Smithdiagram

The Smith diagram, commonly called the Smith chart, is a graphical tool used in radio frequency engineering to represent complex impedance or reflection coefficient for a chosen reference impedance. It provides a compact visual method to analyze and design impedances, admittances, and networks, including transmission lines and matching networks, as well as to assess standing wave ratio.

The diagram plots the complex reflection coefficient in the plane, typically denoted Gamma, with impedance Z normalized to a reference Z0. The fundamental relation is Gamma = (Z - Z0) / (Z + Z0), and Z = Z0 (1 + Gamma) / (1 - Gamma). The center of the chart corresponds to the matched impedance Z = Z0 (Gamma = 0), while the unit circle boundary represents total reflection (|Gamma| = 1). The chart contains a grid of curves corresponding to constant resistance and constant reactance, enabling rapid plotting and transformation of impedances and admittances.

Usage and interpretation often involve tracing how impedance changes along a transmission line or after adding series or parallel components. Moving along a lossless transmission line corresponds to rotating a point around the chart’s center, illustrating how impedance transforms with electrical length. Designers use the Smith chart to visualize impedance matching, calculate SWR, and assess the effects of different network topologies without extensive algebra.

History and scope: the Smith diagram was introduced by Phillip H. Smith in 1939 for Bell Labs and has since become a standard tool in RF and microwave engineering. While modern software aids numerical calculations, the Smith chart remains valued for intuition and rapid hand calculations.