Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.002 – Circuits & Electronics Spring 2007 Quiz #2 25 April 2007 Name: • There are 20 pages in this quiz, including this cover page. Please check that you have them all. • Please wr ite 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 quiz vary in difficulty; moreover, questions of different levels of difficulty are distributed throughout the quiz. If you find yourself spending a long time on a question, consider moving on to later problems in the quiz, and then working on the challenging 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 p age. When finished, 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 quiz, but you may u se a calculator and your double-sided page of notes. • You have 2 hours to complete this quiz. • Good luck! 1A. 1B. 1E. 2A. 2B. 3A. 3D. 1C. 1F. 2C. 3B. 3E. 1D. 1G. 2D. 3C. 3F. 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].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 1B: 5 points Calculate the small-signal gain vo/vi of the circuit shown in Figure 2a. Use the small-signal model of the MOSFET shown in Fig 2b. Assume that the MOSFET is operating in the saturation region. VD D D G S vI G D vO RL vgs gmvgs S S (a) (b) Figure 2. vo = vi 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 1C: 5 points Calculate the small-signal gain u,/ui of the circuit in Figure 3a in terms of RL, gml, and gm2. Assume that both of the MOSFETS are operating in the saturation region, and that the small-signal models of the MOSFETs are as shown in Figure 3b. Figure 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 ID: 5 points The circuit shown in Figure 4 has been at rest with the switch open for a long time. At t = O the switch is closed. Sketch the current ic through the capacitor for t > O on the axes below. Using the circuit parameters R1, R2, C, and Vo,indicate on your sketch (i) the initial value ic(Ot), (ii) the final value ic(oo), and (iii) the time constant. Figure 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 1E: 10 points Consider the circuit illustrated in Figure 5. I(t) iL LR Figure 5. (a) (5 points) Find the inductor current iL(t) for t ≥ 0 in r esponse to the current step I(t) = Istep(t) = I0u(t). Assume that iL(0) = 0. iL(t) = for I(t) = Istep(t) 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 1E (continued): (b) (5 points) Find the inductor current iL(t) for t ≥ 0 in response to the current ramp I(t) = Iramp(t) = I0αtu(t), where α is a constant. Again, assume that iL(0) = 0. iL(t) = for I(t) = Iramp(t) 7 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 1F: 5 points The capacitor in the circuit in Figure 6 has an initial voltage VO on its terminals at t = 0− when a step of voltage Vu(t) is applied at t = 0. Find an expression for the voltage across the capacitor vC for t > 0. vC(t) C R2 R1 V u(t) Figure 6. vC(t) = 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 1G: 10 points Find an expression for the voltage vC(t) for the circuit in Figure 7, assuming that vC(0−) = 0 and iL(0−) = 0. Please express your answer in terms of Λ, L, and C. L C vC iL Λδ(t) Figure 7. vC(t) = 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 2: 20 points Figure 8a shows a buffer comprising a pair of MOSFETs driven by a source whose Thevenin equivalent circuit is represented by th e voltage source vT H and source resistance RT H. vT H RT H vA RLRL vB M1 M2 vC VSVS Source Buffer (a) D G G D S CGS RON S (b) Figure 8. The MOSFETs M 1 and M2 in the bu ffer are identical and th eir behavior is to be modelled by the circuit shown in Figure 8b, wh ere the switch is closed for vGS > VT and is open when vGS < VT. This problem explores the dynamic operation of the buffer, in p articular the delays introduced by the gate-source capacitance CGS. Throughout the problem, assume that RON VT H > VT >VSRL + RON VS > VT 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].First, consider the
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