#Decibel scale equation full#

(See Bode Plot and half logarithm graph.) This allows one to clearly visualize huge changes of some quantity. The decibel's logarithmic nature means that a very large range of ratios can be represented by a convenient number, in a similar manner to scientific notation.The use of the decibel has a number of merits: (In exact terms the power factor is 10 6/10, or about 3.9811, a relative error of about 0.5%.) Similarly, an increase of 3 dB implies an increase in voltage by a factor of approximately √2, or about 1.41, an increase of 6 dB corresponds to approximately four times the power and twice the voltage, and so on. In exact terms, the factor is 10 3/10, or 1.9953, about 0.24% different from exactly 2. It is seen that there is a 10 dB increase (decrease) for each factor 10 increase (decrease) in the ratio of the two power levels, and approximately a 3 dB increase (decrease) for every factor 2 increase (decrease). Thus, if L represents the ratio of a power value P 1 to another power value P 0, then L dB represents that ratio expressed in decibels and is calculated using the formula: When referring to measurements of power or intensity, a ratio can be expressed in decibels by evaluating ten times the base-10 logarithm of the ratio of the measured quantity to the reference level. In April 2003, the International Committee for Weights and Measures (CIPM) considered a recommendation for the decibel's inclusion in the SI system, but decided not to adopt the decibel as an SI unit. In many situations, however, the bel proved inconveniently large, so the decibel has become more common. It was originally called the transmission unit or TU, but was renamed in 1923 or 1924 in honor of the Bell System's founder and telecommunications pioneer Alexander Graham Bell. The bel was originally devised by engineers of the Bell Telephone Laboratories to quantify the reduction in audio level over a 1 mile (approximately 1.6 km) length of standard telephone cable.

5.2.5 Radio power, energy, and field strength.5.1 'Absolute' and 'relative' decibel measurements.5 Common reference levels and corresponding units.For a similar unit using natural logarithms to base e, see neper. The definitions of the decibel and bel use base-10 logarithms. The practice of attaching a suffix in this way, though not permitted by SI, is widely followed. For example, 'dBm' indicates that the reference quantity is one milliwatt, while 'dBu' is referenced to 0.775 volts. The decibel symbol is often qualified with a suffix, which indicates which reference quantity or frequency weighting function has been used.

#Decibel scale equation full#

The full name decibel follows the usual English capitalization rules for a common noun. However, following the SI convention, the d is lowercase, as it represents the SI prefix deci-, and the B is capitalized, as it is an abbreviation of a name-derived unit (the bel).

It confers a number of advantages, such as the ability to conveniently represent very large or small numbers, a logarithmic scaling that roughly corresponds to the human perception of, for example, sound and light, and the ability to carry out multiplication of ratios by simple addition and subtraction. The decibel is useful for a wide variety of measurements in science and engineering (e.g., acoustics and electronics) and other disciplines. Since it expresses a ratio of two (same unit) quantities, it is a dimensionless unit. The decibel ( dB) is a logarithmic unit of measurement that expresses the magnitude of a physical quantity (usually power or intensity) relative to a specified or implied reference level. For other uses, see Decibel (disambiguation).