Editing Gain (electronics) (section)

===Voltage gain===
The power gain can be calculated using voltage instead of power using [[Joule's first law]] <math>P = V^2/R</math>; the formula is:

:<math>\text{gain-db} = 10 \log{\frac{\frac{V_\text{out}^2}{R_\text{out}}}{\frac{V_\text{in}^2}{R_\text{in}}}}~\mathrm{dB}.</math>

In many cases, the input impedance <math>R_\text{in}</math> and output impedance <math>R_\text{out}</math> are equal, so the above equation can be simplified to:

:<math>\text{gain-db} = 10 \log \left(\frac{V_\text{out}}{V_\text{in}}\right)^2~\text{dB},</math>

:<math>\text{gain-db} = 20 \log \left(\frac{V_\text{out}}{V_\text{in}}\right)~\text{dB}.</math>

This simplified formula, the [[20 log rule]], is used to calculate a '''voltage gain''' in decibels and is equivalent to a power gain if and only if the [[Electrical impedance|impedances]] at input and output are equal.