The reflection coefficient, \(\Gamma\), is related to a load, \(Z_\)(a). The Smith chart is a ‘backof-the-envelope’ tool that designers use to sketch out designs. The Smith chart presents a large amount of information in a confined space and interpretation, such as applying appropriate signs, is required to extract values. This section first presents the impedance Smith chart and then the admittance Smith chart before introducing a combined Smith chart which is the form needed in design. Only a few have survived in electrical engineering usage, with Smith charts being overwhelmingly the most important. Once nomographs and graphical calculators were common engineering tools mainly because of limited computing resources. The Smith chart was invented by Phillip Smith and presented in close to its current form in 1937, see. The chart has many numbers printed in quite small font and with signs dropped as there is not room. 5 provides a Quicktime movie of a rectangular graph of the complex- impedance plane morphing into the polar plot of the typical Smith chart. It takes effort to master but fundamentally it is quite simple combining a polar plot used for plotting \(S\) parameters directly, curves that enable normalized impedances and admittances to be plotted directly, and scales that enable electrical lengths in terms of wavelengths and degrees to be read off. Mastering the Smith chart is essential to entering the world of RF and microwave circuit design as all practitioners use this as if it is well understood by others. The Smith chart is a powerful graphical tool used in the design of microwave circuits.
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