Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6 002 Circuits Electronics Spring 2006 Problem Set 4 Issued 3 1 06 Due 3 8 06 Exercise 4 1 Consider the logic function OUT IN1 IN2 IN3 Express OUT as a function of IN1 IN2 and IN3 in the form of a truth table Also implement this logic function using logic symbols and using a small number of n channel MOSFETs and pull up resistors Exercise 4 2 In the circuit shown below an inverter is loaded with a resistor The load resistor models possible leakage along the data path from the inverter to subsequent gates Its resistance is known to satisfy 1 M RL In the presence of this partially known load the inverter must satisfy the static discipline de ned by vOL 0 5 V vIL 1 0 V vIH 1 5 V and vOH 2 0 V Assume that the MOSFET behaves like a switch having threshold voltage VT and on state resistance RON Over what voltage range must VT be designed and at what values must RPU and RON be designed so that the inverter dissipates minimum power while obeying the desired static discipline in the presence of uncertainty in RL RPU 2 5 V RL vIN vOUT Problem 4 1 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 e1 e2 and e3 Express the set of equations in the form e1 G e2 S e3 where G is a 3 3 matrix 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 Note that e4 is not included in the analysis because it is directly sourced by the dependent voltage source from ground and the source voltage can be expressed in terms of the rst three node voltages In this sense it is treated like an independent voltage source Nonetheless state how e4 can be determined from e1 e2 and e3 once the latter node voltages are determined e1 e2 i1 R3 i2 R2 R6 I e3 i1 e4 R4 R1 R5 V Ri2 Problem 4 2 Determine the Thevenin equivalent of each network shown below The coe cients describing the dependent sources satisfy A 0 and G 0 u R2 R1 R2 R3 u v V Au R1 Gu R3 Problem 4 3 This problem uses WebLab to predict and then verify the input output relation of the circuit shown below The circuit can function either as a digital inverter or an analog ampli er To study the circuit this problem is divided into three parts The rst part uses WebLab to measure the MOSFET characteristics that is the relation between vDS and iD for various values of vGS The second part applies a load line analysis to the measurements to predict the input output relation of the circuit The third part uses WebLab to verify the predicted input output relation through direct measurement A Use the following procedure to measure and plot the MOSFET characteristics via WebLab Feel free to modify the procedure as desired Launch WebLab using the procedure given in Problem 2 4 Select Device 6 or Device 7 from the drop down menu of devices These two devices are built to be the same However because they are physically di erent devices they will be slightly di erent electrically For all measurements SMU3 should be grounded To do so select it and set MODE COMM Name the variables but do not select them for downloading To measure the MOSFET characteristics SMU1 must be set to act as an open circuit To do so select it and set MODE I FUNCTION CONS VALUE 0 A and COMPLIANCE 5 V Name the variables but do not select them for downloading SMU4 must be set to sweep vDS over an inner loop To do so select it and set MODE V FUNCTION VAR1 and COMPLIANCE 100 mA Set VAR1 to sweep from 0 V to 5 V in 200 mV steps Finally name both variables and select both for downloading These variables are vDS and iD SMU2 must be set to sweep vGS over an outer loop To do so select it and set MODE V FUNCTION VAR2 and COMPLIANCE 100 mA Set VAR2 to sweep from 1 9 V to 2 5 V in 50 mV steps Finally name both variables but do not select them for downloading Run WebLab to measure the MOSFET characteristics Plot the measured characteristics with vDS on the horizontal axis over the range 0 V to 5 V and iD on the vertical axis over the range 0 mA to 10 mA You can do so directly in WebLab and then capture a screen shot for printing Alternatively you can download the measurements and then plot and print them using another program such as MatLab or Excel Note that the data will not all t within the given range B On the graph produced in Part A plot the vDS iD load line that is imposed by the 5 V power supply and the 500 resistor in the circuit below Using the intersections of the load line with the MOSFET characteristics determine the values of vOUT vDS that correspond to the values of vIN vGS Make a table of the resulting input output relation C Use the following procedure to measure and plot the input output relation of the circuit via WebLab Feel free to modify the procedure as desired To measure the input output relation SMU1 must be set to the power supply voltage of 5 V To do so select it and set MODE V FUNCTION CONS VALUE 5 V and COMPLIANCE 100 mA SMU2 must be set to sweep vIN vGS To do so select it and set MODE V FUNCTION VAR1 and COMPLIANCE 100 mA Set VAR1 to sweep from 0 V to 5 V in 100 mV steps Select the voltage for downloading This variable is the circuit input SMU4 must be set to act as an open circuit while it measures the output vOUT To do so select it and set MODE I FUNCTION CONS VALUE 0 A and COMPLIANCE 5 V Select the voltage for downloading This variable is the output of the circuit SMU3 should remain grounded as it was during the measurement of the MOSFET characteristics Run WebLab to measure the input output relation of the circuit Plot the input output relation of the circuit with both variables ranging from 0 V to 5 V You can do so directly in WebLab and then capture a screen shot for printing Alternatively you can download the measurements and then plot and print them using another program such as MatLab or Excel D On the graph produced in Part C plot the input output relation found in Part B The input output relations found in Parts B and C should be identical 500 5V 2N 7000 vIN vOUT Problem 4 4 This problem studies the two stage n channel MOSFET ampli er shown …
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