Q:

Formula for amplitude of volatge, decibell

There is a formula for power 1 and power 2 to convert to decibell. 10*log(P1/P2), but when I have a amplitude of voltage in DC, formula is 2*10*log(U1max/U2max). Why is there a 2?  Thanks.

A:

Power is \$\dfrac{V^2}{R}\$ therefore (assuming the two R's are the same) the ratio of powers in this form becomes: -
Power ratio = \$\dfrac{V_O^2}{V_I^2}\$ = \$(\dfrac{V_O}{V_I})^2\$
The "square" becomes a multiplier outside of the log hence the 2 multiples by the 10.
For example log(\$x^2\$) = 2log(x)

