MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE 6 002 Circuits and Electronics Quiz 1 October 13 2004 YOUR NAME Recitation Instructor TA General Instructions 1 Please verify that there are 17 pages in your exam 2 Please do all of your work in the spaces provided in this examination booklet In particular try to do your work for each question within the boundaries of the question or on the back side of the page preceding the question Extra pages are also available at the end of the booklet Place the answer to each question within the appropriate answer box 3 You may use one double sided page of notes and a calculator while taking this exam For examiner s use only Part Score 1 2 Part Score 4A 4B 3A 5A TOTAL SCORE 3B 3C 5B 5C 6 002 Circuits and Electronics Fall 2004 Quiz 1 Problem 1 Name 20 Points Find the Th venin equivalent of Network A and the Norton equivalent of Network B Fig 1 and graph their i v relations as viewed from their ports Hint you can use superposition for Network B For purposes of plotting you may assume that V and I are both positive Please label key intercepts on the graphs Figure 1 Page 2 of 17 6 002 Circuits and Electronics Fall 2004 Quiz 1 Name NETWORK A NETWORK B VTH IN RTH RN Page 3 of 17 6 002 Circuits and Electronics Fall 2004 Quiz 1 Problem 2 Name 10 Points Figure 2 shows a circuit implementing a logic function with the convention that a high voltage level denotes a Boolean 1 and a low voltage level denotes a Boolean 0 Write a logic expression relating the output Z to the inputs A B C and D VS RL Z A B D C Figure 2 Z Page 4 of 17 6 002 Circuits and Electronics Fall 2004 Quiz 1 Problem 3 Name 20 Points 3A The engineers at Yikes Inc have developed the cool new 4 terminal device shown below in Fig 3 The marketing team has named the device the BOBAFET in hopes of securing some Hollywood licensing deals Draw vDS vs iD for the BOBAFET for vGB 0 5 V and vGB 2 V Make sure to fully label your plots iD D D D G B vDS G B G B S BOBAFET S vGB 1 V Figure 3 Page 5 of 17 S vGB 1 V 6 002 Circuits and Electronics Fall 2004 Quiz 1 Name 3B Yikes engineers build the circuit shown below in Fig 4 and claim that the circuit behaves like a logic gate Given that the inputs X1 and X2 take on only two values 5 V representing a logical 1 and 0 V representing a logical 0 write a truth table for the circuit and determine the logic function f X1 X2 implemented by the gate if the output is taken between the terminal labeled OUT and ground Figure 4 X1 0 0 1 1 X2 0 1 0 1 OUT f X1 X2 Page 6 of 17 6 002 Circuits and Electronics Fall 2004 Quiz 1 Name 3C Yikes sales team discovers that Lintel Corp uses large numbers of gates in its products and offers to sell the BOBAFET based gate in b to Lintel Lintel s products adhere to a static discipline with VOH 4 5 V VOL 0 5 V VIH 4 V and VIL 0 9 V Lintel hires you as an electronics consultant to determine whether it can use Yikes gates Show that the gates violate Lintel s static discipline under some valid condition or prove that the gate satisfies the static discipline Lintel static discipline satisfied Justification Page 7 of 17 6 002 Circuits and Electronics Fall 2004 Quiz 1 Problem 4 Name 25 Points Figure 5 shows a highly simplified model of a certain type of power converter system Figure 5 4A Find the node voltages e1 and e2 in terms of VA RA RB RC and IC Assume iD 0 Page 8 of 17 6 002 Circuits and Electronics Fall 2004 Quiz 1 Name e1 e2 Page 9 of 17 6 002 Circuits and Electronics Fall 2004 Quiz 1 Name 4B For this part of the problem assume VA 5 V RA 0 5 RB 0 5 RC 1 and IC 2 A The overload behavior of a power converter system is often of interest What value of iD from an external circuit will make vD 0 V iD Page 10 of 17 6 002 Circuits and Electronics Fall 2004 Quiz 1 Problem 5 Name 25 Points Current regulator diodes CRDs are nonlinear two terminal elements that are often used for limiting current flow and providing bias currents in electronic circuits A circuit incorporating a CRD is shown in Fig 6 The vD iD relationship of a CRD for vD 0 may be roughly approximated as 2v 0 2v 2D iD D 5 mA for mA for v D 5 V v D 5 V where vD is expressed in Volts and iD is expressed in mA This characteristic is illustrated in Fig 7 Figure 6 Figure 7 Page 11 of 17 6 002 Circuits and Electronics Fall 2004 Quiz 1 Name 5A Consider the circuit of Fig 6 for parameters vI 5 V RI 1 k Write an equation relating the voltage vD to input voltage vI for this case and solve for voltage vD Note it is possible to do a rough graphical cross check on your answer by drawing a load line on Fig 7 vD Page 12 of 17 6 002 Circuits and Electronics Fall 2004 Quiz 1 Name 5B Assume that VI has been adjusted such that the operating point is at VD 3 V Find the value for the incremental resistance of the CRD by linearizing the expression for iD about this operating point Recall that the incremental resistance also called the smallsignal resistance is the ratio of the incremental change in device voltage to incremental change in device current at the specified operating point rD Page 13 of 17 6 002 Circuits and Electronics Fall 2004 Quiz 1 Name 5C Draw the small signal circuit for the nonlinear circuit in Fig 6 at the operating point in part 5B That is for RI 1 k VD 3 V Make sure to indicate all component values in the small signal circuit What is the expected change in output voltage vD for a small change in input voltage vI 0 1 V Draw and label small signal circuit model vD Page 14 of 17 6 002 Circuits and Electronics Fall 2004 Quiz 1 Name Page for extra work Page 15 of 17 6 002 Circuits and Electronics Fall 2004 Quiz 1 Name Page for extra work Page 16 of 17 6 002 Circuits and Electronics Fall 2004 Quiz 1 Name Page for extra work Page 17 of 17
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