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 final, 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 difficulty; moreover, questions of differ-ent levels of difficulty are distributed throughout the exam. If you find yourself spen ding a long time on a question, consider moving on to later problems in the exam, and then working on the ch allenging problems after you have finished 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 fin ished, 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 final. • Good luck! 1A. 1B. 5. 6. 10. 11. 14. 15. 19A. 2. 7. 12A. 16. 19B. 3. 8. 12B. 17. 19C. 4. 9. 13. 18. 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 vDS S vGS G 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 : 2iDS = 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-si gnal equiva lent 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 triod e 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 inpu ts A and B an d 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 th e logic function O described by the following truth table. A B C O(A, B, C) 0 0 0 1 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 1 1 0 1 1 1 1 0 0 1 1 1 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 A C C B B A A C C BB 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].10−110010110−110010−210−1100101102−100−90−80−70−60−50−40−30−20−10010� � � � Problem 5: 4 points R Cvi vo Figure 4. Let the network depicted in Figure 4 h ave a frequency response given by vo 1 = vi 1 + jωK where K is positive. The magnitude and phase of this frequency response as a function of ω are illustrated by the two plots below . Find the values of ωc, m, φ(ωc), and φ(∞) in terms of the circuit parameters R and C. log � VVoi � � � � VO VI � � � = 1 slope = m ω ωc = 1 log(ω/ωc) φ(ω) φ(∞) φ(ωc) ω ωc = 1 log(ω/ωc)0◦ 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): ωc = m = φ(ωc) = φ(∞) = 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 L vCΛ δ(t) C Q δ(t) Figure 5. Consider the circuit in Figure 5 with two inputs V (t) = Λ δ(t) and I(t) = Q δ(t). The inductor and capacitor have zero
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