Reflection Coefficient

Formula

Description

The reflection coefficient Γ (gamma) quantifies the fraction of an incident wave reflected at an impedance discontinuity. When the load impedance ZL equals the characteristic impedance Z0, Γ = 0 and all power is absorbed (perfect match). An open circuit (ZL = ∞) gives Γ = +1 (total reflection, same polarity). A short circuit (ZL = 0) gives Γ = −1 (total reflection, inverted). The reflection coefficient is directly related to VSWR, return loss, and mismatch loss, and is the fundamental quantity measured by a vector network analyzer (VNA).

Variables

• Γ — Voltage reflection coefficient (−1 to +1, dimensionless)
• Z_L — Load impedance (Ω)
• Z₀ — Transmission line characteristic impedance (Ω)

Practical Notes

Return Loss = −20 × log₁₀(|Γ|) in dB. VSWR = (1 + |Γ|)/(1 − |Γ|). Mismatch Loss = −10 × log₁₀(1 − |Γ|²) in dB. For complex impedances, Γ is a complex number and is plotted on the Smith chart. A |Γ| < 0.1 (VSWR < 1.22, RL > 20 dB) is considered an excellent match. Most RF specifications require |Γ| < 0.33 (VSWR < 2, RL > 9.5 dB).