1Massachusetts Institute of TechnologyDepartment of Electrical Engineering and Computer Science6.002 – Electronic CircuitsFall 2003Quiz 2Please write your name on each page of the exam in the space provided, and circle the name of yourrecitation instructor and the time of your recitation at the bottom of this page.Please verify that there are 16 pages in your exam.To the extent possible, do all of your work on the pages contained within this exam. In particular, tryto do your work for each question within the boundaries of the question, or on the back side of thepage preceding the question. Extra pages are also available at the end of your exam.You may use one double-sided page of notes and a calculator while taking this exam.Good luck!Problem Points Score Grader1 252 253 254 25Total 100Name:Instructor: Perreault Antoniadis Chaniotakis Umans KolodziejskiTime: 10 11 11 11 12 12 1 2 3Name:2Problem 1 – 25 PointsYikes Inc. has manufactured a large batch of identical MOSFETs which unfortunately do not display square-law characteristics. Instead, they are characterized by the following equation when operated in saturation: The MOSFETs operate in saturation whenand. Yikes begins to experimentwith these devices and builds the following circuit containing a single MOSFET . The supply voltage is"!. Assume for this problem that both"!andare greater than 0.RvSVSUiG0=I0GSDM1+-(A) Calculate, the node voltage at the source, assuming saturation. Note that the gate terminal#of theMOSFET is connected to ground. (8 points)$%Name:3(B) What is the maximum value of&for which satisfies the saturation discipline? (5 points)Maximum value of'%(C) For a given value of&, what are the constraints on(*)for which+satisfies the saturation discipline?(5 points)Minimum value of,)%Maximum value of,)%Name:4(D) Draw a small signal model for the two-terminal device constructed by connecting the gate and drain ofthe Yikes MOSFET as shown in the figure below. Derive an expression for the relationship between thesmall signal current.-0/and the small signal voltage-0/. (7 points)vDSiDSM1+$-0/versus1-0/32Name:5Problem 2 – 25 PointsAfter years of research, Yehaa Inc. has invented a new MOSFET which is shown below along with itssmall signal model under the saturation discipline.vDSS+iG0=DiDSGvGS+vgsig0=GSDidsgmvgs=+This new MOSFET has an extremely high transconductance465for reasonable bias values. The onlycatch is that45is highly sensitive to temperature. As a result the traditional amplifiers designed using theMOSFET have unpredictable gains. Yehaa researchers work on this problem, and after a few more monthsannounce they have discovered the breakthrough amplifier circuit shown below. They claim that undercertain conditions the small signal gain of the new amplifier is insensitive to465. In this problem you willverify their claim.VSURSGSRLiDSvODvI+Assume for this problem that the MOSFET always operates under the saturation discipline, and that itis biased such that its transconductance is45.(A) Draw the small signal equivalent circuit for the amplifier. Clearly mark the small signal input7and thesmall signal output8in your circuit. (4 points)(over)Name:6(B) Determine the small signal transfer function8:97for the circuit. (8 points);:<;>=@?Name:7(C) Determine one or more constraints that are required in order for the claims made by the Yehaa re-searchers to be true. In other words, what are the constraints under which the small signal gain is indepen-dent of465. Express these constraints in terms of one or more of the following parameters:465,&BA, and&.(5 points)(D) Emboldened by their recent success, the Yehaa researchers make a second claim that the small signaloutput resistance of the amplifier is independent of&. If true, this property would make the new amplifierseven more appealing to existing customers using the older amplifier model (for which&C).Determine an expression for the small signal output resistance of the amplifier and use it to confirm ordisprove the second claim. (Recall that the small signal output resistance is the Thevenin resistance seenbetween the output node and ground). (8 points)Small signal output resistance%Name:8Problem 3 – 25 Points(A) Sketch by inspectionDFEGin the figure below, forEIHJCgivenKLC6M(). What is the time constantN?Give expressions for initial and final values in your sketch. (8 points)LiR1+-vR2tv0O%Name:9(B) Sketch by inspectionDFEPin the figure below, forEQHRCgiven that the switch is moved from 1 to 2 atESC. What is the time constantN? Give expressions for initial and final values in your sketch. (8 points)C2V0R1C1R2v+-12+-tv0O%Name:10(C) Sketch by inspectionDFEGin the figure below, forEH+Cgiven thatTUC6V()andDLC6V+C. What is thevalue ofW8? Give an expression for the maximum value ofin your sketch. (9 points)+–vLiCtv0X8Y%Maximum value of$%Name:11Problem 4 – 25 PointsMinnie Delay is interested in designing a light in her dorm room that turns brighter gradually when switchedON, and dims gradually when switched off. Having just learned RC circuits in 6.002, she comes up with thefollowing design.AVSRONBswitchSbulbCABR+vBThe bulb can be modeled as a resistance of value&. Similarly, when turned ON, the switch can bemodeled as a resistor of value&BZ\[. Assume thatis a positive DC voltage. The following questionsconcern6], the node voltage at^(note that]is NOT the voltage across the bulb).(A) When the switch is in the ON state, what is the steady state value of the node voltage]? (5 points)Steady state value of$]_%Name:12(B) After being ON for a long time, the switch is turned OFF at time`). Sketch the form of]starting at`D). Clearly indicate the initial values, final values (in the steady state), and the time constantNa). (6 points)tvBT0O)%Name:13(C) After being OFF for a long time, the switch is turned ON at time`cb. Sketch the form of]starting at`b. Clearly indicate the initial value, final value (in the steady state), and the time constantNb. Also, writean expression for]as a function ofE, starting at time`b. Remember that the switch has a resistance&BZ[when turned
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