Decibel
Logarithmic unit used to describe ratios of signal levels  like power or intensity  to a reference level.
The decibel is a logarithmic unit used to describe the ratio of a signal level  like power, intensity or amplitude  to a reference level.
 the decibel express the level of a value relative to a reference value
Two types of decibel are normally used:
 for power ratios  dB is defined as ten times the logarithm in base 10
 for amplitude ratios  root power quantities  a change in amplitude by a factor of 10 corresponds to 20 dB change in level
Decibel Definition  Power Ratios
The decibel level of a signal can be expressed as
L = 10 log (S / S _{ref}) (1)
where
L = signal level (decibel, dB)
S = signal  intensity or power level (signal unit)
S _{ref} = reference signal  intensity or power level (signal unit)
Decibel is a dimensionless value of relative ratios. The signal units depends on the nature of the signal  can be W for power.
A decibel is onetenth of a Bel  named after Alexander Graham Bell, the inventor of the telephone.
Note!  the decibel value of a signal increases with 3 dB if the signal is doubled (L = 10 log (2) = 3).
dB  Power Ratio (S/S_{ref})  Amplitude Ratio (A/A_{ref}) 

40  0.0001  0.01 
20  0.01  0.1 
0  1  1 
3  2  √2 
6  4  2 
10  10  3.162 
20  100  10 
If the decibel value and reference level are known the absolute signal level can be calculated by transforming (1) to
S = S _{ref} 10 ^{(L / 10)} (2)
Decibel Calculator
Example  Lowest Hearable Sound Power
10 ^{12} W is normally the lowest sound power possible to hear and this value is normally used as the reference power in sound power calculations.
The sound power in decibel from a source with the lowest sound hearable can be calculated as
L = 10 log ( (10 ^{12} W ) / (10 ^{12} W ))
= 0 dB
Example  Highest Hearable Sound Power
100 W is almost the highest sound power possible to hear. The sound power in decibel from a source with the highest possible to hear sound power can be calculated as
L = 10 log ( (100 W) / (10 ^{12} W ))
= 140 dB
Example  Sound Power from a Fan
A fan creates 1 W of sound power. The noise level from the fan in decibel can be calculated as
L = 10 log ((1 W) / (10 ^{12} W ))
= 120 dB
Example  Sound Intensity and Decibel
The difference in decibel between sound intensity 10 ^{8} W/m ^{2} and sound intensity 10 ^{4} W/m ^{2} ( 10000 units) can be calculated as
ΔL = 10 log ((10 ^{4} W/m ^{2}) / (10 ^{12} W/m ^{2}))  10 log ((10 ^{8} W/m ^{2}) / (10 ^{12} W/m ^{2}))
= 40 dB
Increasing the sound intensity by a factor of
 10 raises its level by 10 dB
 100 raises its level by 20 dB
 1000 raises its level by 30 dB
 10000 raises its level by 40 dB and so on
Decibel Ratios  Amplitude Ratios
L = 20 log (A / A _{ref}) (3)
where
L = signal level (decibel, dB)
A = amplitude level (signal unit)
A _{ref} = amplitude level level (signal unit)
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