Smith Chart (Telecom)

Telecommunications Engineering

How It Works

In telecommunication antenna and transmission line engineering, the Smith chart provides a comprehensive circular mapping of complex reflection coefficients and transmission line impedances. As a radio frequency signal propagates toward an antenna load, the normalized impedance rotates clockwise around the chart along a circle of constant Voltage Standing Wave Ratio (VSWR), enabling quarter-wave transformers and reactive stubs to eliminate signal reflections.

Governing Equation
z_{in}(l) = (z_L + j tan(β l)) / (1 + j z_L tan(β l))   |   Γ_{in} = Γ_L · e^{-j 2 β l}   |   β = 2π / λ