Power, root-power, and field quantities

From Wikipedia, the free encyclopedia
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.

A power quantity is a power or a quantity directly proportional to power, e.g., energy density, acoustic intensity, and luminous intensity.[1] Energy quantities may also be labelled as power quantities in this context.[2]

A root-power quantity is a quantity such as voltage, current, sound pressure, electric field strength, speed, or charge density, the square of which, in linear systems, is proportional to power.[3] The term root-power quantity refers to the square root that relates these quantities to power. The term was introduced in ISO 80000-1 § Annex C; it replaces and deprecates the term field quantity.


It is essential to know which category a measurement belongs to when using decibels (dB) for comparing the levels of such quantities. A change of one bel in the level corresponds to a 10× change in power, so when comparing power quantities x and y, the difference is defined to be 10×log10(y/x) decibel. With root-power quantities, however the difference is defined as 20×log10(y/x) dB.[3]

In the analysis of signals and systems using sinusoids, field quantities and root-power quantities may be complex-valued.[4][5][6][disputed ]

"Root-power quantity" vs. "field quantity"

In justifying the deprecation of the term "field quantity" and instead using "root-power quantity" in the context of levels, ISO 80000 draws attention to the conflicting use of the former term to mean a quantity that depends on the position,[7] which in physics is called a field. Such a field is often called a field quantity in the literature, but is called a field here for clarity. Several types of field (such as the electromagnetic field) meet the definition of a root-power quantity, whereas others (such as the Poynting vector and temperature) do not. Conversely, not every root-power quantity is a field (such as the voltage on a loudspeaker).

See also


  1. ^ Ainslie, Michael A. (Winter 2015). "A Century of Sonar: Planetary Oceanography, Underwater Noise Monitoring, and the Terminology of Underwater Sound" (PDF). Acoustics Today. 11 (1): 12–19.
  2. ^ ISO 80000:1-2009 § C.3
  3. ^ a b Brian C.J. Moore (1995). Hearing. Academic Press. p. 11. ISBN 978-0-08-053386-5.
  4. ^ ISO 80000-1:2009 § C.2
  5. ^ ISO 80000-3:2006 § 0.5
  6. ^ IEC 60027-3:2002
  7. ^ ISO 80000-1:2009 § C.2