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Source Follower Revisited

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This exercise is a continuation of the previous exercise.

As a reminder:

This problem studies the MOSFET amplifier shown below. 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}.

You previously generated an expression for v_{OUT}, assuming that the MOSFET operates in its saturation region.

Now:

###Part 1

Determine the range of v_{IN} over which the MOSFET operates in its saturation region. Express your answers in terms of VS, VT, R, K, and regular math operators as needed.

Lower Limit =
Upper Limit =

###Part 2 Determine the small-signal gain of the amplifier assuming that the MOSFET operates in its saturation region. Use vIN, VT, R, K, and regular math operators as needed.

\frac{dv_{OUT}}{dv_{IN}}=

###Part 3 Consider the case in which 2RK(v_{\text{IN}} - V_{\text{T}}) \gg 1. For this case, approximate the small-signal gain of the amplifier.

Use vIN for v_{\text{IN}}, VT for V_{\text{T}} as needed.

\frac{dv_{\text{OUT}}}{dv_{\text{IN}}} \approx