Return Loss

RL = −20 × log10(|Γ|)

Quick answer

This calculator solves RL = −20 × log10(|Γ|) for Return Loss. With Reflection Coefficient |Γ| 0.5, the result is 6.021 dB. It solves in 2 directions, so you can enter the values you have and get the one you need.

Calculator

Return Loss (dB)
—

Formula

RL = −20 × log10(|Γ|)

Description

Return loss quantifies how well a load is matched to a transmission line, expressed as a positive dB value. Higher return loss means better matching (less reflection). It is the negative of the reflection coefficient expressed in dB. Return loss is the most common metric displayed on network analyzers (as S11 magnitude) and is used to characterize antennas, connectors, cables, and any RF component. A return loss of 10 dB means 10% of the incident power is reflected, while 20 dB means only 1% is reflected.

Variables

  • RL — Return loss in positive decibels (dB)
  • |Γ| — Magnitude of reflection coefficient (0 to 1)

Practical Notes

Good match: RL > 20 dB. Acceptable: RL > 10 dB. Poor: RL < 6 dB. S11 on a network analyzer is return loss with a negative sign. Return loss and VSWR are related: RL = 20×log10((VSWR+1)/(VSWR-1)). For differential pairs (USB, PCIe), both single-ended (SDD11) and differential return loss are specified.

Symbols and units

Symbol Meaning Default unit Accepted units
RL Return Loss dB dB
gamma Reflection Coefficient |Γ| — —

Step by step

  1. 1. What you know: Reflection Coefficient |Γ| 0.5
  2. 2. The relation: RL = −20 × log10(|Γ|)
  3. 3. Substitute: gamma = 0.5
  4. 4. Result: Return Loss = 6.021 dB

Worked examples

Minimum range

Given: Reflection Coefficient |Γ| 0.025

Result: Return Loss = 32.04 dB

Low range

Given: Reflection Coefficient |Γ| 0.25

Result: Return Loss = 12.04 dB

Typical

Given: Reflection Coefficient |Γ| 0.5

Result: Return Loss = 6.021 dB

High range

Given: Reflection Coefficient |Γ| 0.8

Result: Return Loss = 1.938 dB

Maximum range

Given: Reflection Coefficient |Γ| 8

Result: Return Loss = -18.06 dB

Solving for each variable

Solve for Return Loss

Reflection Coefficient |Γ| 0.025 → 32.04 dB

Solve for Reflection Coefficient |Γ|

Return Loss 0.3 dB → 0.9661

How Return Loss changes with Reflection Coefficient |Γ|

Reflection Coefficient |Γ| (input) Return Loss (result)
0.05 26.02 dB
0.125 18.06 dB
0.25 12.04 dB
0.375 8.519 dB
0.5 6.021 dB
0.75 2.499 dB
2 -6.021 dB
3.5 -10.88 dB
5 -13.98 dB

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Frequently asked questions

How do you calculate Return Loss?

Use RL = −20 × log10(|Γ|). With Reflection Coefficient |Γ| 0.5, Return Loss works out to 6.021 dB.

What is the formula for Return Loss?

The formula is RL = −20 × log10(|Γ|). Return loss quantifies how well a load is matched to a transmission line, expressed as a positive dB value.

How do you find Reflection Coefficient |Γ| when you know the other values?

Rearrange for Reflection Coefficient |Γ|: with Return Loss 0.3 dB, Reflection Coefficient |Γ| is 0.9661.

Related Concepts

All Signal & RF formulas →
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