Electronic Applications of the Smith Chart: In Waveguide, Circuit, and Component Analysis

Chapter 10: Network Impedance Transformations

10.1 L-Type Matching Circuits

The advantages of matching impedances at a junction between two circuits or media have been pointed out in Chap. 9 and elsewhere in this book and need no further explanation here.

One of the most commonly used and generally satisfactory impedance transforming networks for radio frequency applications is the half-section L-type circuit employing two essentially pure reactance elements [19, 149]. At a single frequency and, for most practical purposes, embracing at least the sideband frequencies of a radio telephone transmitter, the simple L-type circuit may be used effectively to transform any load impedance to any desired pure input resistance value. Conversely, the L-type circuit may be employed to accomplish the reverse transformation, that is, to transform any load resistance to any desired complex input impedance value. It is necessary to consider only the former type of transformation, however, since the circuit can always be reversed to make the transformation in the opposite direction. This simplifies the presentation of design information.

It will be seen by referring to Fig. 10.1 that there is a total of eight possible combinations of reactance types, i.e., inductive and capacitive, in an L-type circuit. Each of these eight circuits is capable of transforming a restricted range of complex load impedance values to a given pure resistance value. The transformable impedance values associated with each circuit can conveniently be represented by the impedances within a bounded area on a SMITH CHART. A set of eight such representations...

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