Reflection Coefficient vs. Return Loss vs. VSWR Explained

This document explains the differences between Reflection Coefficient, Return Loss, and VSWR (Voltage Standing Wave Ratio).

Reflection Coefficient

The Reflection Coefficient (RC) represents the ratio of the reflected voltage wave to the incident voltage wave. It’s a crucial parameter in characterizing how well a load is matched to a transmission line. A high reflection coefficient indicates a significant impedance mismatch, meaning a large portion of the signal is reflected back towards the source.

The formula for the Reflection Coefficient is:

$RC = \frac{V_{reflected}}{V_{incident}} = \frac{Z_L - Z_0}{Z_L + Z_0}$

Where:

• $V_{reflected}$ is the amplitude of the reflected voltage wave.
• $V_{incident}$ is the amplitude of the incident voltage wave.
• $Z_L$ is the Load Impedance.
• $Z_0$ is the Characteristic Impedance of the transmission line.

The Characteristic Impedance ($Z_0$) is defined as:

$Z_0 = \sqrt{\frac{R + j\omega L}{G + j\omega C}}$

Where:

• $R$ is the resistance per unit length.
• $L$ is the inductance per unit length.
• $G$ is the conductance per unit length.
• $C$ is the capacitance per unit length.
• $\omega$ is the angular frequency.

The Transmission Coefficient (TC), which represents the proportion of the signal transmitted into the load, is given by:

$TC = \frac{2Z_L}{Z_L + Z_0}$

Return Loss

Return Loss is the logarithmic ratio of the power of the incident wave to the power of the reflected wave, expressed in decibels (dB). It indicates how much of the signal is “lost” due to reflection. A higher return loss (a larger positive number) indicates a better match and less reflected power.

The conversion from Reflection Coefficient to Return Loss is:

$Return Loss = -20 \log_{10} |RC|$

VSWR (Voltage Standing Wave Ratio)

VSWR is the ratio of the maximum voltage to the minimum voltage on a transmission line due to standing waves caused by reflections. It’s always a value greater than or equal to 1. A VSWR of 1 indicates a perfect match (no reflections), while higher values indicate poorer matching and increased reflections.

The conversion from Reflection Coefficient to VSWR is:

$VSWR = \frac{1 + |RC|}{1 - |RC|}$

The conversion from VSWR to Return Loss is:

$Return Loss (RL) = 20 \log_{10} \left( \frac{VSWR + 1}{VSWR - 1} \right)$

The conversion from Return Loss to VSWR is:

$VSWR = \frac{10^{RL/20} + 1}{10^{RL/20} - 1}$