Return loss

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]

The correct definition of return loss is the difference in dB between the incident power sent towards the Device Under Test (DUT) and the power reflected, resulting in a positive sign:

${\displaystyle RL(\mathrm {dB} )=10\log _{10}{P_{\mathrm {i} } \over P_{\mathrm {r} }}}$

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

${\displaystyle RL'(\mathrm {dB} )=10\log _{10}{P_{\mathrm {r} } \over P_{\mathrm {i} }}}$

where RL'(dB) is the negative of RL(dB).

Return loss with a positive sign is identical to the magnitude of Γ when expressed in decibels but of opposite sign. That is, return loss with a negative sign is more properly called reflection coefficient.[1] The S-parameter S₁₁ from two-port network theory is frequently also called return loss,[2] but is actually equal to Γ.

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.

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 V_r to the amplitude of the incident wave V_i is known as the reflection coefficient ${\displaystyle \Gamma }$.

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

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

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

where Z_S is the impedance toward the source and Z_L 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,

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

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 P_i (in absolute decibel units, e.g., dBm) and the reflected power P_r (also in absolute decibel units),

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

In optics (particularly in fiberoptics) a loss that takes place at discontinuities of refractive index, especially at an air-glass interface such as a fiber endface. At those interfaces, 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.

${\displaystyle {\text{ORL}}(\mathrm {dB} )=10\log _{10}{P_{\mathrm {i} } \over P_{\mathrm {r} }}}$

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

• Hybrid balance
• Mismatch loss
• Signal reflection
• Time-domain reflectometer
  • Optical time domain reflectometer

Notes

Bibliography