Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6 002 Electronic Circuits Spring 2000 Homework 5 Issued 3 1 2000 Due 3 8 2000 Exercise 5 1 The digital logic circuit shown below is an N input NAND gate Given that each MOSFET has a threshold voltage VT and an on state resistance RON how large can N be if the circuit is to satisfy the static discipline defined by VL and VH for a given pull up resistance RPU VS RPU OUT IN1 IN2 N MOSFETs INN Exercise 5 2 Implement a 2N input NAND gate when no more than N MOSFETs may be connected in series as illustrated in Exercise 5 1 Exercise 5 3 Following the node method develop a set of simultaneous equations for the network shown below that can be solved to determine the unknown node voltages Express the set of equations in the form e1 G e2 S e3 where G is a 3 3 array of conductance terms and S is a 3 1 vector of terms involving the independent sources You need not solve the set of equations for the node voltages e1 R1 G e3 e2 i Ri R2 e3 R 5 e2 R 3 R4 I V Problem 5 1 This problem studies the two stage MOSFET amplifier shown below The stages are built with identical MOSFETs and pull up resistors A saturation region model for both MOSFETs is given below For simplicity the threshold voltage VT of each MOSFET is assumed to be 0 V Therefore each MOSFET operates in its saturation region provided that its terminal voltages satisfy vDS vGS 0 A Assuming that the first MOSFET operates in its saturation region determine vMID as a function of vIN B Assuming that the second MOSFET operates in its saturation region determine vOUT as a function of vMID Hint make use of the result from Part A C Assuming that both MOSFETs operate in their saturation regions determine vOUT as a function of vIN D Determine the range of vIN and the corresponding range of vOUT over which both MOSFETs operate in their saturation regions E Determine the small signal gain of the amplifier as a function of the operating point output vOUT assuming that the operating point falls within the range found in Part D Save a copy of your solutions to help with Homework 6 VS R R vIN vMID vOUT MOSFET model 0 for vGS 0 iD 0 5KvGS2 for vDS vGS 0 Problem 5 2 This problem studies the MOSFET amplifier shown below A saturation region model for the MOSFET is also given below A Assuming that the MOSFET operates in its saturation region determine vOUT as a function of vIN B Determine the range of vIN and the corresponding range of vOUT over which the MOSFET operates in its saturation region C Determine the small signal gain of the amplifier as a function of the operating point output vOUT assuming that the operating point falls within the range found in Part B Save a copy of your solutions to help with Homework 6 VS vIN vOUT R MOSFET model 0 for vGS VT iD 0 5K vGS VT 2 for vDS vGS VT 0 Problem 5 3 A linear MOSFET amplifier may be constructed using two MOSFETs as shown below Note that the transconductances KA and KB and the threshold voltages VTA and VTB of the two MOSFETs are different A Assuming that both MOSFETs operate in their saturation regions determine vOUT as a function of vIN B Determine the range of vIN over which both MOSFETs operate in their saturated regions C Determine the range of vOUT over which both MOSFETs operate in their saturated regions D What is the small signal gain of the amplifier over the range found in Parts B and C VS KA 2 Saturation i D v GS v TA 2 vIN KB 2 Saturation i D v GS v TB 2 vOUT
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