Smith Chart (Impedance Matching)

Electronics Engineering

How It Works

The Smith Chart is an indispensable graphical calculation tool for high-frequency RF engineering that maps the complex reflection coefficient Γ plane onto normalized impedance coordinates (z = r + jx). Circles of constant normalized resistance r and circular arcs of constant normalized reactance x allow transmission line impedances, standing wave ratios, and stub matching transformations to be computed geometrically without complex transcendental equations.

Governing Equation
Γ = (z_L - 1) / (z_L + 1)   |   z_L = r + jx   |   VSWR = (1 + |Γ|) / (1 - |Γ|)