Naturally, any chart can also be implemented in a computer program, and the Smith chart has, but we must first understand how it works before we can use it either on paper or on the screen. Some measuring instruments such as network analyzers actually use a Smith chart to display conditions on lines and networks. Although the Smith chart is rather old, it is a common design tool in electromagnetics.

As such, it allows calculations of all parameters related to transmission lines as well as impedances in open space, circuits, and the like. The Smith chart is a chart of normalized impedances (or admittances) in the reflection coefficient plane. This has been accomplished in a rather general tool called the Smith chart. Thus, the following proposition: Build a graphical chart (or an equivalent computer program) capable of representing the reflection coefficient as well as load impedances in some general fashion and you have a simple method of designing transmission line circuits without the need to perform rather tedious calculations. You may also recall, perhaps with some fondness, the complicated calculations which required, in addition to the use of complex variables, the use of trigonometric and hyperbolic functions. The reflection coefficient, in turn, was defined in terms of the load and line impedances (or any equivalent load impedances such as at a discontinuity). Voltage, current, and power were all related to the reflection coefficient. The reflection coefficient was used to find the conditions on the line, to calculate the line impedance, and to calculate the standing wave ratio. Reflection coefficients can be read directly from the chart as they are unit-less parameters.A look back at much of what we did with transmission lines reveals that perhaps the dominant feature in all our calculations is the use of the reflection coefficient.

Once an answer is obtained through the graphical constructions described below, it is straightforward to convert between normalised impedance (or normalised admittance) and the corresponding unnormalized value by multiplying by the characteristic impedance (admittance). The most commonly used normalization impedance is 50 ohms. Normalised scaling allows the Smith chart to be used for problems involving any characteristic or system impedance which is represented by the center point of the chart. These are often known as the Z, Y and YZ Smith charts respectively. The Smith chart is plotted on the complex reflection coefficient plane in two dimensions and is scaled in normalised impedance (the most common), normalised admittance or both, using different colours to distinguish between them.

Y smith chart