### What is a Decibel?

Decibal is the unit used to express relative differences in signal strength.
It is expressed as the base 10 logarithm of the ratio of the *powers*
of two signals:

dB = 10 log (P1/P2)

Signal amplitude can also be expressed in dB. Since power is proportional
to the square of a signal's amplitude (e.g., a power ratio of 100 is equivalent
to an amplitude ratio of 10), dB is expressed as follows:

dB = 20 log (A1/A2)

Logarithms are useful as the unit of measurement because (1) signal power
tends to span several orders of magnitude and (2) signal attenuation losses
and gains can be expressed in terms of subtraction and addition.

For example, suppose that a signal passes through two channel segments is
first attenuated in the ratio of 20 to 1 on the first leg and 7 to 1 on
the second. The total signal degradation is in the ratio of 140 to 1. Expressed
in dB, this becomes 13.01 (10 log 20) + 8.45 (10 log 7) = 21.46 dB.

The following table helps to indicate the order of magnitude associated
with dB:

1 dB attenuation means that 0.79 of the input power survives

3 dB attenuation means that 0.50 of the input power survives

10 dB attenuation means that 0.1 of the input power survives

20 dB attenuation means that 0.01 of the input power survives

30 dB attenuation means that 0.001 of the input power survives

40 dB attenuation means that 0.0001 of the input power survives

Randy H. Katz, randy@cs.Berkeley.edu, Last Updated: 29 December
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