Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6 002 Electronic Circuits Fall 2000 Final Exam Please write your name in the space provided below and circle the name of your recitation instructor and the time of your recitation Please verify that there are 19 pages in your exam To the extent possible do all of your work on the pages contained within this exam In particular try to do your work for each question within the boundaries of the question or on the back side of the page preceding the question You may use three double sided pages of notes while taking this exam Final grades in 6 002 will not be given out by phone or by e mail Rather they should be available through WEBSIS by December 22 You may review and take back your final exam at the beginning of IAP in January 2001 from Room NE43 624 Good luck Problem 1 2 3 4 5 6 7 Total Score Name 1 Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY Problem 1 15 Points The Op Amp circuit shown below is very similar to the standard non inverting Op Amp except that RL is some external resistor and we are interested in showing that the current through RL is nearly constant regardless of the value of RL that is the circuit acts like a current source for driving RL A iL vI RL R2 A A Using the Op Amp model shown below derive an expression for iL in terms of vI A R2 and RL Show that this expression for iL becomes independent of RL as A approaches infinity v v v vO v A v v vO 2 Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY B To verify the current source action more directly use the Op Amp model from Part A to find the The venin equivalent resistance looking to the left of terminals AA 3 Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY Problem 2 15 Points This problem involves the circuit shown below You are given that R 1 C 1 F and Amps 1 K 2 Volt2 R 2R V A va 2R C iD vD vC v a is small Characteristics of nonlinear device iD i D 0 when v D 0 2 i D K v D when v D 0 vD A Find the operating point voltage VD and the operating point current ID in the circuit shown above Assume for this part that VA 12V 4 Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY B Now assume that VA is changed such that a new operating point ID0 and VD0 is obtained where VD0 1V Note that this operating point may differ from your answer in Part A Draw the small signal circuit substituting numeric values where possible Label the small signal capacitor voltage vc and the small signal device voltage vd Recall the small signal model for a capacitor is the capacitor itself 5 Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY vd vc t t 6 Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY Problem 3 15 Points A nonlinear device with voltage vd and current id has a characteristic given by id Ie vd where vd 0 and id 0 vd id For all parts of this problem assume that the operational amplifiers are ideal that they are operating in the active region and that the nonlinear device is operating with positive values of vd and id A For the nonlinear element connected as shown below find an expression relating vout to vin id vd v in R v out 7 Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY B For the nonlinear element connected as shown below find an expression relating vout to vin R vd id v in v out C For the operational amplifier circuit shown below find an expression relating vout to vin1 vin2 and vin3 R v in1 v in2 v in3 R v out R R 8 Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY D Find an expression for vout as a function of va and vb for the circuit shown below Hint Use the results of the previous parts of this problem id vA vd R R id vd R R 1 vd R R R id v out id v d vB R 9 Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY Problem 4 15 Points Anna Logue a UROP student working for Professor S has just found a rather strange piece of circuitry in the trash just outside the office of Prof A The circuit has three exposed terminals and it has exactly one resistor one inductor and one capacitor but she cannot see how they are connected because the connections are protected by epoxy She can read the capacitor label it says that the capacitor has a capacitance of 1 F Observation O1 However the other labels are not readable Being a naturally curious MIT student Anna takes the circuit to the 6 002 lab to see what can be determined about this strange device by experiment Anna labels the terminals with the letters x y and z with a marker pen She then takes several measurements First Anna measures the resistances between the terminals of the mystery circuit with an Ohmmeter and makes the following observations x y infinity Observation O2 y z infinity Observation O3 z x 40 Observation O4 Next Anna uses a signal generator which may be modeled as a voltage source to apply a 1 Volt 100 Hz square wave signal from the x terminal to the y terminal She uses her oscilloscope to display the voltage from z to y superimposed on the square wave at the same scale as the square wave as shown in the figure below Observation O5 As you can see she …
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