# Two Stage Amplifier

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This problem studies the two-stage MOSFET amplifier shown below. The first stage is built with an N-channel MOSFET. The second stage is built with a P-channel MOSFET. The P-channel MOSFET is identical to the N-channel MOSFET except for a reversal of some signs, which results in its source and drain being turned upside down. For the N-channel MOSFET, a sufficiently positive gate-source voltage (v_{GSN}) permits a positive drain current (i_{DN} > 0); for a P-channel MOSFET a sufficiently positive source-gate voltage (v_{SGP}) permits a negative drain current (−i_{DP} \gt 0). Thus the current flows from the source to the drain through a P-channel MOSFET which results in a negative i_{DP} (**defined positive into the drain as always**). A comparison of the N-channel and P-channel MOSFET behavioral equations are shown below. Note that K_N, K_P and usually V_{TN} are all positive, while V_{TP} is usually negative. Note too that the voltage subscript order indicates the definition of sign. For simplicity, let V_{TN} = V_{TP} = 0 in this problem.

###Part 1

Assuming that both MOSFETs operate in their saturation region, determine v_{OUT} as a function of v_{IN}. Use `RP`

, `KP`

, `RN`

, `KN`

, and `vIN`

for R_P, K_P, R_N, K_N, and v_{IN}, respectively.

###Part 2

Using your result from above determine the small-signal voltage gain of the amplifier as a function of the input bias voltage vIN. That is, determine v_{OUT}/v_{IN} = dv_{OUT}/dv_{IN} evaluated at V_{IN}. Use `RP`

, `KP`

, `RN`

, `KN`

, and `VIN`

for R_P, K_P, R_N, K_N, and V_{IN}, respectively.

###Part 3

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 vout 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 as necessary.

g_{mN} = | |

g_{mP} = |

###Part 4 Use the small-signal model to determine the small-signal voltage gain v_{out}/v_{in}. Compare this small-signal gain to that found in Part (1) and explain any differences.

###Part 5 Determine the small-signal Thevenin equivalent of the amplifier when it is viewed through its output port.

v_{th} = | |

r_{th} = |