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 (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.[clarification needed]
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
The level of a root-power quantity (also known as a field quantity), denoted LF, is defined by
- 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 = 1/2 loge10 Np;
- 1 dB = 0.1 B = 1/20 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.
- r is the base of the logarithm;
- Q is the quantity;
- Q0 is the reference value of Q.
- Decibel § Definition
- Power, root-power, and field quantities
- Logarithmic scale
- Sound level (disambiguation)
- Leveling (tapered floating point)
- Level-index arithmetic (LI) and symmetric level-index arithmetic (SLI)
- Fletcher, H (1934), "Loudness, pitch and the timbre of musical tones and their relation to the intensity, the frequency and the overtone structure", Journal of the Acoustical Society of America, 6 (2): 59, Bibcode:1934ASAJ....6...59F, doi:10.1121/1.1915704
- Taylor, Barry (1995), Guide for the Use of the International System of Units (SI): The Metric System, Diane Publishing Co., p. 28, ISBN 9780788125799
- ISO 80000-3 (2006), Quantities and units, vol. Part 3: Space and Time, International Organization for Standardization
- Carey, W. M. (2006), "Sound Sources and Levels in the Ocean", IEEE Journal of Oceanic Engineering, 31 (1): 61, Bibcode:2006IJOE...31...61C, doi:10.1109/JOE.2006.872214, S2CID 30674485
- ISO 80000-8 (2007), Quantities and units, vol. Part 8: Acoustics, International Organization for Standardization
- ANSI/ASA S1.1 (2013), Acoustical Terminology, vol. ANSI/ASA S1.1-2013, Acoustical Society of America
- Ainslie, M. A. (2015), "A Century of Sonar: Planetary Oceanography, Underwater Noise Monitoring, and the Terminology of Underwater Sound", Acoustics Today, 11 (1)
- D'Amore, F. (2015), Effect of moisturizer and lubricant on the finger‒surface sliding contact: tribological and dynamical analysis
- IEEE/ASTM SI 10 (2016), American National Standard for Metric Practice, IEEE Standards Association