The Bel (B) is an unit used to express the ratio between two quantities of the same nature (power, current or voltage) in a logarithmic form.
The next formulas are used to calculate power, voltage and current ratios in decibels (1 dB = 0,1 B).
The decibel is derivated from common logarithms (base 10).
Note: Since the decibel is a comparasion unit (not an absolute value), in some cases a reference level must be indicated. When working with amplifiers, for instance, it is common to adopt as a reference or zero level 1 mW (600 Ω).
If 1 mW is adopted as reference, the letter “m” is added to dB, which becomes “dBm”.
Formula 1
dB = 10 log(Pout / Pin)
Where:
dB is the powr gain or loss (pure number)
Log is the common logarithm or of the expression (base 10)
Pout is the outptut Power in watts (W)
Pin is the input Power in watts (W)
Formula 2
dB = 20 log(Vout / Vin)
Where:
dB is the voltage gain or loss (pure number)
Log is the common logarithm of the expression (base 10)
Vout is the output voltage in volts (V)
Vin is the input voltage in volts (V)
Formula 3
dB = 20 log(Iout / Iin)
Where:
dB is the current gain or loss in amperes (A)
Log is the common logarithmi of the expression (base 10)
Iin is the input current in amperes (A)
Iout is the output current in amperes (A)
Application Example:
Na amplifier is Said to have a Power output of 10 W when a 0,5 W sinal is applied to its input. Calculate the power gain in dB.
Data:
Pout = 10 W
Pin = 0,5
dB = ?
Applying formula 1:
dB = 20 log(10 / 5)
dB = 20 log2
dB = 20 x 0,65
dB = 13 dB
