# decibel

In electronics and communications, the decibel (abbreviated as dB, and also as db and DB) is a logarithmic expression of the ratio between two signal power, voltage, or current levels. In acoustics, the decibel is used as an absolute indicator of sound power per unit area. A decibel is one-tenth of a Bel, a seldom-used unit named for Alexander Graham Bell, inventor of the telephone.

Suppose a signal has a power of *P*_{1} watts, and a second signal has a power of *P*_{2} watts. Then the power amplitude difference in decibels, symbolized *S*_{dBP}, is:

*S*_{dBP} = 10 log_{10} (*P*_{2} / *P*_{1})

Decibels can be calculated in terms of the effective voltage if the load impedance remains constant. Suppose a signal has an rms (root-mean-square) voltage of *V*_{1} across a load, and a second signal has an rms voltage of *V*_{2} across another load having the same impedance. Then the voltage amplitude difference in decibels, symbolized *S*_{dBV}, is:

*S*_{dBV} = 20 log_{10} (*V*_{2} / *V*_{1})

Decibels can also be calculated in terms of the effective current (amperage) if the impedance remains constant. Suppose a signal delivers an rms (root-mean-square) amperage of *A*_{1} through a load, and a second signal delivers an rms amperage of *A*_{2} through another load having the same impedance. Then the current amplitude difference in decibels, symbolized *S*_{dBA}, is:

*S*_{dBA} = 20 log_{10} (*A*_{2} / *A*_{1})

When a decibel figure is positive, then the second signal is stronger than the first signal. When a decibel figure is negative, then the second signal is weaker than the first signal. In amplifiers, the gain, also called the amplification factor, is often expressed in decibels. A circuit amplifies only if the decibel figure for the output-to-input power ratio (*S*_{dBP}) is positive.

In sound, decibels are defined in terms of power per unit surface area on a scale from the threshold of human hearing, 0 dB, upward towards the threshold of pain, about 120-140 dB. As examples: the sound level in the average residential home is about 40 dB, average conversation is about 60 dB, typical home music listening levels are about 85 dB, a loud rock band about 110 dB, and a jet engine close up is 150dB.

Decibel units are commonly used in audio equalizers, both the hardware kind and the software kind, as a convenient reference point while editing. Boosting an equalizer band whose center point is 1000 by 3 dB means that you have raised the volume level of that frequency band by 3 dB as it relates to the other frequencies in the sound. A typical equalizer has a range for boosting or diminishing a sound level of +/-18 dB.