Decibels - Logarithmic scale

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A scale describes the relationship between two quantities. The logarithmic scale differs from a linear scale in that the proportion between two quantities isn't constant but rather, has a logarithmic rate. The following table highlights the different proportions, one linear and the other logarithmic, between two quantities X and Y:

Table 3.1. Comparison of a linear scale with a logarithmic scale 

LinearscaleLogarithmicscale
XYXY
11110
222100
3331000
............
nnn10n

The Bel is defined as the logarythm of the ratio between a quantity and its reference value. 1 Decibel equals 10Bel, so the decibel relating to a quantity X is expressed as follows:

Equation 3.1. dBX 

dBX

Which states decibel variations of the quantity X in relation to a fixed reference value X0.

If for example, the quantity we're considering is X and our reference value is X0 = 10, going from X0 to X=1000, we obtain an increase in dB expressed in the following formula:

Decibels and dynamics -








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