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 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 quiz vary in di culty moreover questions of di erent levels of di culty are distributed throughout the quiz If you nd 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 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 quiz but you may use a calculator and your double sided page of notes You have 2 hours to complete this quiz Good luck 1A 2A 1B 1C 1D 1E 1F 1G 2B 2C 2D 3A 3B 3C 3D 3E 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 VDD D G S vI RL G vO D gm vgs vgs S a S 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 g m l 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 a t rest with the switch open for a long time At t O t h e switch is closed Sketch t h e current ic through t h e capacitor for t O on t h e axes below Using t h e circuit parameters R1 R2 C and Vo indicate on your sketch i t h e initial value i c O t ii t h e 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 iL I t R L Figure 5 a 5 points Find the inductor current iL t for t 0 in response to the current step I t Istep t I0 u 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 I0 tu t where 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 R2 vC t R1 C 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 L and C L iL t C vC 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 bu er comprising a pair of MOSFETs driven by a source whose Thevenin equivalent circuit is represented by the voltage source vT H and source resistance RT H Source Bu er VS VS RL vB RL vA vC RT H M1 M2 vT H a D RON D G G CGS S b S Figure 8 The MOSFETs M 1 and M 2 in the bu er are identical and their behavior is to be modelled by the circuit shown in Figure 8b where the switch is closed for vGS VT and is open when vGS VT This problem explores the dynamic operation of the bu er in particular the delays introduced by the gate source capacitance CGS Throughout the problem assume that VT H VT RON VS RL 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 case in which the input to the bu er makes a 0 1 transition The voltage source vT H and the output at the drain of M 1 vB then exhibit the waveforms sketched in Figure 9 vT H VS t vB t1 t Figure 9 2A 5 points Determine the delay t1 indicated in Figure 9 t1 11 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 2B 5 points The voltage …
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