The Smith Chart and S-Parameters

Abstract

In 1939 P.H. Smith developed a chart that is still a key tool in microwave work and is heavily used in this book. This chart is fundamentally admittance and/or impedance scales overlaid on a polar plot of voltage reflection coefficient Γ versus frequency. Reflection coefficient is the ratio of a reflected voltage wave divided by an incident wave. Unlike a DC measurement where only one voltage can be extracted from a given point on a line, microwave measurements can isolate a forward-moving voltage wave from a backward-moving wave using directional couplers. In addition to measuring the magnitude of the incident and reflected wave, the phase difference between the two waves can also be measured. The magnitude and phase of these waves can be expressed as S-parameters (scattering parameters), Z-parameters (impedance parameters), Y-parameters (admittance parameters), or reflection coefficient. Each of these can be calculated from the other [2.1] and each has advantages under different circumstances.