fa05_final v6.doc 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: Problem Points Score Grader 1 8 2 12 3 20 4 20 5 20 6 20 Total 1006.002 Circuits and Electronics Fall 2005 Final Exam Name:______________________________________ Page 2 of 22 (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. ABCDX0000000100100011010001010110011110001001101010111100110111101111X =6.002 Circuits and Electronics Fall 2005 Final Exam Name:______________________________________ Page 3 of 22 (12 points) This problem concerns the following circuit: (A) Assume that the network is operating in the sinusoidal steady state. Determine the responsetvout to the input voltage tVtvSIincos . Note that outv will take the form tVSOcos . (answer box located on the following page)6.002 Circuits and Electronics Fall 2005 Final Exam Name:______________________________________ Page 4 of 22 outv _______________________________________________(B) If the input of this network is inv and the output of the network is outv , 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 Above6.002 Circuits and Electronics Fall 2005 Final Exam Name:______________________________________ Page 5 of 22 (20 points) Consider the following circuit: The excitation tvi is an impulse at 0t of area secondsvolt .ttvi(A) What are the values of ti , tvo, and tvc at 0t ?0i ________________________________ 0ov _______________________________ 0cv _______________________________ (B) What are the values of ti , tvo, and tvc as t ?ti _____________________________ tvo____________________________ tvc____________________________ There is no stored energy for 0tHL310FC7106.002 Circuits and Electronics Fall 2005 Final Exam Name:______________________________________ Page 6 of 22 For the remaining parts of Problem 3, now assume that CLZR1011010(C) Find the natural frequencies of this circuit (i.e. find the roots of the characteristic equation). Give numerical answers. s1 = ____________________________________ s2 = ____________________________________6.002 Circuits and Electronics Fall 2005 Final Exam Name:______________________________________ Page 7 of 22 (D) Sketch the approximate waveform for ti . Clearly label the important features of your sketch with numerical values. Assume that 100ZR .tit6.002 Circuits and Electronics Fall 2005 Final Exam Name:______________________________________ Page 8 of 22 (20 points) The following circuits are driven by a sinusoidal source tvi 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 functionsiovvjHˆˆ. For each circuit, circle the letters of the magnitude and phase 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: G H I J K L6.002 Circuits and Electronics Fall 2005 Final Exam Name:______________________________________ Page 9 of 22 (This page left blank for work – Problem 4 magnitude and phase plots on following page)6.002 Circuits and Electronics Fall 2005 Final Exam Name:______________________________________ Page 10 of 22 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.6.002 Circuits and Electronics Fall 2005 Final Exam Name:______________________________________ Page 11 of 22 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.6.002 Circuits and Electronics Fall 2005 Final Exam Name:______________________________________ Page 12 of 22 (20 points) The circuit symbol for the exponentially acting transistor, or EXPAT for short, is drawn to the right. The voltage KTv between the Knob, K, and the Thingamijig, T, is the input voltage and it controls the current Wi between the Whatchamacallit, W, and the Thingamajig, T. The equations relating the input current, Ki , and the output current, Wi , to the input and output voltages, KTv and WTv , respectively are the following: 0for1KTVvMKveIiMKT, and 0,0for10,0for0WTKTVvKTMWTKTWvvevGvviMWTThese relationships are drawn below for 0KTv, and VvWT3 for an EXPAT for which mAIM1.0 , VVM5.0 , and mSGM4 . The asymptotic values of the curves at large voltages are indicated, and a one volt increment has been used when plotting the family ofWi curves. vKT= 1VvKT= 2VvKT= 3V6.002 Circuits and Electronics Fall 2005 Final
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