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MOSFET Large-signal amplifier

The questions below are due on Friday May 08, 2020; 11:59:00 PM.
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Consider the MOSFET amplifier shown in the figure below. Assume that the amplifier is operated under the saturation discipline. In its saturation region, the MOSFET is characterized by the equation:

i_{DS} = \frac{K}{2}\left(v_{GS}-V_T\right)^2

where i_{DS} is the drain-to-source current when a voltage v_{GS} is applied across its gate-to-source terminals.

For all analytical solutions below, use VS for V_S, RL for R_L, iDS for i_{DS}, vI for v_I, VT for V_T, K for K.

###Part 1 Draw an equivalent circuit for the amplifier based on the SCS model of the MOSFET. From that model, write an expression relating v_O to i_{DS}.

V_O =

###Part 2 Write an expression relating i_{DS} to v_I when v_I \ge V_T.

i_{DS} =

###Part 3

Write an expression relating v_O to v_I.

v_O =