# Field, power, and root-power quantities

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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 was introduced in the 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 linear systems, these definitions allow the distinction between root-power quantities and power quantities to be ignored when specifying changes as levels: an amplifier can be described as having "3 dB" of gain without needing to specify whether voltage or power are being compared; for a given linear load (e.g. an Ω speaker), such an increase will result in a 3 dB increase in both the sound pressure level and the sound power level at a given location near the speaker. Conversely, when ratios cannot be identified as either power or root-power quantities, the units neper (Np) and decibel (dB) cannot be sensibly used.

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

## "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).

## References

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