Massachusetts Institute of TechnologyDepartment of Electrical Engineering and Computer Science6.002 – Circuits & ElectronicsSpring 2004Quiz #328 April 2004Name:Instructor: Kassakian Kassakian Wilson Berggren BerggrenTime: 10 11 12 1 2• Please put your name in the space provided above, and circle the name of yourrecitation instructor together with the time of your recitation.• Do your work for each question within the boundaries of the question. When finished,write your answer to each question in the corresponding answer box that follows thequestion.• This is a closed-book quiz, but calculators are allowed.• Graded quizzes will be returned in tutorial on Monday May 3, and also in Recitationon Wednesday May 5. If you do not attend tutorial and/or recitation on those days,then it is your responsibility to get your quiz from your recitation instructor. You willhave until Monday May 17 to request a quiz grading review, regardless of whether ornot you attend tutorial on Monday May 3 and take back your quiz. If you wish to haveyour quiz grade reviewed, you must return your quiz to your recitation instructor,within the two week period, together with a written explanation of why you thinka grading mistake was made. This is the only way in which a quiz grade will bereviewed.• Good luck!Problem 1 Problem 2 Problem 3 Total GradeProblem 1 – 20%This problem focuses on the circuit shown below, which contains a constant current source,two switches, a capacitor and an inductor. Prior to t = 0, the two switches are closed, andthe capacitor and inductor are both at rest.ICLS1S2+_vCiL(1A) (5%) At t = 0, switch S1 opens. Determine the capacitor voltage vCand the inductorcurrent iLat t = T .vC(T ): iL(T ):(1B) (5%) At t = T , switch S2 opens and then switch S1 closes immediately thereafter.Determine the time at which the capacitor voltage vCnext goes to zero.t:(1C) (5%) Determine the inductor current iLwhen the capacitor voltage vCgoes to zeroasdescribedinPartB.iL:(1D) (5%) When the capacitor voltage vCgoes to zero as described in Part B, switchS2 closes and then switch S1 opens immediately thereafter. After a further periodof duration T , switch S2 opens and then switch S1 closes immediately thereafter.Determine the inductor current iLwhen the capacitor voltage vCnext goes to zero.iL:Problem 2 – 35%The circuit shown below contains a capacitor, an inductor and a MOSFET. Its purpose is todeliver a pulse of current to the inductor. Model the MOSFET as a switch having on-stateresistance RON. Prior to t =0,vC= V , iL= 0, and the MOSFET is held off by vIN.Fort ≥ 0 the MOSFET is turned on by vIN.+_+_vCLvINCiL(2A) (15%) Derive an expression for the inductor current iLfor t ≥ 0. In doing so, assumethat C satisfies C<4L/R2ON.iL(t ≥ 0):(2B) (10%) It is desired that the inductor current iLbe a single pulse of minimal time du-ration with no reversal in sign. Determine the value of C that achieves this objective;C need not satisfy C<4L/R2ON.C:(2C) (10%) Determine the peak, or maximum positive value, of the inductor current iLgiven the design of Part B.Peak iL:Problem 3 – 45%This problem focuses on the network shown below. It contains a current source, a capacitor,an inductor and two identical resistors. It also has a single port. Except for the last part ofthis problem, the network operates in the sinusoidal steady state with the sourced currenttaking the form iS(t)=I cos(ωt). For the last part of this problem, the network is at restuntil the sourced current takes a step of the form iS(t)=Iu−1(t).iSLCRR+_vO(3A) (10%) The output voltage vOat the port takes the form vO(t)=V cos(ωt + φ)insinusoidal steady state. Determine V and φ.V : φ:(3B) (10%) The sinusoidal-steady-state Thevenin equivalent of the network, as viewedfrom its port is shown below. Determine the parameters VTH, φTHandˆZTHthatdefine the equivalent. Note thatˆZTHis the complex Thevenin-equivalent impedance.+_ZTHVTH cos( ω t + φTH )VTH:φTH:ˆZTH:The figures shown below present a numerical evaluation of the magnitude V and the phaseφ of vOas functions of frequency ω for the specific case of I = 100 mA. Use this numericalevaluation to answer Parts C and D of this problem.10210310410510−210−1100101Frequency ω [rad/s]vO Magnitude [V]102103104105−100−50050100Frequency ω [rad/s]vO Phase [Degrees](3C) (15%) Determine the numerical values of R, L and C. Remember to include units.R: L: C:(3D) (10%) Assuming the network is at initially rest, which of the following figures cor-responds to vOfor t ≥ 0giventhatiS(t) = 100 mA u−1(t)?0 1 2 3 4−0.500.5Time [ms]vO [V]0 1 2 3 4−0.500.5Time [ms]vO [V]0 1 2 3 4−0.500.5Time [ms]vO [V]0 1 2 3 4−0.500.5Time [ms]vO [V]0 1 2 3 4−0.500.5Time [ms]vO [V]0 1 2 3 4−0.500.5Time [ms]vO [V]Figure A Figure BFigure C Figure DFigure E Figure FCircle One: A B C D E
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