Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6 002 Circuits Electronics Spring 2004 Final Exam 18 May 2004 Name Instructor Time Kassakian 10 Kassakian 11 Wilson 12 Berggren 1 Berggren 2 Please put your name in the space provided above and circle the name of your recitation 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 the question This is a closed book exam but calculators and a single two sided page of notes are allowed You may review and take back your final exam on or after Thursday May 20 However overall grades for 6 002 will not be determined until Friday May 21 and will be most easily obtained through WEBSIS Good luck Problem 1 Problem 2 Problem 3 Problem 4 Total Grade Problem 1 25 This problem consists of fourteen independent parts having a total of twenty five sub parts All op amps in this problem are ideal Note that all sub parts are weighted equally at only 1 each So if you get stuck on one sub part it might be wise to skip that sub part and move on until later 1A Determine the Thevenin equivalent voltage vTH and resistance RTH of the network shown below vTH RTH 12 2 4A 2 7 1B Determine the ratio vO vS vO vS vs 2 3 vo 1 6 1C Determine vC 0 the time constant that determines the response of the network and an expression for vC t for t 0 Note that u0 t denotes the unit impulse function vC 0 vC t 0 R2 R1 vc vc 0 V0 C Qu0 t 1D Determine iL and the time constant that determines the response of the network iL 2 4 iL 10h 2 3 V0u 1 t 1E Determine the Thevenin equivalent voltage vTH and resistance RTH of the network shown below vTH RTH ib 1K 10V 180 49ib 1F Determine the maximum value of iL max iL closes t 0 iL vc 10 h 10 f vc 0 10V iL 0 0 1G For the logic circuit shown below determine a Boolean expression for the logical output Z as a function of the logical inputs A B and C Boolean Expression For Z Vs R vB vA 1H v z v C Determine iNL iNL iNL iNL vIN 3V vNL See Graph 2mA 10 3 1 4V vNL 1I Determine vO vO Vs vgs3 R vgs vA 1J vo Determine vO t in the sinusoidal steady state vO t C L 10cos t vo 1K Determine dvC dt and diL dt at t 0 that is just after the switch opens diL 0 dt dvC 0 dt 2 iL opens t 0 10mh 1 f vc iL 0 1A vc 0 0V 1L Determine v1 v2 and i1 v1 v2 i1 i1 i1 10 3 10 v1 v1 i2 1K i2 v2 10 3 5 v2 1M The voltage vC in the network below reaches a steady state in a finite time Determine its steady state value and the time t at which it reaches that value Steady state vC t i t 0 vC 1 F i v 0 02A 10 3 Network 0 01A 2x10 3 v vC 0 0 1N 5V 10V Determine the Thevenin equivalent voltage vTH and complex impedance ZTH of the network shown below which operates in the sinusoidal steady state The Thevenin equivalent voltage is defined by its amplitude VTH and its phase TH such that vTH VTH cos t TH VTH TH ZTH Icos t L R C Problem 2 25 The circuit shown below is a free running oscillator that provides a square wave output at v2 All op amps are ideal except that they can saturate at the power supply voltages VS Note that for simplicity the power supply connections to the op amps are not shown in the figure R1 R1 2R1 C 1 2 v1 3 R3 v 2 R2 2A Consider Op amps 1 and 2 Assume that they do not saturate and determine v1 t as a function of v2 t R1 and C v1 t 2B Consider Op amp 3 which is always saturated Determine the value of v1 at which v2 switches from VS to VS and the value of v1 at which v2 switches from VS to VS v1 v2 v1 v2 2C Determine the period over which the oscillator oscillates Period Problem 3 25 This problem concerns the op amp amplifier shown in Figure A below The op amp in that amplifier is modeled by the network shown in Figure B below A Amplifier vIN B Model R1 Input R vOUT v v1 A1v1 R2 C1 v2 A2v2 Output C2 v3 A3v3 v4 v Input R 3A Assume that vIN has been constant for a very long time Determine vOUT in terms of vIN R and the parameters of the op amp model vOUT 3B Consider the op amp model in Figure B Let A1 1 A2 2 A3 5 and R1 C1 R2 C2 0 01 s Further assume that v1 takes the form v1 t V 1 ej t so that v4 takes the form v4 t V 4 ej t where V 1 and V 4 are both complex constants In this case determine the ratio V 4 V 1 V 4 V 1 3C Consider the op amp amplifier in Figure A Assume that vIN takes the form vIN t V IN ej t so that vOUT takes the form vOUT t V OUT ej t where V IN and V OUT are both complex constants In this case determine the ratio V OUT V IN for the model parameters given in Part B V OUT V IN Problem 4 25 This problem analyzes a multi stage MOSFET amplifier To simplify the analysis assume that all MOSFETs are linear have a threshold voltage of 0 V and operate in their saturation region Thus all MOSFETs both n channel and p channel operate according to iD KvGS where iD is defined to be positive into the drain 4A The circuit shown below functions as a current source for its load Determine the source current IS as a function of R1 R2 VS and K IS Load VS IS R1 D G VS R2 S 4B Determine the voltage v3 in the circuit shown below in terms of v1 v2 R3 VS IS and K v3 VS G D R3 D S S V1 VS V3 G V2 IS 4C Determine the voltage v4 in the circuit shown below in terms of v3 R4 VS and K Note that the MOSFET in the circuit is a p channel MOSFET so that vGS 0 vDS 0 and iD KvGS v4 VS V3 S G VS D R4 V3 4D The amplifier shown below is a combination of the circuits analyzed in Parts A B and C of this problem For this amplifier determine vOUT as a function of v1 v2 R1 R2 R3 R4 VS …
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