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274 Direct·Coupled Filters
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Lo' ,
~
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Figure 8.2.
A four-resonator filter with two traps and one L section.
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L
transformations will be given for incorporating distributed (transmission line)
elements. The parallel LC resonators (tank circuits) appearing between each
network node and ground are coupled by the inverters shown in Figure 8.1.
Ideal inverters are lossless, frequency-independent, 90-degree transmission
lines. They are assumed to have characteristic impedances and electrical
lengths that are frequency independent. Practical inverter networks usually
have one of these ideal properties, and the other one is well behaved, with
effects that are easily predicted. The entire prototype network impedance level
may be elevated by transformers or L sections at one or both ends of the
network, so that element values may be located within a suitable range. As far
as prototype calculations are concerned, the source and load terminations are
simply resistances R II
and R NN , respectively.
An example of a practical, direct-coupled network appears in Figure 8.2.
The four resonators connected between each node and ground are evident
enough, but comparison with the prototype network in Figure 8.1 shows that
the inverters have been realized in different ways. The two inverters, between
nodes I and II and nodes II and III, are antiresonant "trap" subnetworks that
cause zeros of transmission at the corresponding frequencies. Also, the source
has been connected by an L section; it could have been connected directly or
by a transformer.
The response of the network in Figure 8.2 could be that shown in Figure
8.3. The rigid limitations of classical network approximation and synthesis
have been relaxed by accepting reasonable first-order approximations of ideal
response shapes, which are both arbitrary and unobtainable using real elements.
Therefore, fairly general selectivity specifications, as shown by the
barriers in Figure 8.3, may be satisfied by direct-coupled filters, which have
great flexibility in both form and component ranges.
This chapter begins with the definition of the prototype network and its
main components: resonators and ideal inverters. The selectivity mechanism
will be derived, and resonator loaded-Q and inverter impedance parameters
will be identified. Next, inductive and capacitive inverters will be introduced,
and their impedance-matching and selectivity effects will be identified. Approximate
selectivity relationships will be developed so that interactions