Definition of Gain

Gain is defined as the ratio of the output signal to the input signal. Because transistor amplifiers often have a quiescent output (a non zero output when the input is zero) we define gain as the derivative of the output with respect to the input. Thus gain is defined as the ratio of the change in output to the change in input.

So far we have not specified the output quantity, the reason is that we can define the gain with respect to any given output and input quantity.

General definition: A =d(Output) / d(Input) if (Output) = 0 when (Input) = 0, then A = (Output) / (Input)

Voltage Gain: A_v = dV_out/ dV_in if V_out = 0 when V_in = 0, then A = V_out / V_in

Current Gain: A_I = dI_out / dI_in if I_out = 0 when I_in = 0, then A = I_out / I_in

Power Gain: A_p = dP_out / dP_in if P_out = 0 when P_in = 0, then A = P_out / P_in

Note that a negative gain means that the sign of the signal is inverted. Negative gain is not possible for Power Gain. |A| less than unity indicate that the output is smaller than the input.

The quantities need not be the same. If the input and output quantities are different, the gain is no longer unitless. The most common examples are transimpedancc gain and transadmittancc gain.

Transmpedancc Gain: A_Z = dV_out / dI_in if V_out = 0 when I_in = 0, then I = I_out / I_in

Transadmittancc Gain: A_Y = dI_out / dV_in if I_out = 0 when V_in = 0, then A = I_out / I_in