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336 Other Direct Filter Design Methods
load effects on mapping and input standing-wave ratio. A theorem concerning
composite bilinear functions between different unit circles is provided as a
fundamental analysis tool for obtaining concise design results.
The load effect analysis is extended to derive a design basis for filters that
absorb rather than reflect energy. These may be viewed as frequency-selective
attenuators (pads). They are substantially less selective than reflection filters,
but there are many important applications for impedance control and damping
of spurious oscillations in system stopbands. Design graphs for several of
these invulnerable (load-independent) filters will be provided.
9.1. Equal-Stub Admittance Filters
The direct-coupled filter design method in Chapter Eight provided a means
for designing transmission line filters, as shown in Figure 9.1. For I-ohm
terminations, the shorted-circuited, quarter-wave transmission line resonators
have loaded Q values
QLK =Y OK*' (9.1)
according to (8.50). Note that the internal resonators in Figure 9.1 c have been
divided into two parallelled resonators so that each may have half the required
Yo (and to minimize the generation or' extraneous electromagnetic modes).
Even so, the Q is too low and the bandwidth too wide for direct-coupled-filter
predictions to apply (see Section 8.5.2), since the transmission line normalized
admittance is within the range 0.1