Google Search

Custom Search

Saturday, November 8, 2008

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: Av = dVout/ dVin if Vout = 0 when Vin = 0, then A = Vout / Vin

Current Gain: AI = dIout / dIin if Iout = 0 when Iin = 0, then A = Iout / Iin

Power Gain: Ap = dPout / dPin if Pout = 0 when Pin = 0, then A = Pout / Pin

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: AZ = dVout / dIin if Vout = 0 when Iin = 0, then I = Iout / Iin

Transadmittancc Gain: AY = dIout / dVin if Iout = 0 when Vin = 0, then A = Iout / Iin

No comments: