a<br />

first-order equivalence. Consider the two branches shown in Figure 9.32. The

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