96_F_exam - are 18 numbered problems with one single sheet...

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Unformatted text preview: are 18 numbered problems with one single sheet per problem statement except for problems 2 and 12 which are on two pages. Including the cover sheet this gives you 21 pages. No blank pages should be in your set. 2. This examination is closed book, closed notes. No reference materials are allowed on your desk. A calculator is permitted. 4. Your examination Code Number MUST APPEAR ON EVERY SHEET. This includes (i) the problem statement sheets, (ii) additional worksheets, and (iii) the examination cover page. DO NOT write your name on any of the materials. 5. Under the rules of the examination, you must choose 3 problems to be handed in for grading. These should be separated from the rest of the examination, and your solution should be attached and stapled directly to the appropriate problem statement. 6. The examination lasts 4 hours starting at 9:30 am, and will and promptly at 1:30 pm. 7.. When you hand in your examination, please follow the procedure below: (a) Check to ensure that your examination Code Number is on EVERY sheet. (b) Separate the eight problems you want to submit for grading. Attach each solution to the problem statement, and place the problems in proper order. (c) Take this cover sheet and attach the remaining 10 (unworked) problems to it in the proper order. Again your examination Code Number should be on every sheet (even though you did not work these problems). (d) Using the list below, CIRCLE the problem numbers you are handing in for grading. CROSS OUT the problem numbers which you do not want graded. (e) Hand in the two sets, i.e., the 8 problems for grading and the 10 unworked problems. Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 1? Problem 18 nw—H._.__-____ ._ . . _.._ . . . . _ _—...___._._. = 1000 were con- SuPpose that a shunt Open-circuited stub of length lA and impedance Zo nected at the source 2 = —l, as illustrated. (d) What should be the stub length [A (in wavelengths A) for maximum load dissipation as in part (c)? I A until-CH!“ ——-—nr—mmmmuq- .. _ . . __ __._.__..__._—..-..-._-_ _ . .._ -_ -— ..."... _ . . ... _ _ Problem 3 Code Numb er: A certain 6-pole, Y-connected‘lr 3 phase, synchronous generator is rated at, 60 Hz, 50 MIA, and 220 V line-line. Assume the machine is magnetically linear (no saturation). Neglect the stator resistance. The following table list the results of an open circuit and short circuit test on the machine. Field grotorz Current {A} ngn Circuit Stator Short Circuit Stator Line Voltage {V line-line} Current {A Z phase} 2 88 42 5 220 105 7 308 147 Assume that the stator of the generator is connected to an ideal 220 V line-line three phase voltage source. Also assume the generator is operating at rated stator current and unity power factor. (a) Determine the synchronous reactance, Xi, of the generator. (b) Determine the power angle, 5. (This is the angle between the field-induced voltage and the terminal voltage. It is sometimes referred to as the “torque angle”) (c) Determine the field (rotor) current. - -- I 4— m‘imI-m mil-J“ __- _I— la.q*F_WHw-—_IF.._..1__.... ... - -- -- - - -- -— -——-——1—-—-—-—-—-—n---—--—-I-—I--n-n-nr nun—rum _.-.- _ .-. . Problem 4 Figure 1: Consider a simple, balanced three phase power system, consisting of a generator, trans- mission line and load. Phase ‘a’ of the system is shown in Figure 1. The transformers in the figure are ideal. The nominal line-to-line voltages in the three sections are: l. Generator: 20 Kv 2. Transmission System: 300 Kv. 3. Load: 150 Kv. The load is 10 + if: MVA. 1. (4) If the current I flowing into the load is I = 115.47 — j74.04 amps, what is the line-to-neutra] voltage at the terminals of the load? 2.. (3) Determine the line-to-neutral voltage at the generator terminals. 3. (3) It is desired to make the voltage magnitude at the load equal to its nominal value by installing one of two possible ‘devica’ in parallel with the load. The two devices are: l) a bank of inductors and 2) a bank of capacitors. Which should you choose and why? Load Problem 5 Code Number: The op amp is ideal. R3 200K R] V I l a: 10K V0 R2 V2°’—_MA’ 10K R4 v =v -v 210K D 1 2 7 VC = 0..,5(v1 -v2) (a). Determine numerical values for the difference mode voltage gain, AD, and the common mode voltage gain, Ac, taken to the V0 output node. (e). Find the input resistance seen by an input signal source applied at V2 . __u.n_-.-_-.uuu-.nm u.- Problem 7 You may need the following constants: = hc/A, or, EPh (EN) = 1242/1 (pm) q = 1.6x10'19 (C) H“ = 0.0259 eV Eph = 8500 cmz/V-s; up = 400 cmz/V-s For GaAs: 13‘ = 1.43 eV at room temperature Mn 11,. = 20:10" cm'3 Problem 8 Code Numb er: Find a general expression for the minimum conductivity of a semiconductor sample in cthbnum 1n terms of the materials carrier mobilities. and intrinsic concentration. Assume bOth carrier types are present. Problem 9 Code Number: Part C: Implement a 2 to 1 MUX below using only three 2-input NAND gates and one inverter. Label the inputs and output. Problem 1 1 Code Number: (0.) Consider the following sequence of memory references from a 430 word program. The memory references are to words numbered from 0-429. ll, 12. 170. 150, 360, 423. 185, 245, 418, 300, 200, 100 Give the page reference string assuming a page size of 100 words, assuming pages are num- bered beginning with 0. Determine the page fault rate for this page reference string, assuming 200 words of primary memory are available to the program and a LRU page replacement algorithm is used. What will the above page fault rate be if a FIFO page replacement algorithm is used instead ? (to) Consider a paging system with 4 Megabytes of secondary storage and average access and transfer time of 6 milliseconds per byte. A paged core memory of size 262,144 bytes is used with 3 microseconds access time. If we want our paging system to look to the user like a memory of 4 Megabytes with a 7 microsecond average access time, what percentage of accesses must occur without a page fault ‘2 Problem 12 (Page 1 of 2) Code Number: Consider a processor with 256 Mbyte main memory, a 4 Gbyte virtual address space and 32 Kbyte pages. The processor has a 64 Kbth direct mapped level 1 cache with 128 byte lines and a 512 Kbyte 4-way set associative level 2 cache with 256 byte lines. (a) Show the breakdown of the virtual address and physical address, i.e., the total number of bits in the address, and the size and location of the fields used to address pages and offsets within a page. Virtual Address Physical Address 5:: . (b) Show the breakdown of the physical address as interpreted by the level 1 cache and level 2 cache. Identify the size and location of the fields of the physical address that are used to address the cache. Make sure you identify the size of each field as well as the total size of the address. Level 1 Cache Level 2 Cache — — (c) How many entries are there in the page table? ((1) What function does the translation lookaside buffer perform? Code Number: Problem 12 (Page 2 of 2) (e) A computer system has 128 Kbyte of main memory and an 8 Kbyte set-associative cache. The cache line size is 512 bytes, and there are 4 lines/set. The following shows the state of cessed: OB 840, 16E54 +— Top of LRU Stack SetO Bottom of LRU Stack Problem 13 Code Number: A Laplace problem: Let. 13(t) be the solution to where (1(1)) and r(D) are polynomials in the differential operator D = 5—1, with real coeffi- cients and the degree of r is less than the degree of a. Show that for some real 0 the weighted energy 5 = [in flow“ dt can be computed as a complex integral \a'here Explain all st-t‘ns involved. In particular. what restrictions, if an}: must be imposed on a? Problem 1 5 Code Number: Consider the joint probability density function _ cyrr I>y,OSIS2,OSySI fxflay) —{ 0 otherwise ' Compute P(X > IIX + Y < 2). _..—....._.._..._._— _ _ . .._— __ . ' ' ' —l- I —.——|--u |.. .._u_ ______ ___ ____ _____ . _____._.____-.-.... . . . . . ..--__....._ Problem 16 Code Number: A linear, time-invariant system Hus) is constructed out of several components as shown below. The frequency response of the filter H1(w) is H1(“’)={ 0, Ian] > 4001.- where To = 1/800 seconds. (3) Find H (in), the frequency reSponse of the overall system. Express your answer in the form H (w) = A(w)e’9l‘l, where AM) and 9(w) are real functions of w. (b) What is the delay of the overall system? (4:) Plot the magnitude and phase of H (in). (d) Find and plot h(t), the impulse response of the overall system. (e) Find the output y(t) if the input is I(t) = 1 + cos(20017t) + sin(600n't) + 6(t — 7). Problem 1 7 Code Number: Consider a “thick” biconvex lens in air as shown in the figure below. The lens radii of curvature are R; = 20cm and R2 = 10cm (both in magnitude) and its refractive index is 1.5. The thickness of the lens is 5 cm. An object is located 8cm to the left of the first surface of the lens. (a) [75%] Using the matrix approach calculate the image distance as measured from the second surface (point V2). In addition, find the image magnification. _ (b) [25%] Now treat this lens as a “thin” lens. Applying all the “thin” lens equations calculate the position of the image and its magnification. Now all distances should be measured from the center of the lens. Useful Equations Translation Matrix m. 1 0 n1 1 n1 (n2 ll‘fi' g; “Bl-G Problem 1 8 Code Number: Michelson Interferometer Ifa gas laser is Operated single-line, single-mode, the output has an extremely narrow spectral bandwidth, AA, that is determined by the Q of the laser resonator cavity. Although A}. is very small, the actual wavelength, A, of the output can drift significantly as the size of the resonator cavity changes with time. This drift can be observed with the help of a Michelson interferometer set up as indicated in the figure. Part of the laser beam, entering from the left, is Split by the beamsplitter BS and then recombined at the observation screen via the two mirrors M1 and M2. Ifthe emerging beams propagate in exactly the same directions and the distances L1 and 1,2 are adjusted so as to equalize the optical path lengths, the beams interfere at the observation screen to produce a pright patch of light (constructive interference). lfthe optic] paths are unequal, the patch of light might be dim or even totally dark (complete destructive interference). Ifthe drift in laser wavelength is to be observed, the distances L1 and L; are made significantly different. As the wavelength changes, the interference conditions at the observation screen change from constructive to destructive and so on, yielding an observation-screen irradiance vs wavelength plot similar to the one shown. Assume that the mirror positions are adjusted such that L1 - L2 = 10 cm and that the laser WW M2 CD (I: I I k__ F I | I l l." I I I | m H “E _ I A ' Irradiance at observation screen gbsewatlon as wavelength 3. drifts about its Green nominal value Operates at a nominal output wavelength of A = 514.5 nm. For what change in wavelength, 6)., does the observed output irradiance change fiom bright to dark to bright again? ...
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96_F_exam - are 18 numbered problems with one single sheet...

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