Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more.  ## Decibel - A Unit for Expressing Ratios

In the context of electrical engineering it is often necessary not only to measure voltage, current and power but also ratios of voltages, current measurements and power readings. Examples of ratios of two voltages are the voltage gain of an operational amplifier, the noise figure, or the gain of an antenna.

Such ratios are dimensionless in principle and can span a vast range. In order to facilitate computation of such ratios, one can use logarithms for the measurements in question, transforming the division into a subtraction and the multiplication into an summation. Logarithm-based ratios are indicated with the designation 'Bel' (after the inventor of the telephone, Graham Bell). However, usually a tenth of a Bel is used: the decibel or dB.

Since the relationship between voltage and power or current and power at a resistance is quadratic, the definition for the unit decibel results in an expression which is different for current and voltage, and for power:

Voltage: dB = 20 lg(V1/V0)

Current: dB = 20 lg(I1/I0)

Power: dB = 10 lg(P1/P0)

If a certain value is defined for V0, I0 or P0, then the quantity dB indicates the ratio between V1, I1 or P1 and the corresponding reference value. The reference value is called the zero level; the indication in dB is generally denoted as the level. When indicating a level, the base factor must also always be indicated, which usually occurs in the form an additional specification attached to the designation dB (e.g. dBμV, dbW or dBm).

In audio technology, the zero-level is specified as that voltage, which allows 1 mW power loss to develop at a resistance of 600 ohms. This level is indicated by 'dBm', and its zero-level amounts to 0.775 V. The same applies (for example in antenna technology) to dBm and dbW, if it is used for indicating the power. Hence, dBm then refers to 1 mW, and dbW to 1 W.

The following table indicates the appropriate voltage and power relationships for the most important dB-values as well as frequently used voltage levels and power data.

 dB V1/V0 P1/P0 dBW dBm Level Power 60 1000 1000000 30 60 774.6 V 1 kW 50 316.2 100000 20 50 244.9 V 100 W 40 100 10000 10 40 77.46 V 10 W 30 31.62 1000 0 30 24.49 V 1 W 20 10 100 -10 20 7.746 V 100 mW 10 3.162 10 -20 10 2.449 V 10 mW 6 2 4 -30 0 775 mV 1 mW 3 1.41 2 -40 -10 244.9 mV 100 μW 0 1.0 1 -50 -20 77.5 mV 10 μW -3 0.707 0.5 -60 -30 24.49 mV 1 μW -6 0.5 0.25 -10 0.3162 0.1 dBW = 10 lg(P/1 W) -20 0.1 0.01 dBm = 10 lg(P/1 mW) = -30 0.03162 0.001 20 lg(V/0.775 V) -40 0.01 0.0001 -50 0.003162 0.00001 -60 0.001 0.000001

Last Update: 2012-10-08