Massachusetts Institute of TechnologyDepartment of Electrical Engineering and Computer Science6.002 – Electronic CircuitsFall 2000Final Exam• Please write your name in the space provided below, and circle the name of your recitationinstructor 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. Inparticular, try to do your work for each question within the b oundaries of the question, or onthe 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 beavailable through WEBSIS by December 22. You may review and take back your final examat the beginning of IAP in January 2001 from Room NE43-624.• Good luck!Problem Score1234567TotalName:1Cite 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 PointsThe Op-Amp circuit shown below is very similar to the standard non-inverting Op Amp exceptthat RLis some external resistor, and we are interested in showing that the current through RLis nearly constant, regardless of the value of RL, that is, the circuit acts like a current source fordriving RL.RLR2iLAA’-+vI-+(A) Using the Op-Amp model shown below, derive an expression for iLin terms of vI, A, R2andRL. Show that this expression for iLbecomes independent of RLas A approaches infinity.vO+v+v+vv+vO+A( )+vv+2Cite 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 tofind the Th´evenin equivalent resistance looking to the left of terminals AA′.3Cite 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 PointsThis problem involves the circuit shown below. You are given that R = 1Ω, C = 1µF , andK =12AmpsVolt2.2R+R2R+vCiD+vDVAva+ is “small”vaCharacteristics of nonlinear device: when wheniD0=vD0≤iDKvD2=vD0>CiDvD-(A) Find the op erating point voltage VDand the operating point current IDin the circuit shownabove. Assume for this part that VA= 12V .4Cite 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 VAis changed such that a new operating point ID0and VD0is 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-signalcapacitor voltage vcand the small-signal device voltage vd. (Recall, the small signal model for acapacitor is the capacitor itself.)5Cite 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].(C) Assume that vais a small step of amplitude A as shown below. Sketch the small-signalresponses vcand vd. Clearly indicate the initial value, the final value, and the time constant foreach graph. Assume that the initial voltage on the capacitor is zero.tvaA0vctvdt6Cite 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 PointsA nonlinear device with voltage vdand current idhas a characteristic given byid= Ieαvdwhere vd> 0 and id> 0.vd+id-For all parts of this problem assume that the operational amplifiers are ideal, that they are operatingin the active region and that the nonlinear device is operating with positive values of vdand id.(A) For the nonlinear element connected as shown below, find an expression relating voutto vin.vin++vdidvoutR--7Cite 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 voutto vin.vin+vdidvoutR+-(C) For the operational amplifier circuit shown below, find an expression relating voutto vin1, vin2,and vin3.vin1voutvin2vin3RRRR+8Cite 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 voutas a function of vaand vbfor the circuit shown below. Hint: Usethe results of the previous parts of this problem.vA+vdid1+vdidvB+vdid+RRRRRRR+++vdidvoutR++++9Cite 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 PointsAnna Logue, a UROP student working for Professor S., has just found a rather strange piece ofcircuitry in the trash just outside the office of Prof. A. The circuit has three exposed terminalsand it has exactly one resistor, one inductor, and one capacitor, but she cannot see how they areconnected, because the connections are protected by epoxy. She can read the capacitor label: itsays that the capacitor has a capacitance of 1µF (Observation O1). However, the other labe ls arenot readable.Being a naturally curious MIT student, Anna takes the circuit to the 6.002 lab to see what can b edetermined 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 measuresthe resistances between the terminals of the mystery circuit with an Ohmmeter, and makes thefollowing observations:x − y: infinity
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