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Direct-Coupled Filten 275
L"
f.,
Log scale
f
Figure 8.3.
Typicaldirect~coupled-filter selectivity specification and response.
among the several design parameters will be obvious. A practical network will
be designed to illustrate these fundamental concepts.
Detailed consideration will be given to practical inverters and resonators.
Resonator developments include dissipation and the equivalence between
lumped and distributed components. A general basis for analyzing any inverter
subnetwork will be presented, and the trap inverter will be analyzed to
show why it increases selectivity without increasing midband loss. End (terminal)
coupling by both L sections and transformers provides a vital degree of
design freedom for elevating filter impedance levels and thus relieving component
restrictions; these techniques will be described.
The selectivity behavior in and near the passband is called the response
shape and is completely determined by the distribution of loaded-Q values
among the resonators in the (ideal) prototype network (Figure 8.1). Four
unique shapes will be discussed in detail. The first three are related:
Chebyshev (overcoupled), Butterworth (maximally flat), and Fano (undercoupled).
The minimum-loss or equal-Q shape will also be considered,
because it is practical, simple, and instructive. Useful formulas for predicting
the required number of resonators for various passband and stopband selectivity
specifications will be furnished. These are well known for all but the Fano
(undercoupled) response; it has several valuable characteristics, including
good pulse response.
Limitations of this approximate, direct-coupled design technique will be
made explicit; it will be shown that they do not eliminate most practical
applications. Certain readily available sensitivity relationships will be noted.
Also, the well-known tuning procedure for these synchronous filters will be
descrihed. Finally, a detailed design procedure, based on a flowchart, will be