BEL

The bel is a logarithmic unit used to express ratios of physical quantities, most commonly power or amplitude, and it is named after Alexander Graham Bell. In its basic form, the bel measures the ratio of two quantities by taking the base-10 logarithm of the ratio.

For a power ratio P2/P1, the level in bels is L_B = log10(P2/P1) bels. Because many practical quantities are field quantities (such as voltage or electric field) rather than power, the bel can also be applied to those via the relationship P ∝ V^2 (for a fixed impedance). In that case L_B = log10((V2/V1)^2) = 2 log10(V2/V1) bels.

In practice, the bel is rarely used directly. The decibel, defined as one tenth of a bel, is the standard unit in most applications: dB = 10 log10(P2/P1) for power or dB = 20 log10(V2/V1) for voltage with constant impedance. Consequently, 1 bel equals 10 decibels.

The bel is a dimensionless logarithmic unit and is not part of the SI, though the decibel is widely used alongside SI units. Common applications include expressing gains, losses, and levels in acoustics, electronics, and communications, such as sound power levels, sound pressure levels, and amplifier gains. For example, a tenfold increase in power corresponds to 1 bel or 10 dB, and a tenfold increase in voltage (with constant impedance) corresponds to 20 dB.