# Return loss

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Return loss

In telecommunications, return loss or reflection loss is the loss of signal power resulting from the reflection caused at a discontinuity in a transmission line or optical fiber. This discontinuity can be a mismatch with the terminating load or with a device inserted in the line. It is usually expressed as a ratio in decibels (dB);

$RL(\mathrm{dB}) = 10 \log_{10} {P_\mathrm i \over P_\mathrm r}$
where RL(dB) is the return loss in dB, Pi is the incident power and Pr is the reflected power.

Two lines or devices are well matched if the return loss is high. A high return loss is therefore desirable as it results in a lower insertion loss. Return loss may be given a minus sign, see below.

## Sign

Properly, loss quantities, when expressed in decibels, should be positive numbers.[note 1] However, return loss has historically been expressed as a negative number, and this convention is still widely found in the literature.[1]

Taking the ratio of reflected to incident power results in a negative sign for return loss;

$RL'(\mathrm{dB}) = 10 \log_{10} {P_\mathrm r \over P_\mathrm i}$
where RL'(dB) is the negative of RL(dB).

Caution is required when discussing increasing or decreasing return loss since these terms strictly have the opposite meaning when return loss is defined as a negative quantity.

## Electrical

In metallic conductor systems, reflections of a signal traveling down a conductor can occur at a discontinuity or impedance mismatch. The ratio of the amplitude of the reflected wave Vr to the amplitude of the incident wave Vi is known as the reflection coefficient Γ.

$\mathit \Gamma = {V_\mathrm r \over V_\mathrm i}$

When the source and load impedances are known values, the reflection coefficient is given by

$\mathit \Gamma = { {Z_\mathrm L - Z_\mathrm S} \over {Z_\mathrm L + Z_\mathrm S} }$

where ZS is the impedance toward the source and ZL is the impedance toward the load.

Return loss is the negative of the magnitude of the reflection coefficient in dB. Since power is proportional to the square of the voltage, return loss is given by,

$RL(\mathrm{dB}) = -20 \log_{10} \left| \mathit \Gamma \right|$

where the vertical bars indicate magnitude. Thus, a large positive return loss indicates the reflected power is small relative to the incident power, which indicates good impedance match from source to load.

When the actual transmitted (incident) power and the reflected power are known (i.e. through measurements and/or calculations), then the return loss in dB can be calculated as the difference between the incident power Pi (in dBm) and the reflected power Pr (in dBm),

$RL(\mathrm{dB}) = P_\mathrm i(\mathrm{dBm}) - P_\mathrm r(\mathrm{dBm})\,$

Return loss is identified with the S-parameter S11 from two-port network theory. [2]

## Optical

In an optical fiber, the loss that takes place at any discontinuity of refractive index, especially at an air-glass interface such as a fiber endface, at which a fraction of the optical signal is reflected back toward the source. This reflection phenomenon is also called "Fresnel reflection loss," or simply "Fresnel loss."

Fiber optic transmission systems use lasers to transmit signals over optical fiber, and a high optical return loss (ORL) can cause the laser to stop transmitting correctly. The measurement of ORL is becoming more important in the characterization of optical networks as the use of wavelength-division multiplexing increases. These systems use lasers that have a lower tolerance for ORL, and introduce elements into the network that are located in close proximity to the laser.

$ORL(\mathrm{dB}) = 10 \log_{10} {P_\mathrm i \over P_\mathrm r}$

where $\scriptstyle P_\mathrm r$ is the reflected power and $\scriptstyle P_\mathrm i$ is the incident, or input, power.

## Notes

1. ^ Except for cases where an active device succeeds in reflecting back more power than was sent into it. This is the case, for instance, with the tunnel diode amplifier.

## References

1. ^ Trevor S. Bird, "Definition and Misuse of Return Loss", IEEE Antennas & Propagation Magazine, vol.51, iss.2, pp.166-167, April 2009.
2. ^ Noel G. Barton, Jacques Periaux, "Coupling of fluids, structures, and waves in aeronautics", proceedings of a French-Australian workshop in Melbourne, Australia, 3–6 December 2001, p.187, Springer, 2003 ISBN 3540402225.

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