3.6: Summary

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Graphical representations of power flow enable RF and microwave engineers to quickly ascertain circuit performance and arrive at qualitative design decisions. Humans are very good at processing graphical information and seeing patterns, anomalies, and the path from one point to another. Two powerful techniques were introduced in this chapter that provide this insight. These are the signal flow graph and the Smith chart. Signal flow graphs enable engineers to solve algebraic problems without using algebraic equations. Signal flow graphs are also a convenient way to develop symbolic expressions. Developing these expressions using algebraic manipulations alone is error prone.

The Smith chart is a richly annotated polar plot for representing reflection and transmission coefficients, and more generally, scattering parameters. The Smith chart representation of scattering parameter data aligns very well with the intuitive understanding of an RF designer. The experienced RF designer is intrinsically familiar with the Smith chart and prefers that circuit performance during design be represented on one. Representing something as simple as an extension of a line length to a two-port is quite complex if described using network parameters other than scattering parameters. However, with scattering parameters this extension results in a change of the angle of a scattering parameter, or on a Smith chart an arc. Scattering parameters relate directly to power flow. So from a Smith chart an experienced designer can ascertain the effect of circuit design on power flow, which then relates to signal-to-noise ratio and power gain. The Smith chart will be an essential tool in many of the topics considered in later chapters.