Decibel scale
The decibel (dB) is a logarithmic unit of measurement that expresses the magnitude of a physical quantity (usually power, intensity, or perceived loudness) relative to a specified or implied reference level. Since it expresses a ratio of two quantities with the same unit, it is a dimensionless unit. A decibel is one tenth of a bel, a seldom-used unit that was named after Alexander Graham Bell. It is the tenth of the unit Bel (B) that was introduced in 1923 and is calculated using 10-base logarithm instead of natural e-based logarithm (which is called then a Neper).
Given the number E and the reference R, the ratio is defined as:
<math>A=10\cdot \log_{10}\frac{E}{R}\ \mathrm{dB}</math>
E and R in electrical engineering and in acoustics are usually energetic values. When voltage or pressure values are used, E and R are squared; thus the formula above can be rewritten as
<math>A=20\cdot \log_{10}\frac{e}{r}\ \mathrm{dB}</math>
For ease of understanding the unit of the reference value, a letter(s) is often written after the term dB, e.g. dBSPL (sound pressure level in dB), dBW (watts expressed in dB). Their reference levels are also pre-defined.
| name | notation | reference level |
| sound pressure level (air) | dBSPL, dBA, dBB, dBC, dBD, dBZ | 20e-6 Pa |
| particle velocity level | dBSVL | 5e-8 m/s |
| sound power level | dBSWL | 1e-12 W |
| sound intensity level | dBSIL | 1e-12 W/m |
| voltage | dBV | 1 V |
| voltage | dBu (unloaded), dBv | 0.775 V (RMS) |
| voltage | dBmV | 1 mV (RMS) |
| voltage | dBuV | 1e-6 V (RMS) |
| electric power | dBW | 1 W |
| electric power | dBm, dBmW | 1 mW |
Other dB 'units' e.g in radars are also used.
