Reflection Coefficient

Reflection coefficient

Whenever an electromagnetic wave on a transmission line meets an impedance discontinuity — an antenna, a load, a badly matched joint — part of it is reflected back. The reflection coefficient Γ (gamma) quantifies that fraction: Γ = (Z_L − Z₀) ÷ (Z_L + Z₀), where Z_L is the load impedance and Z₀ is the characteristic impedance of the line (typically 50 Ω in RF, 75 Ω in video/TV). The result ranges from −1 to +1. The extreme cases are telling: with Z_L = Z₀, Γ = 0 — a perfect match, no reflection at all, and all the energy goes into the load; if the line ends in an open circuit (Z_L → ∞), Γ = +1 (total reflection, in phase); if it ends in a short (Z_L = 0), Γ = −1 (total reflection, inverted). The reflection coefficient is the parent quantity of impedance matching: VSWR ((1+|Γ|)/(1−|Γ|)) and return loss (−20·log₁₀|Γ|) both derive from it, and it is what a Smith chart plots. Minimising |Γ| — matching impedances with transformers, stubs or matching networks — means maximising power transfer and protecting the transmitter. Enter the load impedance and the characteristic impedance.