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General Inverters, Resonators, and End Couplings 293
It is important to interpret the three factors in (8.30). The first two terms
have been extracted in the form typical of the simple capacitive inverter
described in Section 8.2.1: B(wo) is an inverter Yo and (w/wo) is the linear
frequency behavior of capacitive susceptance. Therefore, (8.30) was written
with W > w n
in mind, when the trap appears capacitive.
The analysis in Section 8.1.3 showed that the Zo of each inverter was a.
factor in the coefficient of the highest-degree frequency term in the response
polynomial [see (8.10)-(8.12)]. The first two terms in (8.30) produce exactly
the effect of a simple capacitive inverter. The effect of the third term in (8.30)
is to increase the breakpoint of the asymptote for stopband selectivity by
20 log of its inverse (inverting from admittance to impedance).
The numerator and denominator of the third term are both positive when
W > W n
and W n
> Woo Thus the third term is unity when
[
2]-1/2
w/wn = 2-(::) . (8.31 )
An analysis of the third term in (8.30) in light of (8.31) reveals that the trap
increases selectivity above the trap frequency, except for the case where
w n
/ Wo Wo and W > W n
leads to the following rule: classify the
trap as a simple C inverter in (8.27), and increase the loss estimate by .
(wn/wo)2- 1
20 log 2
l-(wn/w,)
(8.32)
When w n / W o