Note that this latter format omits the absolute-value bars around magnitude G in complex-notation formats that include the angle sign (/_), the preceding variable or constant is assumed to represent magnitude. 4), which is equivalent to the complex reflection coefficient G for single-port microwave components.Īnd that | G |e j q is often expressed as G /_θ. In essence, the Smith chart is a special plot of the complex S-parameter s 11 (Ref. Courtesy of Agilent Technologies.Īlthough the Smith chart can look imposing, it’s nothing more than a special type of 2-D graph, much as polar and semilog and log-log scales constitute special types of 2-D graphs. RF electronic-design-automation programs use Smith charts to display the results of operations such as S-parameter simulation. 3), Smith chart displays can provide an easy-to-decipher picture of the effect of tweaking the settings in a microwave network in an EDA program ( Figure 1), a Smith chart display can graphically show the effect of altering component values.įigure 1. 1, “From the time I could operate a slide rule, I’ve been interested in graphical representations of mathematical relationships.” It’s the insights you can derive from the Smith chart’s graphical representations that keep the chart relevant for today’s instrumentation and design-automation applications. Although calculators and computers can now make short work of the problems the Smith chart was designed to solve, the Smith chart, like other graphical calculation aids (Ref. 1) as a graph-based method of simplifying the complex math (that is, calculations involving variables of the form x + j y ) needed to describe the characteristics of microwave components.

Smith chart applet