Editing Gain (electronics) (section)

===Current gain===
In the same way, when power gain is calculated using current instead of power, making the substitution <math>P = I^2 R</math>, the formula is:

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

In many cases, the input and output impedances are equal, so the above equation can be simplified to:

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

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

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

The "current gain" of a [[bipolar transistor]],  <math>h_\text{FE}</math> or <math>h_\text{fe}</math>, is normally given as a dimensionless number, the ratio of <math>I_\text{c}</math> to <math>I_\text{b}</math> (or slope of the <math>I_\text{c}</math>-versus-<math>I_\text{b}</math> graph, for <math>h_\text{fe}</math>).

In the cases above, gain will be a dimensionless quantity, as it is the ratio of like units (decibels are not used as units, but rather as a method of indicating a logarithmic relationship).  In the bipolar transistor example, it is the ratio of the output current to the input current, both measured in [[ampere]]s. In the case of other devices, the gain will have a value in [[SI]] units. Such is the case with the [[operational transconductance amplifier]], which has an open-loop gain ([[transconductance]]) in [[siemens (unit)|siemens]] ([[mho]]s), because the gain is a ratio of the output current to the input voltage.