# dB, dBW, dBm, Logarithm, ...

What is a Decibel ?

Decibel is the unit used to express relative differences in signal strength.

Decibel is expressed as the base 10 logarithm of the ratio of the power of two signals : dB = 10 x Log10 (P1/P2)
Where Log10 is the base 10 logarithm and P1 and P2 are the powers to compare
(Log10 is different from Ln or LN = Neparian Logarithm, base e logarithm)

Signal amplitude can also be expressed in dB. Since power is proportional to the square of a signal's amplitude, dB is expressed as follows : dB = 20 x Log10 (V1/V2)
Where V1 and V2 are the amplitudes to compare

1 Bell (not really used in current) = Log10(P1/P2)

1 decibel (dB) = 1 Bell / 10 = 10 * Log10(P1/P2)

dBr = dB (relative) = dB = 10 * Log10(P1/P2)

base 10 Logarithm rules
Log10 (AxB) = Log10 (A) + Log10 (B)
Log10 (A/B) = Log10 (A) - Log10 (B)
Log10 (1/A) = - Log10 (A)
Log10 (0,01) = - Log10 (100) = -2
Log10 (0,1) = - Log10(10) = - 1
Log10 (1) = 0
Log10 (2) = 0,3
Log10 (4) = 0,6
Log10 (10) = 1
Log10 (20) = 1,3
Log10(2 x 10) = Log10(2) + Log10(10) = 1 + 0,3
Log10 (100) = 2
Log10 (1 000) = 3
Log10 (10 000) = 4

Logarithm and dB (decibel)
Power Ratio dB = 10 x log10 (Power Ratio)
AxBx dB = 10 x Log10(A) + 10 x Log10(B)
A/Bx dB = 10 x Log10(A) - 10 x Log10(B)
1/Ax dB = + 10 x Log10(1/A) = - 10 x Log10(A)
0,01- 20 dB = - 10 x Log10(100)
0,1- 10 dB = 10 x Log10(1)
10 dB = 10 x Log10(1)
23 dB = 10 x Log10(2)
46 dB = 10 x Log10(4)
1010 dB = 10 x Log10(10)
2013 dB = 10 x (Log10(10) + Log10(2))
10020 dB = 10 x Log10(100)
1 00030 dB = 10 x Log10(1 000)
10 00040 dB = 10 x Log10(10 000)

dBm = dB milliwatt = 10 x Log10 (Power in mW / 1 mW)
Power Ratio dBm = 10 x
Log10 (Power in mW / 1 mW)
1 mW1 mW / 1 mW = 10 dBm = 10 x Log10(1)
2 mW2 mW / 1 mW = 23 dBm = 10 x Log10(2)
4 mW4 mW/1mW=46 dBm = 10 x Log10(4)
10 mW10 mW/1mW=1010 dBm = 10 x Log10(10)
0,1 W100 mW/1mW=10020 dBm = 10 x Log10(100)
1 W1000 mW/1mW=100030 dBm = 10 x Log10(1 000)
10 W10 000mW/1mW=10 00040 dBm = 10 x Log10(10 000)

dBW = dB Watt = 10 x Log10 (Power in W / 1 W)
Power Ratio dBW = 10 x Log10 (Power in W / 1 W)
1 W1 W / 1 W = 10 dBW = 10 x Log10(1)
2 W2 W / 1 W = 23 dBW = 10 x Log10(2)
4 W4 W / 1 W = 46 dBW = 10 x Log10(4)
10 W10 W / 1 W = 1010 dBW = 10 x Log10(10)
100 mW0,1 W / 1 W = 0,1-10 dBW = -10 x Log10(10)
10 mW0,01 W / 1 W = 1/100-20 dBW = -10 x Log10(100)
1 mW0,001W/1W=1/1000-30 dBW = -10 x Log10(1000)

Power/Voltage Gain
dB Power Ratio Voltage Ratio dB Power Ratio Voltage Ratio
01,001,00 1010,003,16
11,261,12 1112,593,55
21,581,26 1215,853,98
32,001,41 1319,954,47
42,511,58 1425,125,01
53,161,78 1531,625,62
63,982,00 1639,816,31
75,012,24 1750,127,08
86,312,51 1863,107,94
97,942,82 1979,438,91
1010,003,16 20100,0010,00

Attenuation (dB) = 10xLog10(Pin/Pout) = 20xLog10(Vin/Vout)

Gain (dB) = 10xLog10(Pout/Pin) = 20xLog10(Vout/Vin)

Gain (dB) = - Attenuation (dB)

Power (W) = voltage (V) x Voltage (V) x Z (Ohm) = V x V / Z = V x I

So Gain(dB) = 10 x Log10(Pout/Pin) = 10 x Log10((Vout x Vout / Zout) / (Vin * Vin / Zin))
if Zin = Zout, Gain(dB) = 10 x Log10(Vout x Vout / Vin /Vin) =
10 x (Log10(Vout / Vin) + Log10(Vout / Vin)) = 10 x 2 x Log10(Vout / Vin) = 20 x Log10(Vout / Vin)

Si, après avoir consulté les rubriques qui vous sont proposées,
vous souhaitez faire part de votre avis, de vos suggestions, ...,
alors n'hésitez pas, envoyez un E-Mail à :