MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6 002 Circuits and Electronics Fall 2005 Final Exam December 20 2005 YOUR NAME Recitation Instructor TA General Instructions 1 Please verify that there are 22 pages in your exam booklet 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 three double sided pages of notes and a calculator while taking this exam For examiner s use only fa05 final v6 doc Problem Points 1 8 2 12 3 20 4 20 5 20 6 20 Total 100 Score Grader 6 002 Circuits and Electronics Fall 2005 Final Exam Name 8 points This problem considers the following NMOS digital logic circuit The circuit has four inputs A B C and D and one output X If a high voltage represents a 1 and a low voltage represents a 0 write the output X as a Boolean function of A B C and D in the answer box at the bottom of this page The truth table may be used as a guide to finding the function but is not a requirement A 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 B 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 C 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 D 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 X X Page 2 of 22 6 002 Circuits and Electronics Fall 2005 Final Exam Name 12 points This problem concerns the following circuit A Assume that the network is operating in the sinusoidal steady state Determine the response vout t to the input voltage v in t V SI cos t Note that vout will take cos t the form VSO answer box located on the following page Page 3 of 22 6 002 Circuits and Electronics Fall 2005 Final Exam vout B Name If the input of this network is vin and the output of the network is vout circle only one of the following terms that best describes the filtering function performed by the network Low Pass High Pass Band Pass Band Stop None of the Above Page 4 of 22 6 002 Circuits and Electronics Fall 2005 Final Exam Name 20 points Consider the following circuit There is no stored energy for t L 10 3 H C 10 7 F The excitation vi t is an impulse at t 0 of area vi t A i0 0 vc 0 it t What are the values of i t vo t and vc t at t vo 0 B volt seconds What are the values of i t vo t and vc t as t vo t vc t Page 5 of 22 0 6 002 Circuits and Electronics Fall 2005 Final Exam Name For the remaining parts of Problem 3 now assume that R C 1 Z0 10 1 L 10 C Find the natural frequencies of this circuit i e find the roots of the characteristic equation Give numerical answers s1 s2 Page 6 of 22 6 002 Circuits and Electronics Fall 2005 Final Exam D Name Sketch the approximate waveform for i t Clearly label the important features of your sketch with numerical values Assume that R Z 0 10 it t Page 7 of 22 6 002 Circuits and Electronics Fall 2005 Final Exam Name 20 points The following circuits are driven by a sinusoidal source vi t in the steady state On the following pages there are six sketches of magnitudes on log log graphs labeled A F and six sketches of phase on linear log graphs labeled G L for possible transfer v o v i For each circuit circle the letters of the magnitude and phase functions H j plots which could represent the behavior of that circuit Each circuit matches only one magnitude and one phase plot Magnitude and phase plots may be reused Magnitude A B C D E F Phase G H I J K L Magnitude A B C D E F Phase G H I J K L Magnitude A B C D E F Phase G H I J K L Magnitude A B C D E F Phase Page 8 of 22 G H I J K L 6 002 Circuits and Electronics Fall 2005 Final Exam Name This page left blank for work Problem 4 magnitude and phase plots on following page Page 9 of 22 6 002 Circuits and Electronics Fall 2005 Final Exam Name Transfer function magnitude plots for Problem 4 Note The horizontal axes in these sketches indicate zero on the log scale You are looking for the correct approximate shape of the plot do not worry about the frequency scale along the horizontal axes The vertical scales may differ among sketches Page 10 of 22 6 002 Circuits and Electronics Fall 2005 Final Exam Name Transfer function phase plots for Problem 4 Note The horizontal axes in these sketches indicate zero phase angles You are looking for the correct approximate shape of the plot do not worry about the frequency scale along the horizontal axes The vertical scale may differ among sketches Recall that one may shift phase angles by multiples of 360 without changing the result Page 11 of 22 6 002 Circuits and Electronics Fall 2005 Final Exam Name 20 points The circuit symbol for the exponentially acting transistor or EXPAT for short is drawn to the right The voltage v KT between the Knob K and the Thingamijig T is the input voltage and it controls the current iW between the Whatchamacallit W and the Thingamajig T The equations relating the input current i K and the output current iW to the input and output voltages v KT and vWT respectively are the following iK IM 1 e v KT VM for v KT 0 and iW 0 GM v KT 1 e vWT VM for v KT 0 vWT 0 for v KT 0 vWT 0 These relationships are drawn below for v KT 0 and vWT 3 V for an EXPAT for which I M 0 1 mA VM 0 5 V and GM 4 mS The asymptotic values of the curves at large voltages are indicated and a one volt increment has been used when plotting the family of iW curves vKT 3V vKT 2V vKT 1V Page 12 of 22 6 002 Circuits and Electronics Fall 2005 Final Exam A Name In general the small signal linear equivalent circuit for a three terminal transistor like the EXPAT has four elements and can be represented by the following circuit Find expressions for the four small signal elements g i g r g …
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