The Smith Chart

Abstract

This chapter develops the Smith Chart by beginning with why the Smith chart works! This provides not only a theoretical derivation of the chart but physical insight into its basis and use. The fact that reflection coefficient magnitude changes in angle only (not magnitude) on a lossless transmission line is shown to be a way to determine the input impedance to a mismatched line, and that this underlies the use of the Smith chart. It is shown how contours of constant resistance and reactance in the rectangular impedance plane are mapped to the reflection coefficient plane by the bilinear transformation relating impedance to reflection coefficient, resulting in the Smith chart. Impedance and admittance Smith charts are presented, with load tuning examples. Slotted line measurements, which underlie standing wave theory, are demonstrated. Numerous practical techniques are presented, including: reading VSWR as r, negative resistance Smith charts, navigating the chart on constant radius (reflection coefficient) or constant resistance (reactance tuning) contours, using Smith chart software, estimating tuning bandwidth, use of approximate tuning for broader bandwidth, reading frequency contours on the chart, using the chart without transmission lines (arbitrary Z o ), constant Q circle tuning, and graphical means for tuning and for finding lumped equivalent circuits (as for lengths of transmission lines).