# The Decibel

The decibel (dB) is the unit of relative power. If one signal is twice as loud as another, it has a gain of 3dB. One advantage of expressing power in decibels is that, in a multi-stage amplifier, the power gains of the stages can simply be added together.

The general expression for calculating the decibel gain of a circuit (or an antenna) is:-

10 Log10( | Power Out |  | ) dB gain
------------ | --------
Power In |

Enter values for 'Power Out' and 'Power In' and press the ' = ' button.

## dBW

The UK amateur radio licence expresses the maximum permitted output power for each band in dBW. This is the output power, in dB, relative to 1 Watt. To express this in Watts, the following formula can be used:-

Antilog( | dBW |  | ) Watts
------ | --------
10 |

## Antenna Gain

The gain of an antenna is relative to either a theoretical, isotropic aerial (dBi) or relative to a half-wave dipole (dBd).

## Voltage Gain

The dB gain of one voltage relative to another can be calculated with the formula:-

20 Log10( | V Out |  | ) dB gain
------- | --------
V In |

However, the result is only correct when the input and output impedances of the circuit are the same.