MT2_Version_A - E83 40, Fall 2008 Prof. Chang-Hasnain Test...

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: E83 40, Fall 2008 Prof. Chang-Hasnain Test #2 Version A 10:10 am — 11:00 am, Monday October 27. 2008 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"). double-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. Remember to put down units. Points will be taken off for missed unit. Last (Family) Name: First Name: Student ID: Discussion Session: Signature: Score: Problem 2 (24 pts) Problem 3 (16 pts) — Page 1 of9 Problem 1: Transient Response of RLC circuits (40 pts) Consider the circuit shown below A 1 Ja a) Derive the differential equation for i._(t) (20 pts) C .._' _-: z 01% (l KCLOA I I; o ) Ommiiqr. (I) 2 avg /<‘ (I? + 5/ L; (3) a 9Q“ (/15 J (1i chf—"z IHZ‘L :- + gear rang {‘33 I ,QI—i; +[CL"L : LC, dzf L W— Page 2 019 b) Let L = 1 H, C = 1/3 F, R = 4 Q, I = 2A. What is the undamped resonant frequency 010? It is ok to express your answer as a square root. (5 pts) .zh __L_. CJO"LC /' I (an: __ r. “C /UC‘/3) {Yi‘ wongflfe” oft/3111:. U)— (51‘ c) What is the damping ratio Q? Is this system over-, critically, or under- damped? Again, it is ok to have square roots in your answer. (10 pts) _ r if¢¢=>¢ fie,“ >{ ? , _ floverdamped O critically damped O underdamped d) Write down the general form of the solution. Give numerical values for the forced response . You don’t need to solve for any other constant (K1, K2, 51,2 etc.) (5 pts) \SD/U‘IJ-Qfl OVPfC/CJFEZEC')? (Cis'L/J/l '1 - :3; . L01) 2 K; as” +Kz 6- +390.) 1. ' - r.- -. I - 1 Z 2‘ or: .. ._ .r 1.: .C 4 9 aw I La] (3 $103117 KYLE—{6. “g LL- h alf- ‘* O '9 LC Page 3 of9 Problem 2: I‘d-Order Circuit (24 points) Consider the circuit shown below Using complex impedances, derive the transfer function H(w)=Vom/V.,, as a function of R5, C, L and RL. (12 pts) Bring your answer into one of the standard forms known from lecture (high-pass, (a) low-pass band-pass, band-reject (notch) filter} . “h H’L‘I Had); fins-vats ELL ‘9 Us ‘VLT MC mo)— RL ' w Q’— : “"-—'-——;1—”_1 *- g4.” AF/C._i/‘:E £L+Kr+drv2-wtz v’imjfiee I; u _I_ ELF LL, LU L Wit: “’bfi- K. ’61., RA‘I'R; HKCU)‘: ‘~—- Q) 31—— : - fl+fl+'_é“_‘~__l/ZI ;;/_W‘_ L 3 We re w» Hum/E: 1; I. /+' w 533 Page 4of9 (b) What type of filter does this circuit implement? (3 pts) 0 Low-pass 0 High-pass fl Band-pass O Band-rej ect (Notch) (c) Depending on your answer in part b), answer one of the following 3 questions ((i) — (iii)) {9 ptsl (i) If your answer in part b) is either high- or low-pass filter: Write down the break frequency mg, the slope of |H{w)2| in dB/decade for very small and very high frequencies respectively as well as the order of the filter. Page 5 of9 (ii) If your answer in part b) is ba nd-pass filter: Write down the resonance frequency mg, the quality factor Q of the filter as well as the slope of |H(w)2| in dB/decade for very small and very high frequencies. d8 slope (co<<) = =10 “fit. slope (a)>>) = 320 :9}, (iii) If your answer in part b) is ba nd-reject (notch) filter: Write down the resonance frequency (no, the quality factor Q of the filter as well as the values of lleFl in dB for very small and very high frequencies. Page 60f9 Problem 3: 1st Order Bode Plots (16 pts) Consider the circuit shown below Vin e Vout 3} Using compiex impedances, derive the transfer function H(m)=Vou[/Vi,. as a function of R and L(6 pts) / /_l w)“ {QTUWL U'I‘r-f HUM/L b) What is (:13 or 030 (depending on the transfer function you came up with in an of the system? (Give your answer again as a function of R and L) (2 pts) wOFJL UEWL R H/ WO'L Page7of9 c) What type of filter does this circuit implement? (2 pts) 0 Low-pass High-pass O Band-pass O Band-reject (Notch) d) Sketch the magnitude Bode plot on the graph below. Make sure you mark all important characteristics of your graph (important values of on, slopes, pass-band value). (6 pts) Be aware of the fact that the frequency axis is logarithmic frequency w (radianslsecl PageSofB Problem 4: Bode Plots (20 pts) Given is the following transfer function: K ()=—- M HIKE-£1 where K = 0.5 and Y = 100 in the graphs below sketch the amplitude and phase transfer functions for the two cases where x = 1 and x = 10. Make sure you clearly mark important characteristics (any slopes of magnitude response as well as magnitude and phase at w=Yl in your graphs and you clearly indicate any differences between the two cases. Be aware of the fact that the frequency axis is logarithmic. --6u_’r3 2010g[H(a))| *2 6 JG - 96:18 / {0 me 5000 iOJOOO Phase of H[w) [degrees] I [0 {00 {090 {0090 ‘J frequency w {radiansisec) Page 9 of 9 ...
View Full Document

This note was uploaded on 10/24/2009 for the course EE 40 taught by Professor Chang-hasnain during the Fall '07 term at University of California, Berkeley.

Page1 / 9

MT2_Version_A - E83 40, Fall 2008 Prof. Chang-Hasnain Test...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online