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A MOSFET in its active region operates as a voltage-controlled current source where the gate-to-source voltage directly regulates the drain current. This transconductance relationship allows the gate voltage to modulate the current flowing through the device, enabling precise control of output current based on input voltage variations.

The load resistor converts the MOSFET's output current into a voltage by directing the drain current through it. The output voltage is obtained by subtracting the voltage drop across the load resistance from the supply voltage, producing an inverted output voltage shifted by the supply voltage.

The voltage-transfer characteristic plot illustrates the relationship between output drain voltage and input gate voltage, highlighting the amplifier's active region where the curve has a steep slope for maximum gain. However, this region exhibits nonlinearity in drain voltage, making the plot essential for identifying optimal operating conditions.

Applying a gate-to-source DC voltage bias at the quiescent point positions the MOSFET within the active region's nearly linear segment. When a small time-varying signal overlays this DC bias, the device operates within a short linear portion of its characteristic curve, resulting in amplified output drain voltage with minimal distortion.

The small AC signal modulates the gate voltage around the Q-point, causing proportional variations in drain current. These current variations are translated into a larger output voltage across the load resistor through small signal analysis of MOSFET amplifiers, achieving signal amplification.

The active region provides a steep slope on the voltage-transfer characteristic curve, delivering maximum gain for amplification. Although this region exhibits nonlinear drain voltage behavior, positioning the MOSFET at an appropriate Q-point within this region enables nearly linear amplification of small input signals.

The MOSFET amplifier amplifies AC signals by biasing at a Q-point within the active region and allowing small input signals to modulate the gate voltage. The resulting drain current variations are converted to larger output voltages across the load resistor, effectively amplifying weak AC signals for practical applications.