# The Decibel

The decibel (dB) is the unit of relative power. If one signalis twice as loud as another, it has a gain of 3dB. One advantage ofexpressing 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 theoutput 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 becalculated with the formula:-

 20 Log10( V Out ) dB gain ------- -------- V In
However, the result is only correct when the input and output impedancesof the circuit are the same.