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Unformatted text preview: E83 40, Fall 2008
Prof. ChangHasnain
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").
doublesided 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‘IJQﬂ 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‘dOrder 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 (highpass, (a) lowpass bandpass, bandreject (notch) filter} . “h H’L‘I
Had); ﬁnsvats ELL ‘9 Us ‘VLT MC
mo)— RL ' w Q’— :
“"—'——;1—”_1 * g4.” AF/C._i/‘:E
£L+Kr+drv2wtz 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 Lowpass 0 Highpass ﬂ Bandpass O Bandrej 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 lowpass 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 ndpass 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 ndreject (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‘rf 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 Lowpass Highpass O Bandpass O Bandreject (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, passband
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 ...
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This note was uploaded on 10/24/2009 for the course EE 40 taught by Professor Changhasnain during the Fall '07 term at University of California, Berkeley.
 Fall '07
 ChangHasnain

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