About the Reflection Coefficient Calculator
The reflection coefficient Γ is the fundamental quantity describing impedance mismatch in RF and microwave systems. It is defined as the ratio of the reflected voltage wave to the incident voltage wave at a port: Γ = (ZL − Z₀)/(ZL + Z₀), where ZL is the load impedance and Z₀ is the reference system impedance (typically 50 Ω). When ZL = Z₀, Γ = 0 and all power is delivered to the load. When ZL is an open circuit or short circuit, |Γ| = 1 and all power is reflected.
Complex vs Magnitude-Only Γ
The full reflection coefficient is a complex number: Γ = |Γ|∠θ. The magnitude |Γ| tells you how much power is reflected (|Γ|² = reflected power fraction). The phase angle θ tells you where the reflection appears on a transmission line — at the load, θ depends on the nature of the reactance. This is why the Smith chart, which plots Γ in the complex plane, is such a powerful design tool: it maps all passive impedances onto the unit circle |Γ| ≤ 1.
Key Relationships
All common mismatch metrics derive directly from |Γ|. VSWR = (1+|Γ|)/(1−|Γ|) — the ratio of voltage maximum to minimum on the line. Return loss RL = −20·log₁₀(|Γ|) dB — how many dB below the incident signal the reflected signal is. Mismatch loss ML = −10·log₁₀(1−|Γ|²) dB — the power lost due to reflection. A return loss of 20 dB means |Γ| = 0.1 and only 1% of power is reflected, while 99% is delivered to the load.
Practical Design Targets
Most RF systems specify a minimum return loss of 10–15 dB (VSWR ≤ 2:1) at all ports. Precision measurements and low-noise receivers typically require 20+ dB return loss. Antenna specifications often quote VSWR directly: a 2:1 VSWR corresponds to 11% reflected power and a 9.5 dB return loss. Using this calculator, engineers can quickly check whether a given load impedance meets specification without going to a VNA.