Inter American University of Puerto Rico Bayamón Campus School of Engineering Department of Electrical Engineering. ELEN 3311 Electronics I

Transcription

1 Inter American University of Puerto Rico Bayamón Campus School of Engineering Department of Electrical Engineering ELEN 3311 Electronics I Final Exam Tuesday, May 24 Name: Enter all your work and your answers directly in the spaces provided on the printed pages. Full credit will only be given to answers that you neatly transfer to the spaces on the printed pages. Answers must be derived or explained, not just simply written down. Problem Value Grade Total 100

2 Problem 1: (80 points) The nonlinear resistor inside the three-terminal device shown below is characterized by the equations: v B = ri A i B 0 Region I i B = 0 v B ri A Region II These equations trace the following curves in the v B -i B plane for i A1 > i A2 > 0: In each region, the three-terminal device may be modeled as shown below: 2

3 The three-terminal device is placed inside the circuit shown below: (A) Find an algebraic equation for the v B -i B constraint imposed by R OUT and V SS and graph this load line in the v B -i B plane. Mark the points corresponding to solutions of the circuit. Assume ri A1 > V SS > ri A2 > 0. v B -i B constraint: 3

4 (B) Draw the circuit substituting the model of the device in Region I. (C) Find an algebraic expression for the v IN -v OUT relation in Region I. v OUT = (D) Find the small-signal gain vout in Region I using the expression obtained in the previous part. Assume any necessary large-signal values if needed. v out = 4

5 (E) Draw the circuit substituting the model of the device in Region II. (F) Find an algebraic expression for the v IN -v OUT relation in Region II. v OUT = (G) Find the small-signal gain vout in Region II using the expression obtained in the previous part. Assume any necessary large-signal values if needed. v out = 5

6 (H) Find the range of v IN for which the circuit is operating in Region I. v IN (I) Find the range of v IN for which the circuit is operating in Region II. Verify that the ranges obtained in this and the previous part complement each other. v IN 6

7 (J) Find the value of v OUT at the transition between Regions I and II using both equations and verify that the values of v OUT are the same. v OUT = (K) Plot the v IN -v OUT any asymptotes. relation showing clearly all transition values, any intercepts and/or 7

8 (L) Draw the small-signal circuit diagram for Region I and find the small-signal gain. Verify that each gain is the same as the one found before. Remember that all elements in the small-signal circuit must be linear. v out = 8

9 (M) Draw the small-signal circuit diagram for Region II and find the small-signal gain. Verify that each gain is the same as the one found before. Remember that all elements in the small-signal circuit must be linear. v out = 9

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11 Problem 2: (20 points + 20 bonus points) The nonlinear resistor inside the circuit shown below is characterized by the equation: i Q = αv 3 Q These equations trace the following curve in the v Q -i Q plane: 11

12 (A) Find an algebraic equation for the v Q -i Q constraint imposed by v IN and R IN and graph these load lines in the v Q -i Q plane for v IN > 0 and v IN < 0. Mark the points corresponding to solutions of the circuit. v Q -i Q constraint: 12

13 (B) Find an algebraic expression for the v IN -v OUT v OUT. relation. Do not solve the equation for v IN -v OUT relation: (C) (5 bonus points) Find the small-signal gain vout using the expression obtained in the previous part assuming all the necessary large-signal values. v out = 13

14 (D) (15 bonus points) Sketch the v IN -v OUT relation. Hint: Use load-line analysis using the graph given below. 14

15 (E) The nonlinear resistor can be replaced by a linear resistor r Q as shown below. Assume the circuit is biased at some large signal V Q and find an algebraic expression for r Q. r Q = (F) Find the small-signal gain. Partial credit will be given if the gain includes r Q. Full credit will be given to a gain expression without r Q. v out = 15