The decibel (dB) is a logarithmic unit used to express the ratio of two values of a physical quantity, often power or intensity. One of these values is often a standard reference value, in which case the decibel is used to express the level of the other value relative to this reference. One decibel is one tenth of one bel, named in honor of Alexander Graham Bell; however, the bel is seldom used. The unit is used for a variety of measurements in science and engineering, such as electrical power and voltage, light and sound intensity.
In radio systems, the term is usually used in the RF amplification and antenna systems, using the concept of "gain", or how much the effective signal is increased (or decreased) between the system's input and output.
The decibel is not a core unit of measurement. It's just a mathematical convenience, but a powerful one. First, calculations done in the core units, such as watts, that must be done with multiplication and division, can be done in decibels with simple addition and subtraction.
For example, suppose you have a two-stage power amplifier system, followed by coax and an antenna. The first amplifier stage increases the power of the incoming signal by 1,000 times; while the second stage increases it by 100 times. The signal loses half of its power traveling through the coax; then the antenna focuses the signal to increase the effective transmitted power in the desired direction by 4 times. Using watts, the final effective power leaving the antenna is
1,000 x 100 ÷ 2 x 4, or 200,000 times greater than the signal entering the power amplifier.
Using decibels, the same system output is 30 + 20 - 3 + 6, or 53 dB gain.
The next reason, as you can see from the above example, is that the numbers used in core unit calculations can get rather large and cumbersome.
Finally, measurements in decibels are more closely related to the actual effect produced at a distant receiver. "One decibel represents a just-detectable change in signal strength, regardless of the actual value" (in watts, for example) "of the signal."* A 20 dB increase in signal represents 20 observable steps in increased signal. The actual power ratio (100 to 1) corresponding to 20 dB gives an exaggerated idea of the improvement in communications to be expected.
For power conversions, the formula for converting watts to dB is: dB = 10 log10(P1/P2)
For voltage conversions, the formula for converting watts to dB is: dB = 20 log10(V1/V2)
A popular term used in power measurement is dBm, meaning decibels referenced to one milliwatt. This would make "P2" in the above formula equal to one milliwatt. This changes decibels from a comparison between two numbers to an actual measurement unit.
Of course, we must caution that any dB calculation assumes that all components of the system being considered (radio, transmission line, antenna, etc.) have the same impedance. Otherwise, the results will be meaningless.
Some good rules of thumb for remembering the conversions are:
Note a few things in the above:
1.) Each time the decibels go up by 3, the core unit doubles.
2.) Likewise, each time the decibels go down by 3, the core unit halves.
3.) By mathematical coincidence, 10 dB is equal to an increase of 10 times the core unit.
4.) When counting up by 10s of decibels (10, 20, 30, etc.), the the first digit in the decibel number (1, 2, 3, etc.) equals the number of zeros that follow the one (1) of the core unit (10, 100, 1,000, etc.).
* The ARRL Antenna Book, 21st Edition.
ITU-R Recommendation V.574.5, Use of the Decibel and the Neper in Telecommunications
A Tutorial on the Decibel complied by Ward Silver, N0AX (from the ARRL website) (PDF)
Note: dB meter image from wikimedia.