How is a Smith chart normalized?

Normalizing a Smith chart allows a single printed chart to be used for systems of any characteristic impedance, whether it is a 50-ohm coaxial cable, a 75-ohm TV line, or a 300-ohm twin-lead. Without normalization, you would need a different chart for every possible system impedance. To achieve this, you reassign the prime center’s impedance value. The prime center is the exact middle point of the chart, which has a default normalized value of 1.0 (purely resistive). If you are working with a 50-ohm transmission line, you define the prime center as 50 ohms. All actual impedances to be plotted on the chart are then divided by 50, converting them into normalized values. This mathematical scaling makes the Smith chart an incredibly flexible and universal tool.