A correspondent has suggested to me that my practice of giving Return Loss as a positive dB value is wrong, citing US FS-1037C.
US FS-1037C has been superseded by ANS T1.523-2001, Telecom Glossary 2000, and the wording in the latter is identical to the former, so let’s discuss the more current document.
ANS T1.523-2001 gives a definition of Return Loss:
return loss
The ratio, at the junction of a transmission line and a terminating impedance or other discontinuity, of the amplitude of the reflected wave to the amplitude of the incident wave. Note 1: Return loss is usually expressed in dB. Note 2: Return loss is a measure of the dissimilarity between impedances in metallic transmission lines and loads, or between refractive indices in dielectric media, e.g., optical fibers. Note 3: In a metallic transmission line, return loss is given by
where Z1 is the impedance toward the source and Z2 is the impedance toward the load, and the vertical bars indicate magnitude. Note 4: For dielectric media, e.g., optical fibers, see reflection loss
The definition is internally inconsistent.
- The text says
of the amplitude of the reflected wave to the amplitude of the incident wave
, . The amplitude of the wave could be expressed as a voltage or current, the ratio ofof the amplitude of the reflected wave to the amplitude of the incident wave
will usually be than 1.0, and conversion to dB will yield a negative value. - The equation is 10 times the log of the inverse of ρ (the magnitude of the complex (voltage) reflection coefficient Γ). ρ is usually less than 1.0, and so the inverse of ρ is usually greater than 1.0, and the log of 1/ρ will usually be positive. They then multiply by 10 which is wrong, ρ is a voltage ratio and they should multiply the log by 20 to get the power ratio in dB.
ANS T1.523-2001, Telecom Glossary 2000 contains several errors and is internally inconsistent so it is not a credible reference for the purpose of defining Return Loss.
(IEEE 1988) defines Return Loss as:
(1) (data transmission) (A) At a discontinuity in a transmission system the difference between the power incident upon the discontinuity. (B) The ratio in decibels of the power incident upon the discontinuity to the power reflected from the discontinuity. Note: This ratio is also the square of the reciprocal to the magnitude of the reflection coefficient. (C) More broadly, the return loss is a measure of the dissimilarity between two impedances, being equal to the number of decibels that corresponds to the scalar value of the reciprocal of the reflection coefficient, and hence being expressed by the following formula:
20*log10|(Z1+Z2)/(Z1-Z2)| decibel
where Z1 and Z2 = the two impedances.
(2) (or gain) (waveguide). The ratio of incident to reflected power at a reference plane of a network.
Return Loss expressed in dB wrt a real reference impedance will usually be a positive number in passive networks.
The article Can the magnitude of the complex reflection coefficient (ρ) be greater than 1 used an unusual example where Return Loss would indeed be negative.
For most practical cases at HF and above, and ALL cases where Zo is real above, ρ will be less than unity, and Return Loss positive.
Links / References
- ANS T1.523-2001, Telecom Glossary 2000 at http://www.atis.org/tg2k/
- IEEE. 1988. IEEE standard dictionary of electrical and electronic terms, IEEE Press, 4th Edition, 1988.