Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6 002 Circuits Electronics Spring 2007 Final Exam 21 May 2007 Name There are 31 pages in this nal including this cover page Please check that you have them all Please write your name in the space provided above and circle the name of your recitation instructor along with the time of your recitation IMPORTANT The problems in this exam vary in di culty moreover questions of di er ent levels of di culty are distributed throughout the exam If you nd yourself spending a long time on a question consider moving on to later problems in the exam and then working on the challenging problems after you have nished all of the easier ones Do your work for each question within the boundaries of that question or on the back of the preceding page When nished enter your answer to each question in the corresponding answer box that follows the question Remember to include the sign and units for all numerical answers This is a closed book exam but you may use a calculator and three double sided pages of notes You have 3 hours to complete this nal Good luck 1A 1B 2 3 4 5 6 7 8 9 10 11 12A 12B 13 14 15 16 17 18 19A 19B 19C 19D Final Score 1 Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY Problem 1 8 points D G vDS vGS S Figure 1 A MOSFET shown in Figure 1 operating in the triode region has a characteristic iDS rela tionship which depends on both vDS and vGS 2 iDS K vGS VT vDS vDS 2 where vGS VT and vDS vGS VT The small signal relationship between ids vgs and vds can be expressed by an equation of the form ids Avgs Bvds where A and B are constants Assume that the device is biased at an operating point VGS VDS 1A 4 points Draw the 2 element small signal model for the device which is operating in the triode region Express the element values in terms of A and B Small signal equivalent circuit 2 Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY 1B 4 points Find the values of the constants A and B in the two element small signal model for the MOSFET operating in the triode region ids Avgs Bvds Formulate your answers in terms of the variables K VGS VT and VDS A B 3 Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY Problem 2 4 points A and B are 1 bit numbers Each of them can take on the positive integer values 0 or 1 Implement an adder which takes the two inputs A and B and produces a 1 bit sum output Z The sum output Z must saturate at 1 which means that if the sum is greater than 1 the circuit must output a 1 You may use as many inverters NAND gates and NOR gates as you like in your circuit Your adder design 4 Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY Problem 3 4 points Consider the logic function O described by the following truth table A 0 0 0 0 1 1 1 1 B 0 0 1 1 0 0 1 1 C 0 1 0 1 0 1 0 1 O A B C 1 0 0 0 1 1 0 1 Show how to implement the function O using only two input NAND gates and inverters Hint Remember the relations indicated by Figure 2 A B A B C A B C C A B C Figure 2 5 Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY Problem 3 continued Implementation of O 6 Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY Problem 4 4 points Figure 3 In the circuit in Figure 3 the current reading from the ammeter is 4 mA with the switch open and 3 mA with the switch closed where iDs K 2 uGs VT What are VT and K Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY Problem 5 4 points R vi C vo Figure 4 Let the network depicted in Figure 4 have a frequency response given by 1 vo vi 1 j K where K is positive The magnitude and phase of this frequency response as a function of are illustrated by the two plots below Find the values of c m c and in terms of the circuit parameters R and C log VVoi VO c 1 log c VI 10 1 0 slope m 1 10 1 10 0 0 10 1 10 c 0 10 1 log c 10 20 30 40 c 50 60 70 80 90 100 2 10 1 0 10 10 1 10 2 10 8 Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY Problem 5 continued c m c 9 Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY Problem 6 4 points iL t L vC C Q t Figure 5 Consider the circuit in Figure 5 with two inputs V t t and I t Q t The inductor and capacitor have zero initial state i e vC t 0 0 and iL t 0 0 What are the inductor current iL and the capacitor voltage vC at t 0 At what frequency osc will the circuit oscillate vC 0 iL 0 osc 10 Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY Problem 7 4 points vO R4 R5 R2 R3 R1 C iO Figure 6 What is the time constant for the circuit depicted in Figure 6 11 Cite as Anant Agarwal and Jeffrey Lang course materials for 6 002 Circuits and Electronics Spring 2007 MIT OpenCourseWare http …
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