Layout - Introduction to Microelectronic Circuits - Solved Exam, Exams of Microelectronic Circuits

Download Layout - Introduction to Microelectronic Circuits - Solved Exam and more Exams Microelectronic Circuits in PDF only on Docsity! UC BERKELEY EECS 40, Spring 2007 Page 1 of 8 EECS 40, Spring 2007 Prof. Chang-Hasnain Test #2 October 8, 2007 Total Time Allotted: 50 minutes Total Points: 100 1. This is a closed book exam. However, you are allowed to bring one page (8.5” x 11”), single-sided notes. 2. No electronic devices, i.e. calculators, cell phones, computers, etc. 3. SHOW all the steps on the exam. Answers without steps will be given only a small percentage of credits. Partial credits will be given if you have proper steps but no final answers. 4. Draw BOXES around your final answers. 5. Remember to put down units. 1 point will be taken off per missed unit. Last (Family) Name:_____________________________________________________ First Name: ____________________________________________________________ Student ID: ___________________________ LAB Session : ________________ Signature: _____________________________________________________________ Score: Problem 1 (16 pts) Problem 2 (28 pts): Problem 3 (56 pts): Total UC BERKELEY EECS 40, Spring 2007 Page 2 of 8 1. (16 pts) Phasors and complex numbers a) (6 pts) Convert V !" = V to phasor notation. Both polar and exponential form are acceptable. V !" = 4 2 ! j8 2 ! j2 2 = 4 2(1! j 2) 2(1! j 2) = 2 2"0 V (pink) V !" = 4 2 + j8 2 + j2 2 = 4 2(1+ j 2) 2(1+ j 2) = 2 2!0 V (white) V !" = 4 2 ! j8 2 ! j2 2 = 4 2(1! 2) 2(1! j 2) = 2 2"0 V (yellow) b) (3 pts) What is v(t), in cosinusoidal form? Assume frequency is ω. v(t) = 2 2 cos(!t) V (all) c) (4 pts) Convert V 2 !"! V to phasor notation. Both polar and exponential form are acceptable. 2 2 1 90 j V j e ! = = = " !" V (yellow and pink) V !" 2 = ! j = e ! j " 2 = 1#! 90 V (white) d) (3 pts) What is v2(t), in cosinusoidal form? Assume frequency is ω. 2 ( ) cos( ) 2 v t t ! "= + V (yellow and pink) v 2 (t) = cos(!t " # 2 ) V (white) UC BERKELEY EECS 40, Spring 2007 Page 5 of 8 3. (56 pts) We have a circuit with R, L, C and v(t) as an input. (a) (16 pts) If vC(t) is the voltage across the capacitor C, we can formulate the 2nd order circuit as follows. What are A,B, and f(t)? Express them in terms of R,L,C and v(t). A = R L B = 1 LC f (t) = v(t) LC (b) (5 pts) The undamped resonance frequency 0 is 0=10 4 Hz and L is 10mH, what is the value of C? ! o = 1 LC C = 1 ! o 2 L = 1 (104 rad / s)2(.01H ) = 10"6 F (c) (10 pts) By adding another 300 Ohm resistor in parallel to the R, connecting at points A and B, see Figure below, we find the circuit is critically damped. What is the value of R? (NOTE: If you did not get the value for C from part b, full credit awarded for solution including C as a variable.) 2 2 ( ) ( ) ( ) ( )c c c d v t dv t A Bv t f t dt dt + + = A B 300Ω A B UC BERKELEY EECS 40, Spring 2007 Page 6 of 8 ! = 1 Thus: " =# o R eq 2L = 104 rad / s R eq = 2L(104 rad / s) = 2(.01H )(104 rad / s) = 200$ R eq = R(300) R + 300 = 200$ R = 2 3 (R + 300) R = 600$ (d) (5 pts) Is the original circuit (without the 300 Ohm parallel resistor, see Figure below) overdamped or underdamped? UC BERKELEY EECS 40, Spring 2007 Page 7 of 8 ! = " # o Thus: " = R 2L = 600 2(.01H ) = 30000 # o = 104 rad / s ! = 3 Thus the original circuit is overdamped. Intuitively, the original circuit has a higher resistance, thus more energy is lost across the resistor, damping the circuit more than the critically damped case. (e) (20 pts) We change the configuration of L and C to be in parallel as shown below, with the original values for R, L and C – the values you got from parts a- c. What is the resonance frequency ω0? What is the damping ratio ? Is this circuit under-, critically, or over- damped? (NOTE: If you did not get the values of RLC from parts a-c, you will get full credit if you can give all possible if-then’s.) If a Thevenin to Norton conversion is performed on the voltage source and resistor, it becomes apparent that this is a parallel RLC circuit. We then use the equations for a parallel RLC circuit: !