http://en.wikipedia.org/wiki/Decibel:

When referring to measurements of amplitude it is usual to consider the ratio of the squares of X (measured amplitude) and X0 (reference amplitude). This is because in most applications power is proportional to the square of amplitude. Thus the following definition is used:


Similarly, in electrical circuits, dissipated power is typically proportional to the square of voltage or current when the impedance is held constant. Taking voltage as an example, this leads to the equation: