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Unformatted text preview: EECS 314 Winter 2009 Homework set 6 Students name ___________________________ Discussion section # _______ (Last, First, write legibly, use ink) (use ink) Instructor is not responsible for grading and entering scores for HW papers lacking clear information in the required fields above 2009 Alexander Ganago Page 1 of 2 Problem 1 The RC circuit response to a pulse The Big Picture Assuming that before the arrival of the pulse, at time t =0 the circuit was under DC steadystate conditions, one can easily find that the capacitor voltage at time t >0 is expressed as V C = V S 1 e t where the time constant is = R C When the pulse begins, the capacitor is gradually charging. Note that the circuit does not know that the pulse will end: its response, according to the equation above, is exactly as it would be for a switch closed forever or an infinitely long pulse. When the pulse ends, the capacitor is gradually discharging. Remember the continuity demand! In the circuit above, the discharge has the same time constant: recall that a voltage source of zero voltage (at time t > t ) acts as a short circuit. The Assignment Part 1 (10 points) Given R = 150 , determine the range of capacitances such that the capacitor voltage V C reaches at least 3.5 V within the pulse duration of 200 ps (1 picosecond = 1012 sec). This duration of a clock pulse corresponds to the frequency of 2.5 GHz, typical of todays computers. Your result: _________________________________________ Part 2 (10 points) Given C = 2.5 pF, determine the range of resistances such that the capacitor voltage V C reaches at least 3.5 V within the pulse duration of 200 ps. Your result: _________________________________________ Part 1 2 3 Total EECS 314 Winter 2009 Homework set 6 Students name ___________________________ Discussion section # _______ (Last, First, write legibly, use ink) (use ink) Instructor is not responsible for grading and entering scores for HW papers lacking clear information in the required fields above 2009 Alexander Ganago Page 2 of 2 Problem 1, continued Part 3 (20 points) Assume t = 2 and sketch on the grids below: the capacitor voltage, and the resistor voltage. On the circuit diagram (repeated here for your convenience) show the reference marks for the resistor voltage. On the grids below, assume that the tick marks indicate the beginning and the end of the pulse. Calculate the maximal value of the capacitor voltage, and of the resistor voltage. Your results: v C, max = ____________ V v R, max = ____________ V Show your work for all parts. EECS 314 Winter 2009 Homework set 6 Students name ___________________________ Discussion section # _______ (Last, First, write legibly, use ink) (use ink) Instructor is not responsible for grading and entering scores for HW papers lacking clear information in the required fields above 2009 Alexander Ganago Page 1 of 2...
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This note was uploaded on 10/28/2009 for the course EECS 314 taught by Professor Ganago during the Winter '07 term at University of Michigan.
 Winter '07
 Ganago

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