Level (logarithmic quantity)


In science and engineering, a power level and a field level are logarithmic magnitudes of certain quantities referenced to a standard reference value of the same type.
  • A power level is a logarithmic quantity used to measure power, power density or sometimes energy, with commonly used unit decibel.
  • A field level is a logarithmic quantity used to measure quantities of which the square is typically proportional to power, with commonly used units neper or decibel.
The type of level and choice of units indicate the scaling of the logarithm of the ratio between the quantity and its 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
  • P is the power quantity;
  • P0 is the reference value of P.

    Field (or root-power) level

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
  • ;
  • .

    Standards

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
  • r is the base of the logarithm;
  • Q is the quantity;
  • Q0 is the reference value of Q.
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.

Logarithmic frequency ratio

The logarithmic frequency ratio of two frequencies is the logarithm of their ratio, and may be expressed using the unit octave corresponding to the ratio 2 or the unit decade corresponding to the ratio 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. In this context, the reference frequency is taken to be C, four octaves below middle C.