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MOSFET Ranges

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This problem studies the MOSFET amplifier shown below. This amplifier is commonly called a 'Source Follower' because v_{OUT} at the MOSFET source tends to follow v_{IN} (approximately). Assume that the MOSFET operates in its saturation region, defined by i_D = 0.5K \left( v_{GS} − V_T \right)^2 and 0 \leq v_{GS} − V_T \leq v_{DS}.

Assuming that the MOSFET operates in its saturation region, determine v_{OUT} as a function of v_{IN}. Use vIN, VT, R, K, and sqrt as needed.

v_{OUT} =