Level (logarithmic quantity)
- A power level is a logarithmic quantity used to measure power, power density or sometimes energy, with commonly used unit decibel (dB).
- A field level (or root-power level) is a logarithmic quantity used to measure quantities of which the square is typically proportional to power, etc., with commonly used units neper (Np) or decibel (dB).
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.
Level of a power quantity, denoted LP, is defined by
- P is the power quantity;
- P0 is the reference value of P.
Field (or root-power) level
- F is the root-power quantity, proportional to the square root of power quantity;
- F0 is the reference value of F.
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.
- 1 B = 1/ loge10 Np;
- 1 dB = 0.1 B = 1/ loge10 Np.
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 1 Np = 1. This is motivated by simplifying the expressions involved, as in systems of natural units.
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
- 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 r = e. For the level of a power quantity, the base of the logarithm is r = e2.
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