Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6 002 Circuits and Electronics Spring 2003 Handout S03 065 Final Exam Tuesday May 20 2003 Name Recitation Instructor circle one Baldo Hutchinson Kolodziejski Schindall Wilson Recitation Hour circle one 9 10 11 12 1 2 NOTE THAT PROBLEMS HAVE WEIGHTS RANGING FROM 10 TO 16 Problem Points Score Grader 1 16 2 10 3 12 4 12 5 10 6 12 7 14 8 14 Total 100 1 Name PROBLEM 1 Joe Nerdle who took 6 002 some time ago wants to assemble a three input AND gate He finds sufficient identical MOSFETS of unknown specifications The several parts below are independent A In fifty words or less describe measurements which Joe can make to determine the threshold voltage VT and the on resistance RON of the FETs Include a circuit diagram if you wish Joe establishes a static discipline in which a logical one corresponds to v 4 volts and a logical zero corresponds to v 1 volt A three input NAND gate and the switch resistor model for the FET are shown below 5 V D 7 k vD vC G SW The switch SW is vGS open for vGS VT closed for vGS VT RON vB S vA B Write a Boolean expression which describes the logical function of this gate 2 Name For the remaining parts of this problem use these values RON 1k VT 1V C When vA vB vC 5V determine vD D Because Joe wants an AND gate he connects the output of the gate above to a FET inverter as shown below 5 V 7 k 7 k When he builds this circuit he finds that vD is low for all input conditions Explain vC vB vA vGS vD E In an effort to understand the reason the AND gate does not work Joe isolates the inverter and connects an oscilloscope to its output as shown below 5 V 5 V 7 k 7 k vO C vO t vertical input C 2x10 11 F He can t find a scope probe so he uses a long piece of coaxial cable This unfortunate arrangement provides a capacitive load of C 20pF 2 10 11 F to the inverter The resulting circuit is the one shown above right Sketch and label the waveform vO t which Joe sees on the scope when the switch changes the input voltage from 5 V to 0 V at t 0 Also sketch and label the waveform vO t which Joe sees on the scope much later t 5 when the switch changes the input voltage from 0 V to 5 V at t 0 Show asymptotes and determine the time constant Use the coordinates provided on page 4 3 Name Waveform when switch moves from 5 volts to 0 volts at t 0 vO volts 5 0 t seconds 5 Waveform when switch moves from 0 volts to 5 volts at t 0 vO volts 5 0 t seconds 5 4 Name PROBLEM 2 The circuit below contains both dependent and independent sources I R1 a a v R2 R2 2v Determine a Thevenin equivalent circuit at terminals a a Specify polarities and element values 5 Name PROBLEM 3 A FET used as an amplifier is shown in the circuit below 15 V RL R1 C2 vi C1 vO VO vo R2 The capacitor C1 couples the incremental input voltage vi to the gate Because it is an open circuit for DC vi does not affect VGS the operatingpoint value of the gate tosource voltage R1 R2 500k The FET is described by iD 0 K 2 vGS K 0 4 mA V2 for vGS VT VT 2 for vGS VT and vDS vGS VT VT 2V A Determine VGS and RL such that the operating point of the amplifier is VO 7V ID 0 2mA B Determine the incremental transconductance gm of the FET at the operating point defined in part A 6 Name C Given that R1 R2 500k determine R1 and R2 such that the desired value of VGS is established D Employing the usual incremental model for the FET sketch and label a complete incremental model for the circuit Label elements of the model by their symbols NOT by their numerical values 7 Name PROBLEM 4 A quartz piezoelectric crystal exhibits a strong high Q resonance which is why it is used as time or frequency standards in clocks tuners etc RS circuit symbol for a quartz crystal C L equivalent circuit for a quartz crystal A A quartz crystal is used in the filter below Determine the transfer function of this filter That is find A s VV O where s j Express your result as a ratio of polynomials in s I RS C L VI R VO Let R RS 8 Name For a specific set of element values in this circuit the transfer function is A s 2 5 103 s2 5 s 0 25 1014 103 s for s in sec 1 B Sketch the frequency dependence of the magnitude and phase of A j on the coordinates provided on page 10 Determine and label the resonant frequency 0 the magnitude A0 and phase of A j 0 at that frequency and the high and low frequency asymptotes of magnitude and phase Determine the bandwidth of the resonance defined by the frequencies where A A0 2 9 Name 1 0 1 A 0 01 0 001 0 0001 0 00001 2 A radians 4 0 4 2 104 105 107 106 radians 10 108 109 Name PROBLEM 5 The circuit below is driven by vI t 20 cos t R1 C vI t R1 R2 1 k 103 vO t C 0 05 F 5x10 8 F R2 Using the indicated element values the transfer function is j 2 104 Vo 0 5 j 104 Vi Determine vO t for 104 sec 1 11 Name PROBLEM 6 The circuits below function as filters in the sinusoidal steady state Vi Vo Vi Vo Vi Vo Vi Vo Vi Vo Vi Vo Vi Vo Vi Vo Label those which are Low Pass Filters with LP Label those which are High Pass Filters with HP Label those which are Band Pass Filters with BP Label those which are Band Stop Filters with BS Extra space is provided on page 13 Grading will be based on correct 3 incorrect 12 Name This page intentionally left blank 13 Name PROBLEM 7 The op amp circuit below employs a diode which may be assumed ideal and an n channel FET The op amp has very high gain The characteristics of both are shown 10 V FET D iD vDS D G R1 6 2 k R2 2 7 k R2 S R1 vI 10 V G 0 K 2 vGS2 iD vGS vGS 0 vGS 0 vDS vGS VT 0 K 0 1 mA V2 S vO 10 V Diode i v i v 0 Sketch the nonlinear transfer characteristic vO vs vI on the coordinates below for 20 V vI 20 V vO volts 10 20 10 vI volts 0 …
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