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Concept
Level (logarithmic quantity)
Summary
In science and engineering, a power level and a field level (also called a root-power 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 (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 (for instance, the square of voltage is proportional to power by the inverse of the conductor's resistance), 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 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.
Level of a power quantity, denoted LP, is defined by
where
P is the power quantity;
P0 is the reference value of P.
The level of a root-power quantity (also known as a field quantity), denoted LF, is defined by
where
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.
The neper, bel, and decibel (one tenth of a bel) are units of level that are often applied to such quantities as power, intensity, or gain. The neper, bel, and decibel are related by
1 B = 1/2 loge10 Np;
1 dB = 0.1 B = 1/20 loge10 Np.
Decibel#Conversions and Neper#Units
Level and its units are defined in ISO 80000-3.
Official source
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