Editing Decibel (section)

=== Root-power (field) quantities ===
{{main|Power, root-power, and field quantities}}
When referring to measurements of root-power quantities, it is usual to consider the ratio of the squares of ''F'' (measured) and ''F''<sub>0</sub> (reference). This is because the definitions were originally formulated to give the same value for relative ratios for both power and root-power quantities. Thus, the following definition is used:
: <math>
L_F = \ln\!\left(\frac{F}{F_0}\right)\,\text{Np} = 10 \log_{10}\!\left(\frac{F^2}{F_0^2}\right)\,\text{dB} = 20 \log_{10} \left(\frac{F}{F_0}\right)\,\text{dB}
</math>

The formula may be rearranged to give
: <math>
F = 10^\frac{L_F}{20\,\text{dB}} F_0
</math>

Similarly, in [[Electronic circuit|electrical circuits]], dissipated power is typically proportional to the square of voltage or current when the [[Electrical impedance|impedance]] is constant. Taking voltage as an example, this leads to the equation for power gain level ''L''<sub>''G''</sub>:
: <math>
L_G = 20 \log_{10}\!\left (\frac{V_\text{out}}{V_\text{in}}\right)\,\text{dB}
</math>
where ''V''<sub>out</sub> is the [[root-mean-square]] (rms) output voltage, ''V''<sub>in</sub> is the rms input voltage. A similar formula holds for current.

The term ''root-power quantity'' is introduced by ISO Standard [[ISO/IEC 80000|80000-1:2009]] as a substitute of ''field quantity''.  The term ''field quantity'' is deprecated by that standard and ''root-power'' is used throughout this article.