Contrary to much popular usage, the decibel (dB) is not actually aunit of any particular quantity, but rather an expression of the ratio between two quantities, such as, power, voltage, current, acoustic pressure. Many sensors, including our own ears, respond to stimuli in a logarithmic fashion, that is, an increase of 10dB results in a doubling of loudness. This allows a huge range of intensities. Asthe dB compares the logarithmic quantities, it agrees with our perceptive comparisons. To calculate the ratio, in dB, of two power levels, P1 and P2, the formula is: dB = 10 log (P1/P2). If the quantities are voltages, currents or sound pressure levels, X1 and X2, the formula becomes: dB = 20 log (X1/X2). If the quantities X1 and X2are both measured in the same impedances, their dB ratio will be numerically equal to the dB ratio of their equivalent powers. If their impedances Z1 and Z2 are unequal, the dB ratio of their power can be found from: dB = 20 log (X1/X2) + 10 log (Z2/Z1). Negative dB ratios will result when P1 (or X1) is less than P2 (or X2), while positive values indicate that P1 (or X1) is greater than P2 (or X2).
