ln() vs. log()

[Andres]

Actually, Bel is the original unit and the power of signal S, measured in Bel is

log (S / Sref) [using base-10 log]

As this unit was not convenient enough, a smaller unit became more popular. It is the deci Bel, which is a tenth part of a Bel. Hence the symbol is dB, with a lower case d and an upper case B. As the unit is the tenth part of the Bel, a 10-times multiplier should be applied to the magnitude.

So the power of signal S, measured in dB is

10 log (S / Sref) [using base-10 log]

Bels and deciBels are intended to compare powerlike quantities. As the power of an electrical signal is related to the square of the voltage, V (or, for that matter, the square of the current, I), it is usually possible to state that the power of signal S, measured in dB is

20 log (V / Vref) or 20 log (I / Iref) [using base-10 log]

However, this is valid only if the voltage (or current) of the signal and the reference are measured over the same impedance value. Otherwise, these formulas cannot be used.

Please disregard any idiomatic or formatting mistake.

(04-18-2016 01:25 PM)Tugdual Wrote:  Also decibel is
\[20*\log _{ 10 }{ (\frac { V }{ { V }_{ ref } } ) }\]

I also find it interesting because it tells me the # of digits you need to write a number in base 10.