Decibel

Decibel (dB)

The decibel is simply a means of expressing the relative difference in the size of two values. This has many uses when dealing with audio.

The bel is simply log₁₀ (A/B). The decibel is then 10^-1 bels (i.e. 0.1 bels) or 10 log₁₀ (A/B) to effectively allow a higher precision to be quoted.

Sound level

Often people quote decibels as a measure of sound level, though are unaware of what it means. Sound intensity is measured in Watts per metre square (Wm^-2). The threshold of hearing (at 1000 Hz) is defined as 0.00002 Nm^-2 or .000000000001 (10^-12) (Wm^-2). Consequently, sound level is defined as 10 log₁₀ (I/10^-12). However the human ear does not have a linear response across all frequencies (i.e. it's not as sensitive to low notes as it is to higher ones) and loudness is subjective. Consequently, another unit exists, often referred to as dBA, which is based on a model of the human ear and considers the difference in sensitivity across different frequencies.

Electrical circuits

dB is also used to express the gain (or attenuation) in electrical circuits used to process a signal (e.g. an amplifier or a mixing desk). Faders on mixing desks for instance may be marked from -infinity to +10. With the fader set to 0dB the signal going in will be at the same level as that coming out. Less than 0 will result in a gain less than 1 and so will be attenuated, while a positive value will result in an increased output.

In electricity, power is defined as V²/R consequently, when referring to signals relative to their voltage, we need to multiply by 2.
So, e.g. if an amplifier has a gain of 60dB, and a signal with voltage of 5mV is input, there will be and output of 5V. (60 = 20 log (V_out/0.005), 3 = log (V_out/0.005), so 1000 = V_out/0.005, V_out = 5V.

It is convenient to remember that doubling the voltage corresponds to gain of 6 dB.

It should be clear from the above that there is a difference between measuring sound level and electrical gain, (even though both are expressed in dB) and that markings on electrical equipment refer to amplification of signals and not the sound level output through the speakers.

Seehttp://otto.cmr.fsu.edu/~elec4mus/topics/decibel.html for more details