Level (logarithmic quantity)


In science and engineering, a power level and a field level are logarithmic measures of certain quantities referenced to a standard reference value of the same type.
The type of level and choice of units indicate the scaling of the logarithm of the ratio between the quantity and it reference value, though a logarithm may be considered to be a dimensionless quantity. The reference values for each type of quantity are often specified by international standards.
Power and field levels are used in electronic engineering, telecommunications, acoustics and related disciplines. Power levels are used for signal power, noise power, sound power, sound exposure, etc. Field levels are used for voltage, current, sound pressure.

Power level

Level of a power quantity, denoted LP, is defined by
where
The level of a root-power quantity, denoted LF, is defined by
where
If the power quantity P is proportional to F2, and if the reference value of the power quantity, P0, is in the same proportion to F02, the levels LF and LP are equal.
The neper, bel, and decibel are units of level that are often applied to such quantities as power, intensity, or gain. The neper, bel, and decibel are related by
Level and its units are defined in ISO 80000-3.
The ISO standard defines each of the quantities power level and field level to be dimensionless, with. This is motivated by simplifying the expressions involved, as in systems of natural units.

Related quantities

Logarithmic ratio quantity

Power and field quantities are part of a larger class, logarithmic ratio quantities.
ANSI/ASA S1.1-2013 defines a class of quantities it calls levels. It defines a level of a quantity Q, denoted LQ, as
where
For the level of a root-power quantity, the base of the logarithm is.
For the level of a power quantity, the base of the logarithm is.

Frequency level

Frequency level of a frequency f is the logarithm of a ratio of the frequency f to a reference frequency f. The reference frequency is C, four octaves below middle C.
In electronics, the octave is used as a unit with logarithm base 2, and the decade is used as a unit with logarithm base 10:
In music theory, the octave is a unit used with logarithm base 2. A semitone is one twelfth of an octave. A cent is one hundredth of a semitone.