Smith Chart and Impedance Matching

This chapter introduces the concept of the transmission line (TL) theory, impedance matching, and how the Smith Chart can be used for impedance matching. The Smith chart was developed by P. W. Smith as a graphical tool to analyze and design TL circuits, in 1939. It can be used for the conversions between reflection coefficients and normalized impedances. The single-stub impedance matching (tuning) is to connect a single open-circuited or short-circuited lossless stub line in shunt (parallel) or series with an existing lossless TL for matching a (possibly complex-valued) load impedance to the TL of characteristic impedance. To implement an LC ladder using stubs, the chapter uses Richard's transformation to convert lumped elements to stubs and then use Kuroda's identities to transform series/parallel stubs into parallel/series stubs. Real load impedance can be matched to a feed line of characteristic impedance by using a λ/4-length lossless line called a quarter-wave impedance transformer.