ee40sp08_mt2_solns

ee40sp08_mt2_solns - EE 40: Introduction to Microelectronic...

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Unformatted text preview: EE 40: Introduction to Microelectronic Circuits Spring 2008: Midterm 2 Venkat Anantharam 03/19/08 Total Time Allotted : 50 min Total Points: 50 1. This is a closed book exam. However, you are allowed to bring two pages (8.5 x 11) notes, with writing on both sides. 2. No electronic devices, i.e. calculators, cell phones, computers, etc. 3. Show the steps used to arrive at your answer, where necessary. Partial credit will be given if you have the proper steps but an incorrect answer. A correct answer for a problem involving multiple steps where it is not clear how you arrived at the answer may not be given full credit. 4. Write your final answers into the boxes. 5. Remember to put down units. Last (Family) Name: First Name: Student ID: Lab Section: Signature: Max Score 1 (a-g) 10 1 (h-k) 10 2 6 3 (a) 4 3 (b) 4 4 10 5 6 Total 50 1 1. (20 pts total) In the circuit shown above the current source is a DC source. The switch is open prior to time 0, and the current has reached steady state prior to time 0. At time 0 the switch closes. The reference configuration to use for each circuit element in solving the problem is shown in the figure. Please provide all answers in terms of I s , R , L , and C . (a) What is i L (0- )? (2 pts) i L (0- ) = I s (because cap is open circuit in DC steady state) (b) What is v C (0- )? (2 pts) v C (0- ) = 0 (because inductor is short circuit in DC steady state) (c) What is i L (0 + )? (1 pt) i L (0 + ) = i L (0- ) = I s (d) What is v C (0 + )? (1 pt) v C (0 + ) = v C (0- ) = 0 2 (e) What is i 1 (0 + )? (2 pts) Using KVL, v 2 (0 + ) = v C (0 + ) + v 1 (0 + ) = v 1 (0 + ) i 2 (0 + ) = i 1 (0 + ) . Combining this with i 2 (0 + ) + i 1 (0 + ) = I s , we get: i 1 (0 + ) = I s / 2 (f) What is i C (0 + )? (1 pt) i C (0 + ) =- I s / 2 (because i C (0 + ) + i L (0+) = i 1 (0 + )) (g) What is dv C dt (0 + )? (1 pt) dv C dt (0 + ) = 1 C i C (0 + ) =- I s 2 C 3 For your convenience the circuit after the switch closes at time t = 0 is redrawn below. Use the same reference configurations as in the original figure. The rest of the problem refers to the situation after time 0. (h) Writing an appropriate KVL equation, express i 1 ( t ) in terms of v C ( t ) (and the parameters I s , R , L , and C if needed) for t + . (2 pts) Ri 1 ( t ) + v C ( t ) = Ri 2 ( t ) Ri 1 ( t ) + v C ( t ) = R ( I s- i 1 ( t )) 2 Ri 1 ( t ) =- v C ( t ) + RI s i 1 ( t ) =- v C ( t ) / 2 R + I s / 2 (i) Using KCL at node A , express i L ( t ) in terms of v C ( t ) and the parameters for t + . (2 pts) i L ( t ) + i C ( t ) = i 1 ( t ) i L ( t ) =- 1 C dv C dt ( t ) + i 1 ( t ) i L ( t ) =- C dv C dt ( t )- v C ( t ) 2 R + I s 2 (j) Write down a differential equation that...
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ee40sp08_mt2_solns - EE 40: Introduction to Microelectronic...

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