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Chapter Six
Impedance Matching
Impedance matching is the design of a network or transducer so that a
terminating impedance is transformed exactly to a desired impedance at a
frequency, or is transformed approximately over a band of frequencies. Figure
6.1 shows the situation where load impedance Z, may be specified as some LC
subnetwork terminated by a resistance or by complex numbers associated with
arbitrary frequencies. The desired input impedance Z;" may be similarly
specified or may be contained in a neighborhood described as some maximum
standing-wave ratio (4.59). Section 9.6 will consider dissipative network transformations;
in this chapter only lossless, passive networks are considered.
Impedance transformation is usually desired for control of power transfer
from a fiuite impedance source, and is thus related to the same requirements
discussed in Chapter Three for doubly terminated filters. There is one important
difference: impedance matching usually is concerned with given terminating
impedances that are complex, not simple resistances. This results in simple
restrictions for single-frequency transformations. There are complicated constraints
when matching complex impedances over a band of frequencies.
These problems will be considered in order of increasing generality.
Chapter Six begins with impedance matching at a single steady-state
frequency, first with two- and three-element networks composed of a combination
of inductors and capacitors, and then with one or two cascaded
transmission lines. It is remarkable that these subjects are seldom treated in
modern electrical engineering curricula, even though they appear in almost all
pertinent texts and handbooks published before 1960. Practicing engineers
responsible for radio frequency circuit design invariably query prospective
employees about L, T, pi, and perhaps transmission line matching because it is
a matter of frequent concern. The treatment here includes tried and true
concepts, which will be extended to broadband matching and direct-coupled
filters (Chapter Eight) as well, especially the idea of the loaded Q of an
impedance. The Smith chart as a means of visualizing the matching process
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