MASSACHUSETTS INSTITUTE OF TECHNOLOGYDepartment of Electrical Engineering and Computer Science6.002 – Electronic CircuitsFall 2002Final ExamName:Recitation Section:Recitation Instructor: Teaching Assistant:Enter all your work and your answers directly in the spaces provided on theprinted pages. Make sure that your name is on all sheets. Use the backs of theprinted pages as scratch paper, but we will only give full credit to answers that you neatlytransfer to the spaces on the printed pages. Answers must be derived or explained, not justsimply written down. The quiz is closed book, but calculators and both sides of one812× 11page of notes are allowed.This quiz contains 16 pages including the cover sheet. Make sure that your quiz contains all16 pages and that you hand in all pages except the last page.Problem Points Grade Grader1 202 203 164 205 24Total 100Name: 2Problem 1: (20 points) The circuit below shows a single-stage amplifier designed around a“MOXFET”, a hypothetical transistor similar to a MOSFET, except thatiD=K3(vGS− VT)3For the purposes of this problem, assume that the MOXFET gain parameter K =0.625mA/V3and that its threshold voltage is VT=2.2V .In the circuit above, VS=10V , R1=30kΩ, R2=70kΩ, RD=37.5kΩandC =0.15µF.Thesaturation-region models for the MOXFET are shown below, where (a) is the large-signal (bias)model, and (b) is the small-signal (incremental) model.(A) The amplifier output voltage will be of the form vOUT= VOUT+ vout(t). Determine VOUT(anumerical value is required).VOUT= VName: 3(B) Find an expression for the transconductance gmin terms of the symbolic MOXFET parametersVTand K and the operating point VGS.(Donot evaluate your answer numerically.)gm=(C) For an input signal of the form vi(t)=VIcos ωt, the complex amplitude of the output signalvout(t) will be of the formˆVout= G0jωτ1+jωτVIIn terms of the transconductance gmand the circuit parameters, find expressions for the high-frequency gain G0and the time constant τ.(Donot evaluate your answers numerically.)G0=τ =Name: 4(D) The small input signal is now given by vi(t)=(Vacos ωt+Vb)u(t). The resulting output signalhas the formvout(t)=(Vccos(ωt + φ)+Vd+ Vee−βt)u(t)Determine Vc, φ, Vd, Veand β in terms of ω, Va, Vb, τ and G0, where τ and G0are defined inpart (C).Vc=φ =Vd=Ve=β =Name: 5Problem 2: (20 points) Consider the RLC circuit shown below.(A) The voltage source is a unit step at time t = 0. Three circuit variables, vC, vL, and iLare presented plotted against time, as shown in the three figures on the next page. Time ismeasured in milliseconds on the horizontal axes. The vertical axes may represent voltage,measured in Volts, or current, measured in Amperes, as appropriate.The traces are labeled 1, 2, and 3. (The label is in the upper right corner of each trace.) Youare to identify the traces: which trace is which circuit variable? Circle the circuit variable thatcorresponds to the indicated trace below:Trace 1: vCvLiLTrace 2: vCvLiLTrace 3: vCvLiLName: 6Note: Time is measured in milliseconds on the horizontal axes. The vertical axesmay represent voltage, measured in Volts, or current, measured in Amperes, asappropriate. The arrows represent the slope of t he curve at t =0+.Name: 7(B) Assume the inductance L is 75µH.(i) What is the approximate numerical value of the capacitance?C =(ii) What is the approximate numerical value of the resistance?R =(iii) Estimate the Q of the circuit. Circle the best answer:Q<11<Q<10 10 <QName: 8(C) For each question circle the correct completion.(i) If the resistance R is increased, the Qincreases. decreases. remains t he same.(ii) If the capacitance C is increased, the Qincreases. decreases. remains t he same.(iii) If the inductance L is increased, the oscillatory periodincreases. decreases. remains t he same.(iv) If the capacitance C is increased, the oscillatory periodincreases. decreases. remains t he same.(D) After a long time T , vsreturns to zero and the stored energy decays.(i) If the capacitance C is increased, the time at which the stored energy falls to half itsvalue at time Tincreases. decreases. remains t he same.(ii) If the inductance L is increased, the time at which the stored energy falls to half its valueat time Tincreases. decreases. remains t he same.(iii) If the resistance R is increased, the time at which the stored energy falls to half its valueat time Tincreases. decreases. remains t he same.Name: 9Problem 3: (16 points)The source vs(t) has the waveform shown in the graph on the next page. The nonlinear elementN has the i-v relation sketched below. Assume that the op-amps are ideal (i.e., infinite gain, noinput current, zero output resistance, no saturation).On the axes provided, sketch the waveforms of va(t), vb(t)andvo(t). Follow the time divisionsindicated in the graph and label the amplitude of your waveforms. If any of your graphs containsimpulses, be sure to indicate their area.Name: 10Name: 11Problem 4: (20 points)A simple MOSFET inverter is shown above. The input-output relationship is also shown above(NOT to scale), where the MOSFET has been modeled using the familiar square-law relationshipiDS=K2(vGS− VT)2in the saturation region, and the triode region is compressed onto the single curveiDS=K2v2DSThe MOSFET parameters are VT=1V and K =1mA/V2.(A) Determine the voltages V1and V2in the input-output graph for this inverter.V1= VV2= VName: 12Two identical inverters from part (A) are cascaded to form the buffer circuit shown below.The input-output relationship is qualitatively sketched below (NOT to scale).(B) Determine the voltages VA, VB, VCand VD.VA= VVB= VVC= VVD= VName: 13(C) For a given input voltage each transistor in the buffer circuit will be in one of three regions ofoperation: cutoff (CO), saturation (SAT) and triode region (TR). As the input voltage vINisincreased from 0 to 4V , the buffer passes through four states. In the following table, indicatethe four states by circling the region of operation of the transistors for each range of inputvoltage.Input Voltage M1 M20V<vIN<VTCO SAT TR CO SAT TRVT<vIN<VCCO SAT TR CO SAT TRVC<vIN<VDCO SAT TR CO SAT TRVD<vIN< 4V CO SAT TR CO SAT TRName: 14Problem 5: (24 points) Match the indicated variable to the form of its response for t>0+bycircling the appropriate letter corresponding to the choices offered in the last page. Note: Theparameters VS, IS, ΛS, QS, V0and I0are all positive.vS= VSu(t) vS=ΛSδ(t)iL(0−)=0 vC(0−)=0
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