# Source Follower Rerevisited

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Consider again the amplifier described in this previous exercise from this week. In this problem, let v_{IN} = V_{IN} + v_{in} and v_{OUT} = V_{OUT} + v_{out}, where V_{IN} and V_{OUT} are the large-signal components of v_{IN} and v_{OUT}, respectively, and v_{in} and v_{out} are the small-signal components of v_{IN} and v_{OUT}, respectively.

###Part 1

Using your result from the earlier problem, recall the small-signal voltage gain of the amplifier as a function of the input bias voltage v_{IN}. That is, recall v_{out}/v_{in} = dv_{OUT}/dv_{IN} evaluated at V_{IN}.

###Part 2

Again assume that the MOSFET is biased so that it operates in its saturation region. Develop a small-signal circuit model for the amplifier that can be used to determine v_{out} as a function of v_{in}. In doing so, assume that V_{IN} defines the operating point around which the small- signal model is constructed, and evaluate all small-signal model parameters in terms of `VIN`

, `VT`

, `R`

, `K`

, (etc) and other mathematical operators as needed.

###Part 3
Use the small-signal model to determine the small-signal voltage gain v_{out}/v_{in}. Compare this small-signal gain to that found earlier. Use `R`

and `gm`

for R and g_m, respectively.

###Part 4
Determine the small-signal Thevenin equivalent of the amplifier when it is viewed through its output port. Use `R`

, `gm`

, and `vin`

as needed.

v_{th} = | |

r_{th} = |