Appendix
CU8890-0000
35
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 = 10
level 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
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
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
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
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