Decibel

Decibel is a logarithmic unit used to describe the ratio of the signal level - power, sound pressure, voltage, intensity, etc.

Most signal systems - as sound power or sound intensity, human speech, sonar, microwaves, radio signals and fiber optics - can be described by

• transmitting power
• transmission path loss
• receiver sensitivity

Transmitting power, path loss and receiver sensitivity are absolute power values - Watts in the SI system.

The Definition of Decibel

Decibel is a logarithmic unit used to describe the ratio of the signal level - power, sound pressure, voltage or intensity or several other things.

The decibel can be expressed as:

decibel = 10 log(P / P_ref )         (1)

where

P = signal power (W)

P_ref = reference power (W)

A decibel is one-tenth of a Bel - named after Alexander Graham Bell, the inventor of the telephone.

Note! Doubling the signal level increases the decibel with 3 dB (10 log (2)).

If we know the decibel value and the reference level, the absolute level can be calculated by transforming (1) to:

P = P_ref 10^{(decibel / 10)}         (2)

Example - Sound Intensity and Decibel

The difference in sound intensity of 10^-8 watts/m² and 10^-4 watts/m² (10,000 units) can be calculated in decibels as

ΔL_I = 10 log( (10^-4 watts/m²) / (10^-12 watts/m²) ) - 10 log( ( 10^-8 watts/m²) / ( 10^-12 watts/m²) )

    = 40 dB

Increasing the sound intensity by a factor of

• 10 raises its level by 10 dB
• 100 raises its level by 20 dB
• 1,000 raises its level by 30 dB
• 10,000 raises its level by 40 dB and so on

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