Bel
For the Mesopotamian deity, see Bel (god)
A bel (symbol B) is a unit of measure of ratios of power levels, i.e., relative power levels. It is mostly used in telecommunication, electronics and acoustics. Invented by engineers of the Bell Telephone Laboratory, it was originally called the transmission unit or TU, but was renamed in 1923 or 1924 in honour of the laboratory's founder and telecommunications pioneer Alexander Graham Bell.
The bel is a logarithmic measure. The number of bels for a given ratio of power levels is calculated by taking the logarithm, to the base 10, of the ratio. Therefore, one bel corresponds to a ratio of 10:1. Mathematically, the number of bels is calculated as B = log10(P1/P2) where P1 and P2 are power levels. The neper is a similar unit which uses the natural logarithm.
The bel is too large for everyday use, so the decibel (dB), equal to 0.1 B, is more commonly used. One decibel is equivalent to a ratio of about 1.259:1. It is defined as 10 log10(P1/P2) where P1 and P2 are the powers.
The decibel is not an SI unit, although the CIPM has recommended its inclusion in the SI system.
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2 Typical abbreviations 3 Common misconception: +3 dB means "times two" 4 References |
Uses
Optics
In an optical link, if a known amount of optical power, in dBm (decibel.milliwatts), is launched into a fibre, and the losses, in dB (decibels), of each component (e.g. connectors, splices, and lengths of fibre) are known, the overall link loss may be quickly calculated by simple addition and subtraction of decibel quantities.
Acoustics
The decibel is often used in acoustics to quantify sound levels relative to some 0 dB reference. The reference may be defined as a sound pressure level (SPL), commonly 20 micropascal (20 μPa). To avoid confusion with other decibel measures, the term dB(SPL) is used for this. The reference can also be defined as the sound intensity at the threshold of human hearing, which is conventionally taken to be one picowatt per square metre (1 pW/m²), roughly the sound of a mosquito flying 10 feet (3 m) away.
The reason for using the decibel is that the ear is capable of hearing a very large range of sound pressures. The ratio of the sound pressure that causes permanent damage from short exposure to the limit that (undamaged) ears can hear is more than a million. Because the power in a sound wave is proportional to the square of the pressure, the ratio of the maximum power to the minimum power is more than one trillion. To deal with such a range, logarithmic units are useful: the log of a trillion is 12, so this ratio represents a difference of 120 dB.
Psychologists have found that our perception of loudness is roughly logarithmic, see Weber-Fechner Law. In other words, you have to multiply the sound intensity by the same factor to have the same increase in loudness. This is why the numbers around the volume control dial on a typical audio amplifier are related not to the absolute power amplification, but to its logarithm.
Various frequency weightings are used for acoustical measurements to approximate the changes in sensitivity of the ear to different frequencies at different levels. These include the dB(A), dB(B), and dB(C) weightings.
Sounds above 85 dB are considered harmful, while 120 dB is unsafe and 150 dB causes physical damage to the human body. Windows break at 163 dB. Jet airplanes are 165 dB. Eardrums pop at 190 to 198 dB. Shock waves and sonic booms are 194 dB. Sounds around 200 dB can cause death to humans and are generated near bomb explosions. The space shuttle is around 215 dB. Nuclear bombs are 240 dB to 258 dB. Even louder are earthquakes, tornados, hurricanes and volcanoes.
To do: these example SPLs could do with distances from source...
In radio electronics, the decibel is used to describe the ratio between two measurements of electrical power. It can also be combined with a suffix to create an absolute unit of electrical power. For example, it can be combined with "m" for "milliwatt" to produce the "dBm". 0 dBm is one milliwatt, and 1dBm is one decibel greater than 0 dBm, or about 1.259 mW.
To contrive a more serious example, consider converting a large decibel figure into its linear ratio, for example 120 dB. This is correctly calculated as a ratio of 1012 or one trillion. But if we use the assumption that 3 dB means "times 2", we would calculate a ratio of 2120/3 = 240 = 1.0995 × 1012, for a 10% error.Electronics
The decibel is used rather than arithmetic ratios or percentages because when certain types of circuits, such as amplifiers and attenuators, are connected in series, expressions of power level in decibels may be arithmetically added and subtracted. Telecommunications
In telecommunications, decibels are commonly used to measure signal-to-noise ratios.Seismology
Earthquakes are measured on the Richter scale, which is expressed in bels. (The units in this case are always assumed, rather than explicit.)Typical abbreviations
Absolute measurements:
Relative measurements:
Common misconception: +3 dB means "times two"
Not exactly. As stated above, decibels are defined so that +10 dB means "ten times the power". From this, we calculate that +3 dB actually multiplies the power by 103/10. This is a ratio of 1.9953 or about 0.25% different from the "times 2" ratio that is sometimes assumed. A level difference of +6 dB is 3.9811, about 0.5% different from 4.
