Massachusetts Institute of TechnologyDepartment of Electrical Engineering and Computer Science6.002 – Circuits & ElectronicsSpring 2006Problem Set #4Issued 3/1/06 – Due 3/8/06Exercise 4.1: Consider the logic function OUT = IN1 · (IN2 + IN3). Express OUT as afunction of IN1, IN2 and IN3 in the form of a truth table. Also, implement this logic function usinglogic 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 resistormodels possible leakage along the data path from the inverter to subsequent gates. Its resistance isknown to satisfy 1 MΩ <RL. In the presence of this partially known load, the inverter must satisfythe static discipline defined by vOL=0.5V,vIL=1.0V,vIH=1.5V,andvOH=2.0 V. Assumethat the MOSFET behaves like a switch having threshold voltage VTand on-state resistance RON.Over what voltage range must VTbe designed, and at what values must RPUand RONbe designed,so that the inverter dissipates minimum power while obeying the desired static discipline in thepresence of uncertainty in RL?2.5VRPU+vOUT−RLvINProblem 4.1: Following the node method, develop a set of simultaneous equations for thenetwork shown below that can be solved to determine the unknown node voltages e1, e2and e3.Express the set of equations in the formGe1e2e3= Swhere G is a 3 × 3 matrix of conductance terms and S is a 3 × 1 vector of terms involving theindependent sources. You need not solve the set of equations for the node voltages.Note that e4is not included in the analysis because it is directly sourced by the dependent voltagesource from ground, and the source voltage can be expressed in terms of the first three nodevoltages. In this sense, it is treated like an independent voltage source. Nonetheless, state how e4can be determined from e1, e2and e3once the latter node voltages are determined.βi1e1R3i1e2R6e4Ri2R1i2VR2R4e3R5IProblem 4.2: Determine the Thevenin equivalent of each network shown below. The coeffi-cients describing the dependent sources satisfy A>0andG>0.vR1R2+−+u−AuR3V+ u −R2+−R1GuR3Problem 4.3: This problem uses WebLab to predict and then verify the input-output relationof the circuit shown below. The circuit can function either as a digital inverter or an analogamplifier. To study the circuit, this problem is divided into three parts. The first part uses WebLabto measure the MOSFET characteristics, that is, the relation between vDSand iDfor various valuesof vGS. The second part applies a load-line analysis to the measurements to predict the input-outputrelation of the circuit. The third part uses WebLab to verify the predicted input-output relationthrough 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 arebuilt to be the same. However, because they are physically different devices, they will beslightly different 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; andCOMPLIANCE = 5 V. Name the variables, but do not select them for downloading.• SMU4 must be set to sweep vDSover an inner loop. To do so, select it and set: MODE =V; FUNCTION = VAR1; and COMPLIANCE = 100 mA. Set VAR1 to sweep from 0 Vto 5 V in 200-mV steps. Finally, name both variables and select both for downloading.These variables are vDSand iD.• SMU2 must be set to sweep vGSover an outer loop. To do so, select it and set: MODE= V; FUNCTION = VAR2; and COMPLIANCE = 100 mA. Set VAR2 to sweep from1.9 V to 2.5 V in 50-mV steps. Finally, name both variables, but do not select them fordownloading.• Run WebLab to measure the MOSFET characteristics.• Plot the measured characteristics with vDSon the horizontal axis over the range 0 V to5V,andiDon the vertical axis over the range 0 mA to 10 mA. You can do so directlyin WebLab, and then capture a screen shot for printing. Alternatively, you can downloadthe measurements, and then plot and print them using another program such as MatLabor Excel. Note that the data will not all fit within the given range.(B) On the graph produced in Part (A), plot the vDS-iDload line that is imposed by the 5-V powersupply and the 500-Ω resistor in the circuit below. Using the intersections of the load linewith the MOSFET characteristics, determine the values of vOUT= vDSthat correspond to thevalues 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 viaWebLab. Feel free to modify the procedure as desired.• To measure the input-output relation, SMU1 must be set to the power supply voltage of5 V. To do so, select it and set: MODE = V; FUNCTION = CONS; VALUE = 5 V; andCOMPLIANCE = 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 Vto 5 V in 100-mV steps. Select the voltage for downloading. This variable is the circuitinput.• SMU4 must be set to act as an open circuit while it measures the output vOUT.Todoso,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 char-acteristics.• 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 to5 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 usinganother program such as MatLab or Excel.(D) On the graph produced in Part (C), plot the input-output relation found in Part (B). Theinput-output relations found in Parts (B) and (C) should be identical.5V500 Ω2N7000+vOUT−vINProblem 4.4: This problem studies the two-stage n-channel MOSFET amplifier shown below.The two stages are built with
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