The decibel (dB)

The **decibel** (**dB**) is a logarithmic unit used to express the ratio between two values of a physical quantity, often power orintensity. One of these quantities is often a reference value, and in this case the decibel can be used to express the absolute level of the physical quantity, as in the case of sound pressure. The number of decibels is ten times the logarithm to base 10of the ratio of two power quantities, or of the ratio of the squares of two field amplitude quantities. One decibel is one tenth of one **bel**, named in honor of Alexander Graham Bell. The bel is seldom used without the *deci-* prefix.

The definition of the decibel is based on the measurement practices in telephony of the early 20th century in the Bell Systemin the United States. Today, the unit is used for a wide variety of measurements in science and engineering, most prominently in acoustics, electronics, and control theory. In electronics, the gains of amplifiers, attenuation of signals, andsignal-to-noise ratios are often expressed in decibels. The decibel confers a number of advantages, such as the ability to conveniently represent very large or small numbers, and the ability to carry out multiplication of ratios by simple addition and subtraction.

A change in power by a factor of 10 corresponds to a 10 dB change in level. A change in power by a factor of two approximately corresponds to a 3 dB change. A change in voltage by a factor of 10 results in a change in power by a factor of 100 and corresponds to a 20 dB change. A change in voltage ratio by a factor of two approximately corresponds to a 6 dB change.

The decibel symbol is often qualified with a suffix that indicates which reference quantity has been used or some other property of the quantity being measured. For example, **dBm** indicates a reference level of one milliwatt, while **dBu** is referenced to approximately 0.775 volts RMS.

In the International System of Quantities, the decibel is defined as a unit of level or of level difference, equal to one-tenth of a bel. The bel is then defined in terms of the neper, an alternative unit of level of root-power quantities, applicable when thenatural logarithm (base *e*) is used to define the level.

dB | power ratio | amplitude ratio | ||
---|---|---|---|---|

100 | 10 000 000 000 | 100 000 | ||

90 | 1 000 000 000 | 31 623 | ||

80 | 100 000 000 | 10 000 | ||

70 | 10 000 000 | 3 162 | ||

60 | 1 000 000 | 1 000 | ||

50 | 100 000 | 316 | .2 | |

40 | 10 000 | 100 | ||

30 | 1 000 | 31 | .62 | |

20 | 100 | 10 | ||

10 | 10 | 3 | .162 | |

6 | 3 | .981 | 1 | .995 (~2) |

3 | 1 | .995 (~2) | 1 | .413 |

1 | 1 | .259 | 1 | .122 |

0 | 1 | 1 | ||

−1 | 0 | .794 | 0 | .891 |

−3 | 0 | .501 (~1/2) | 0 | .708 |

−6 | 0 | .251 | 0 | .501 (~1/2) |

−10 | 0 | .1 | 0 | .316 2 |

−20 | 0 | .01 | 0 | .1 |

−30 | 0 | .001 | 0 | .031 62 |

−40 | 0 | .000 1 | 0 | .01 |

−50 | 0 | .000 01 | 0 | .003 162 |

−60 | 0 | .000 001 | 0 | .001 |

−70 | 0 | .000 000 1 | 0 | .000 316 2 |

−80 | 0 | .000 000 01 | 0 | .000 1 |

−90 | 0 | .000 000 001 | 0 | .000 031 62 |

−100 | 0 | .000 000 000 1 | 0 | .000 01 |

An example scale showing power ratios x and amplitude ratios √x and dB equivalents 10 log_{10} x. It is easier to grasp and compare 2- or 3-digit numbers than to compare up to 10 digits. |

#http://en.wikipedia.org/wiki/Decibel