"Decibel" - A
decibel is a logarithmic unit representing a change ratio and, because it represents a ratio, the dB is, itself, a dimensionless unit (that is, it doesn't imply milliwatts, watts, or any other particular unit of measurement). The dB unit is 1/10th of a "bel", named after Alexander Grahm Bell. (Originally the ratio was called the TU "Transmission Unit" but was renamed in the 1920's by the engineers at Bell Telephone Laboratory) A bel is the exponent of 10 (hence, the logarithm) representing a ratio. An example will clarify this definition. Suppose that a signal is transmitted with a power level of 100 mW. At some distance from the transmitter the signal is measured and found to have attenuated to a level of 1 mW. The ratio of the measured signal to the original signal is 1:100. The measured signal is 100 times smaller than the original. The number 100 is equal to 10 raised to the second power (100=10^2). The exponent (2) is the "bel" unit. It could be said that the measured signal was 2-bels less than the transmitted signal. As it turns out, the bel ratio metric is too big for most measurements and so the deci-bel (1/10th of a bel) is the common value used. In the example, the transmitted signal has experienced a 20 dB loss at the measurement point. In practical terms, when a dB value goes up or down by 3 it means that the ratio between the two measured values is 2 (up) or 1/2 (down). If a signal experiences an attenuation of 3dB it is now half as strong as it was originally. A value of 3 dB implies .3 bels (since 1 bel = 10 decibels), and 10^.3=1.995 (essentially=2). To convert from dB to the ratio, divide the dB value by 10 (to convert to bels) and use the resultant number as an exponent of 10.
"dB milliwatts" - The dB ratio is used in conjunction with a predetermined denominator to represent actual units of measurement (as opposed to dimensionless ratios). When the denominator of the ratio is 1 milliwatt the resulting logarithmic representation of milliwatts is called a "dB milliwatt". Hence, 10 dBm = 10^1 milliwatts = 1 mW. Applying the rules for dB ratios, and using 1mW as the denominator in the calculations, the following conversion formulae may be applied