Each of these circles has a constant normalized resistance value. The first family of circles is tangent to a point on the right side of the outer circle along the center horizontal line. 1) is constructed from three families of circles. Negative resistance values do occur with some regularity in directional antenna systems however, they are not manifested in passive circuits and not represented on the basic Smith chart as we will infer shortly. Finally, note we are only considering positive resistance values. Recall “ELI the ICE man” and that voltage leads current by 90 degrees in an inductor and vice-versa in a capacitor. The reason for the sign change is how voltage and current are related in inductors and capacitors. Inductive reactance is defined as positive, while capacitive reactance is negative. The difference in these two equations results from the flavor of reactance. Impedance can be written a number of different ways however, you probably will see the Cartesian forms below more often than not. It is the complex sum of the resistance and reactance components, and thus, in ac circuits describes not only the ratio of voltage and current, but also the relative phase angles. Impedance is a measure of the opposition of the flow of current in an alternating current circuit. In the simplest form, if 50? is our reference value, then 50, 100 and 25? normalized would become 1?, 2? and 0.5? respectively. For obvious reasons values of 50 and 75? are the most common bases utilized. When impedance is normalized, it is related to a reference value as a multiple. One good working definition of the Smith chart is that it is simply a graphical calculator for normalized impedance and associated RF parameters.
While calculation methods can be performed via computer or calculator with a greater degree of accuracy, the Smith chart still remains a venerable and useful tool for the RF engineer. Although the basis for the chart is deeply rooted in complex variable theory, you do not have to be a graduate-level mathematician to appreciate and have a solid working knowledge of the chart. Upon initial look, the Smith chart appears to be quite complicated.
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