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 1 2 3A 3B 3C Score Part 4A 4B 5A 5B 5C Score TOTAL SCORE___________________6.002 Circuits and Electronics Fall 2004 Quiz #1 Name:_______________________________ Page 2 of 17 Problem 1 (20 Points) Find the Thévenin 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 16.002 Circuits and Electronics Fall 2004 Quiz #1 Name:_______________________________ Page 3 of 17 NETWORK (A) NETWORK (B) VTH = IN = RTH = RN =6.002 Circuits and Electronics Fall 2004 Quiz #1 Name:_______________________________ Page 4 of 17 Problem 2 (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. Figure 2 RLZABCDVS Z =6.002 Circuits and Electronics Fall 2004 Quiz #1 Name:_______________________________ Page 5 of 17 Problem 3 (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. DSGBDSGBvGB < 1 VvGB > 1 VBOBAFET+-vDSiDDSGB Figure 36.002 Circuits and Electronics Fall 2004 Quiz #1 Name:_______________________________ Page 6 of 17 (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 X2 OUT 0 0 0 1 1 0 1 1 f(X1, X2) =6.002 Circuits and Electronics Fall 2004 Quiz #1 Name:_______________________________ Page 7 of 17 (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?6.002 Circuits and Electronics Fall 2004 Quiz #1 Name:_______________________________ Page 8 of 17 Problem 4 (25 Points) Figure 5 shows a highly simplified model of a certain type of power converter system. (4A) Find the node voltages e1 and e2 in terms of VA, RA, RB, RC, and IC. (Assume iD = 0.) Figure 56.002 Circuits and Electronics Fall 2004 Quiz #1 Name:_______________________________ Page 9 of 17 e1 = e2 =6.002 Circuits and Electronics Fall 2004 Quiz #1 Name:_______________________________ Page 10 of 17 (4B) For this part of the problem, assume VA = 5 V, RA = 0.5 Ω, RB = 0.5 Ω, RC = 1 Ω, 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 =6.002 Circuits and Electronics Fall 2004 Quiz #1 Name:_______________________________ Page 11 of 17 Problem 5 (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: ⎭⎬⎫⎩⎨⎧≥<−=V5v)mA(5V5v)mA(0.2v2viDD2DDDforfor where vD is expressed in Volts, and iD is expressed in mA. This characteristic is illustrated in Fig. 7. Figure 6 Figure 76.002 Circuits and Electronics Fall 2004 Quiz #1 Name:_______________________________ Page 12 of 17 (5A) Consider the circuit of Fig. 6 for parameters vI = 5 V, RI = 1 kΩ. 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 =6.002 Circuits and Electronics Fall 2004 Quiz #1 Name:_______________________________ Page 13 of 17 (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 small-signal resistance, is the ratio of the incremental change in device voltage to incremental change in device current at the specified operating point.) rD =6.002 Circuits and Electronics Fall 2004 Quiz #1 Name:_______________________________ Page 14 of 17 (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 kΩ, VD = 3 V.) Make sure to indicate all component values in the
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