Knowledge of the basis and use of the Smith chart, a graphical presentation of the reflection coefficient with normalized impedance as a parameter overlay, is a sine qua non for the microwave engineer. Originally created as an aid to determining the input impedance to a transmission line, the Smith chart has become a universal aid to the design of matching circuits and to the display of measured data.
In the 1930s, when Phillip Smith [1–3] invented the graphical solution that facilitated the determination of how impedances were transformed by lengths of transmission lines, digital computers were unavailable to engineers. Engineers employed graphing strategies to gain insight into the variations produced by the independent variables of complex formulas. However, such insight was not forthcoming by attempting directly to graph the input impedance formula (4.14‐2 ), repeated below, for a transmission line.
The key to obtaining insight into this transformation was to recognize that, although impedance varies in a complex manner as one moves away from the load along a lossless transmission line, reflection coefficient variation is quite simple! In traveling from the load to the generator along a lossless line, only the angle of the reflection coefficient changes, not its magnitude (Fig. 5.1‐1).
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