Prelim_exam_sol_sp01 - Copy

Prelim_exam_sol_sp01 - Copy - ECE Ph.D PRELIMINARY...

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Unformatted text preview: ECE Ph.D. PRELIMINARY EXAMINATION SOLUTIONS - SPRING 2001 <9. f iron of thickness 1). A current here no is the permeability of me and conductivity of... (a) Solve for A straight, long copper wire of radius a is covered with a layer 0 I flows in the wire. The copper has a permeability pm = no, w a vacuum, and a conductivity am. The iron has a permeability In terms of the total current I , solve for the current density J in each region. (b) the magnetic field intensity H in each region as a function of r. (c) Solve for the magnetic flux density B in each region. SpI/IVI'D ZDOl jaw .. E f .. 3—": : {ca (‘9‘:- ‘L r“ “T? (gram) j: "1 jca'fifié‘ # JFG‘ /~;/'/ 3“”; (ran-r5 J“??- => E ‘- “(CA1 (co 4" (51*5-1)G- '1) £92.— ...—\ u: QTWM Hco: Tcu‘TTI-L‘L it, H6 2D. ’3. '\_/ Preliminary Examination Problem: EM Area Scott Consider the time-domain reflectometer (TDR) system connected to the transmission line system shown below. The voltage V recorded by the TDR is also shown when the source voltage is a 64 V step. 21 and Z; are the characteristic impedances of the transmission lines and 2;, is the impedance of the load. The transit times 1:] and 1:; are the times required for a wave the travel the length of the transmission lines. Determine the impedances Z], 24, 2;, and the transit times I; and 1:2. T ONE QUESTION FROM EPTG FOR PhD PRELIM EXAM: MARCH 2001 A 230/115 volt, 60 Hz single phase transformer is rated at 100 kVA. The values of its parameters referred to the HV side are as follows: gc = 0.02 Siemens; bm = 0.0325 Siemens ; (d) Draw the cantilever form of the equivalent circuit of this transformer (the parallel branch is at the input to the circuit) using the HV side as the primary. Insert the parameter values into your circuit. (f) For the load condition in (1)) find the core loss, the resistance loss (or copper loss), and the efficiency of the transformer. SOLUTIONS (a) Draw the circuit (b) 1'2 (load current referred to primary side) = 75000/(108 x 2) = 347 amps Input voltage phasor = 216 + 347A25_8(0_01+ j0_06) = 228.25 +j 17.3 Input voltage magnitude = 228.9 volts Percentage regulation = 100(228.9 - 216)/2l6 = 6 % (c) Core loss = 228.9 x 228.9 x 0.02 = 1048 watts Copper loss = 347 x 347 x 0.01 = 1204 watts Total loss = 1048 + 1204 = 2252 watts Output power = 75000 x 0.8 = 60000 watts Efficiency = 100 x 60000/(60000 + 2252) = 96.3 % Solution to Problem 1: a) By KVL: vs— iR— v.3I = 0 2 e'i’lt u(t) — RC dvo/dt — v0 = 0 In standard form: vadt + Vo/t = 6"“It u(t) /1: where ‘E = RC = 500 usec b) Homogeneous solution: by integration dvaih/ + Vo/‘f :: 0 : VO’h = Aeqft 0) Particular solution: by method of undetermined coef. vo,p(t) = Be'm u(t) dvoah/dt = -oLBe"m (t>0) :> -orBe"""‘t + Be"It = e'm/‘t :> B(l-0Lt)=1 :> B=1/(1-oL1:)=2.O (1) Applying boundary condition v0(t=0) = 0: vo,h(0) + vo,p(0) = 0 :> A = -2.0 : Vo(t) = 6-1000t_ 26-20001] Solution to Problem 2: a) AV2=IAgm Rpllro = 1/2 -10mS- IOkQ “20 k0 = 33.3 vyK-T I -1, (6L) 37:3? a?) -—a=—9 : a. 10A 0 ( .43 > 3; (eBVVIE: I) (ea-'hqo Du! = 4'03 X10 fl _ n L '1)... D “fifmflfl Dh=“"§37>P=*P? - '1 m b @Nol—l % Lh'dbnr‘h 3 21,:- N =[0Joo )(Jgfio) (169%)L @360 “Win-S [0.52.4.0 + 0L £2.03XI5159) ] Elggomw.5)(o_ouv) (lap-ysyy‘ ('4) [Ema gigofilyh/ r3 Problem 9a A B ) c I - . F D Add mixed logic notation (separate function from implementation!) A B c ) - - F o Convert all gates to OR gates A . B . c , I - * F o * . Add inverters (“s above match all unmatched lines and bubbles) A >. D ,4. >. -— Soil/find?” Consider the following set of processes with the CPU burst times and arrival times given / in milliseconds. Process CPU-burst Arrival time P1 9 0 P2 4 2 P3 2 3 P4 6 5 P1 P2 P3 P4 9 4 2 6 Tput thme O 9 13 15 21 P1 9 O O 0 0 9-0= 0-0=O P2 4 O O O 13 -2=1 1 9-2=7 P3 2 2 0 O 15-3=12 13-3=10 P4 6 6 6 O 21-5=16 15-5=10 43/4=12 27/ =6.75 P1 P3 P2 P4 9 2 4 6 Tput Wtime O 9 11 15 21 P1 9 O 0 O 0 9-0=9 0-0=0 P2 4 4 0 0 15-2=13 1 l-2=9 P3 2 0 0 O 11-3=3 9-3=6 P4 6 6 6 O 21-5=l6 15-5=10 46/4=11 S 25/4=6.25 P1 P2 P3 P2 P4 P1 2 l 2 3 6 7 Tput thme 0 2 3 5 8 14 21 . P1 9 7 7 7 7 7 0 21-0=21 14-2=12 P2 4 3 3 0 o 0 3—2= 5-3=2 From P3 2 O 0 0 0 5-3= 3-3= P4 6 6 O 0 14-5= 8-5= SOLMT‘IOA/ O // Computer Engineering Prelim Problem Consider a 2-way set-associative write-through cache with 4-word blocks containing 32 words in total. For the following sequence of hexadecimal word addresses, label each reference a hit or miss and show the final contents of the cache. Assume the cache is initially empty and LRU replacement is used. Assume that the data stored in each memory location is equal to the location’s word address, i.e. location 1A contains data 1A, etc. 1A, C3, A9, 13, 55, F0, 1C, 32, 3A, 54, E3, Fl tau-$5 M1951 hH' I5“ M's-s mini miss MW5N+ nits MS '3 B I __ 3 1:.$(T\(HKGI\ - HKR -.-.- 2,... = A gen 9 E35 ‘+ KP “LA-rt K = A OSA 1+K|R JKIR E'Iq -'_‘-'.-_- zv‘jOzfi) {E 1i r’7+/f I“: 5 E M "‘ 6’ __....,___ O :LlrjflHJJJ *(7 *7/37) /——g"7' ' F'— fl Z;7'/o/T J I 'F " “I . J yf?/r?¢ : [email protected] I'éCIFC’ZJ x i L J ! L! {I Ha. I". r i! JZD‘ - € r #6 9ylfi A/f” "LC; / “‘3' {wawwj ...a r Cf?" ' 61/ 6’42” 2 /v--* 62,: I ’ : 2 7‘9???" ZULU" F '— rh / I '"' --- c, KW’J ___. Ire/0 A a * r M”) wsCZWé az/oa) /§"L%WW“¢ 2b 1 f 4' fl/I’S’Jzkrijr/corim/z .- 1 61/ r " (I - . 1 x"; ’1 H A f" E/d‘i/ :. J .I __ 0 is I'L— L1, : 30 fat/Qt: /—€rl 6? Consider the symmetric doublet (two element) lens shown below, with surface radii as specified. The element spacing is d, and each element has refractive index n = 1.5. Optics and Photonics b. Determine an expression for the focal length of the doublet in terms of the element focal lengths and d. Use symbols for the element focal lengths if the part a result was not found. l l _ t 1 “Cl ref? Ex 1:1. '9 L SL2: : PL :1" [600 in CW5 c. At what spacing, d, will the net focal length be equal to that of the front element (and perhaps that of the back element as well)? (Q:-(\ '2: HOCW ...
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This note was uploaded on 09/23/2010 for the course ECE 0000 taught by Professor Ddaa during the Fall '10 term at Georgia Tech.

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Prelim_exam_sol_sp01 - Copy - ECE Ph.D PRELIMINARY...

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