Calculating with decibels

In communication technology power is expressed in decibels (dB), a tenth of the unit Bel. It is the logarithmic ratio between two quantities with the same unit.

A reference variable (P1), e.g. a milliwatt (mW) is compared with the measured variable (P2). The logarithmic correlation was discovered by Alexander Graham Bell, in whose honor the unit Bel was named.

Since the number values would be too unwieldy if the Bel was used, it was agreed to use 1/10 of the value, i.e. the decibel.

Definition of the level difference: Level difference [dB] = 10 log ([P1] / [P2]).

Definition of a power ratio: power ratio = 10level difference/10

The advantage of expressing the powers and losses (attenuations) in dB is that the calculation method for power ratios can be replaced by a lower calculation method for the dB calculation.

 

Power ratio

dB calculation

Multiplication or division

Addition or subtraction

Exponent

Factor

Examples of power ratios

Factor

Amplification [dB]

x 1

+0 dB

x 1.25

+1 dB

x 2

+3 dB

x 4

+6 dB

x 10

+10 dB

x 16

+12 dB

x 100

+20 dB

x 1000

+30 dB

Factor

Attenuation [dB]

x 1

-0 dB

x 0.8

-1 dB

x 0.5

-3 dB

x 0.25

-6 dB

x 0.1

-10 dB

x 0.6

-12 dB

x 0.01

-20 dB

x 0.001

-30 dB

Examples of calculations with decibels

Change

in dB

10 / 2 = 5

10 - 3 = 7

2 x 2 x 2 = 8

3 + 3 + 3 = 9

2 x 100 = 200

3 + 20 = 23

1000 / 2 = 500

30 - 3 = 27