In small-signal analysis, a MOSFET transistor amplifier acts as a linear amplifier when operating in its saturation region. The gate-to-source voltage (V_GS) of the MOSFET is the sum of the DC biasing voltage and the small time-varying input signal. This combination sets up the operating point and modulates the drain current (I_D) that flows from the drain to the source. When a small AC signal is superimposed on the DC bias voltage at the gate, the instantaneous drain current comprises three parts:

The DC bias current (I_D0) is the quiescent current with no signal applied.

A component that varies linearly with the input signal is considered for amplification purposes.

A nonlinear component is a function of the input signal's square and leads to distortion in the amplified output.

For small signals, where the amplitude of the AC component of V_GS is sufficiently small, the nonlinear component of the drain current (which includes terms proportional to the square of the input signal) becomes negligible. By ignoring these nonlinear terms, the MOSFET's behavior can be linearly approximated, greatly simplifying analysis.

The MOSFET's transconductance (g_m), represents the rate of change of drain current in response to changes in V_GS , evaluated at the bias point is defined by:

Where V_GS0 is the DC bias voltage.

In the linear region of operation, the small-signal output current (i_d) is given by:

Where v_gs is the small-signal component of V_GS, the voltage gain (A_v) of the amplifier is given by:

Where R_L is the load resistance connected to the drain, the negative sign in the voltage gain equation indicates that the output signal is inverted relative to the input signal.