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Unformatted text preview: ECE Pb...
Preliminary Examination Fall 2000 PhD. Preliminary Examination Code Number:
Fall 2000 Instructions: 1. Please check to ensure that you have a complete exam booklet. There are 18 numbered problems, with Problem 10 occupying 2 pages and the rest one page each. Including the
cover sheet, you should have 20 pages. There should be no blank pages in your booklet. 2. The examination is closed book and closed notes. No reference material is allowed at
your desk. A calculator is permitted. 3. You may work a problem directly on the problem statement (if there is room) or on blank sheets of paper available from the exam proctor. Do not write on the back side of any
sheet 4. Your examination Code Number MUST APPEAR ON EVERY SHEET. This includes this cover sheet, the problem statement sheets, and any additional worksheets you turn in.
DO NOT write your name on any of these sheets. WRITE LEGIBLY ll! 5. Under the rules of the examination, you must choose 8 problems to be handed in for grading. Each problem to be graded should be separated from the rest of'the materials,
stapled to the associated worksheets, and placed on top of the apprOpriate envelope in the front of the exam room. DO NOT TURN IN ANY SHEETS FOR THE OTHER 10 l!
6. The examination lasts 4 hours. from 9:30 AM to 1:30 PM. 7. When you hand in the exam, (a) Check to see that your Code Number is on EVERY sheet.
(b) Separate the 8 problems to be graded as explained above. (c) On the section at the bottom of this page, CIRCLE the problem numbers that you
are turning in for grading.
(d) Turn in this cover sheet (containing your Code Number) and the 8 problems to be (e) All other material is to be placed in the discard box at the front of the room. You
are not allowed to take any of the exam booklet pages from the room! 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 17 Problem 13 2.5 nanoseconds. You may assume that the cable is not made from any magnetic 6: e. b. Given that the cable is marked, “Characteristic impedance = 50 ohms,” ﬁnd th ll l 1nductance and capacxtance (per umt length) of the cable. (Assume the cable is  F/m PROBLEM 2 Code Number: “ Image Theory and Capacitance per unit length PROBLEM 3 Code Number: A 20 kV, 60 Hz, 100 MVA, 2pole, 3phase synchronous turbogenerator has a synchronous
reactance 4 Ohms/phase. It is synchronized to the 20 kV network, following which the active
power output is raised to 50 MW, and rotor current adjusted so that the machine generates no
reactive power (Q = 0). Calculate the percentage increase, or decrease of the rotor current
compared with its value during synchronization. Neglect the effects of saturation. PROBLEM 4 Code Number: * A 11,000/2,200 V, 250 kVA, 60 Hz, single phase transformer has the following parameters:
Rm. = 1.3 Ohms, RI, = 0.05 Ohms, Rem) = 2.4 kOhms, X1“. = 4.5 Ohms, le = 0.16 Ohms,
Xmaw, = 0.8 kOhms, where subscript "iv" and "hv" refer to the low and high voltage sides of
the transformer, while “C(lv)" refers to the equivalent parameters of the core referred to the low voltage side of the transformer. The high voltage terminals of the transformer are
connected to a voltage source equal to rated voltage of the transformer. a) Determine the no load current. b) If the low voltage terminals are shorted, determine the supply voltage
required to pass the rated current through the short circuit. PROBLEM 5. Code Number: Refer to the following small—signal equivalent circuit for a common source FET ampliﬁer for parts
(a) through (e). a. Calculate the midband voltage gain A“, in dB. b. Calculate the upper cutoff frequency L. c. Sketch the Bode plot of [Arldg labeling all pole frequencies and asymptotic slopes. d. Sketch the Bode plot of 1A,, labeling all pole frequencies and asymptotic values. e. Calculate the approximate ﬁ'equency at which the voltage gain is unity: [Atlas = 0 dB. Circuit Element Value PROBLEM 6 Code Number: “ a) Determine the Thevenin equivalent circuit for the following circuit: R}: R4:
2m 3V 2.5142
0 b R2: R3: T
“‘9 1m T“ b) What is the value of the load resistor that would maximize the power delivered by the circuit to the load when placed between the output terminals (a) and (b) in the ﬁgure
above? PROBLEM 7 Code Number: “It Use the following constants in your calculations: q=1.6x10"9 C, c=3x108 m/s, h=6.63x10'34 Js,
kT/q=0.026 V. Si material parameters to use: n1: 101°cm'3, un=l360 cmz/Vs, up=460 cmst, Eg=1.ll eV. An ntype silicon cube (2 mm on a side) has 2 mV applied between two Opposing faces. A
current of 3 mA results from this applied voltage. (a) What is the majority canier and majority carrier concentration? (b) What is the minority carrier and minority carrier concentration?
(c) What is the hole current? (d) What is the electron current?
(e) What is the resistance of this sample? PROBLEM 3 Code Number: '_—l———l—_. Use the following constants in your calculations: q=1.6x10"'9 C, c=3x108 m/s,
h=6.63x10'34 Js, kT/q=0.026 v. Si material parameters to use: ni= 10'°cm'3, un=l360 mst, up=460 cmst, Eg=l .11
eV, In: 1,, =100 us. A Si pn junction has doping on the p side of the junction that is 4 times that on the 11 side
of the junction. diode. Label the x and y axes intercept values using combinations of the following variables only: q, Nd, xn. Note that xl1 is the interface between the n quasineutral
region and the depletion region. (b) Draw a graph of the equihbnum electric ﬁeld as a ﬁmction of position for this diode. or decreased in comparison to the equilibrium values.
(t) Draw the band diagram for this diode under a forward bias of 0.4 V, indicating where
Evp, Em, Eip, Bin, Fm Fp, Em, ECWVM , and V.I (the applied bias) appear in the diagram.
(g) Draw a graph of the charge density as a ﬁmction of position for this diode under a
reverse bias of 1.4 V. Do not label the axes values, but indicate which values have (i) Draw the band diagram for this device under a reverse bias of 1.4 V, indicating where
Em Em, Eip, Bin, Fm Fp, Em, ECWVM , and V.ll (the applied bias) appear in the diagram. PROBLEM 9 Code Number: LW R2, 0x0100
ADD R3, R2, R2
AND R4, R2, R3
SLL R5, R4, 1
XOR R6, R5, R5
SUB R6, R2, R0
BEQ R5, R2, LABEL1
SUB R6, R0, R2
LABEL1: SW R6, 0x0200
Aﬁer execution,
R2 = 0x (hexadecimal) R3 = Ox (hexadecimal) R4 = 0x (hexadecimal)
R5 = 0x (hexadecimal)
Memory Location 0x0200 contains 0x (hexadecimal) MIPS Instruction Meaning ADD Rd, Rs, Rt  Rd = Rs + Rt AND Rd, Rs, Rt  Rd = Rs bitwise logical AND I BEQ Rs, Rt, address  Branch to address, only if Rs = Rt LW Rd, address  LOAD  Rd gets contents of memory at address
SLL Rd, Rs, count  Shift left logical (use Oﬁll) by count bits SUB Rd, Rs, Rt  Rd = Rs  Rt SW Rd, address  STORE  memory at address gets contents of Rd XOR Rd, Rs, Rt  Rd = Rs bitwise logical XOR Rt PROBLEM 10 ' Code Number: We wish to design a 2input. 2output sequence detector which produces an output ‘1' everytime the
sequence 0101 is detected and an output '0' at all other times. For example. when the input sequence is 010101 . the corresponding output sequence is 000101 .
The state transition map for the sequence detector is given below where A.B.C,D represent the states of the detector and XfY on the transition arrow represent the inputloutput. Using state assignments A=00.
3:01. C=10 and D=11: 0/0 PROBLEM 10, cont. Code Number: * flops with a period of 40ns and IN is the input to the sequence detector. Assume that the delay of each flip ﬂop is 10ns, the flip flops are initially reset to ‘0” (01 = 0, 00 = 0) and the basic gates do not have any delays. PROBLEM I 1 Consider a virtual memory management unit for an Acme 9000 micrOprocessor. Virtual memory
is paged. and byte addressable, with 326B (gigabytes) of physical memory. and 2KB (kilobyte)
pages. Vinual addresses are 40 bits. (3) (4 pts) Considering only one process, how many bytes (maximum) are necessary for a single level page table. Be sure to explain your answer. Round up to an integral number of bytes. Assume the same number of bits sufﬁce to locate a page in or out
of physical memory. (b) (3 pts) Suppose you decide to page the page table with a two level scheme. The ﬁrst level
(root) table would be pinned in memory. How large in bytes (maximum) would the root table be? PROBLEM 12 Code Number: Use basic logic gates such as ANDS. NAN Ds. 0R5, NORS (no latches or ﬂipleps) to complete the design
of an asynchronous sequential network that implements the primitive flow table below. The circuit has
two inputs (A and B) and one output (Z). There is no “clock” input. Critical races must be avoided and the logic should be minimized. Please start with a merger diagram. {ABE Row# £01 to) (u) LL01 .2.
1 1 2 3 0
2 1 2 4 o
3 1 5 3 0
4 6 4 3 1
5 6 5 3 0
6 1 6 5 0 PROBLEM 13 Code Number: Consider the block diagram given below. (3) Find the range of K for stability. (to) Find the steady—state error to a command r(t) = u(t) (where u(t) is a unit step).
(0) Identify the kind of controller that is being used in this problem.
(d) Why is this type of controller generally used? (e) Give the value of gain K that yields damping ratio of l; = 0.707 and damped natural frequency of
(0.. = 5.4. Code Number: in x(t) . Ya) (a) For R = 2.0, ﬁnd the Laplace transfer function ﬁrm the input x(t) to the output y(t).
(b) Find the steady state response to x(t)= 1+ 4cos(2t) + 2cos(10tl) for R = 20.
(c) Sketch the magnitude part of the Bode plot for this circuit when R = “Pﬂ'wlﬂ PROBLEM 15 Code Number: m Consider the following system for discretetime ﬁltering of a continuoustime signal: ——IIIIIIr————_——I—____———_——— :r:(t) ; CIdea:D yln] DldealC : 9(1)
to to
: Converter Converter :
§_ Ts — l/fs T. — 1/1; i For this problem, assume that the sampling rates of the C—to—D and D—to—C converters are f5 = 5000 Hz, and that the input signal is periodic so that it can be written as a. Fourier
Series in the following form: (3.) Determine whether or not the input signal will be “aliased” when it is sampled. Give
a reason to justify your answer. (b) If the impulse response of the LTI system is h[n] = 5[n] + 5[n — 5], determine the
frequency response of the discretetime LTI system. In addition, make a plot of the
magnitude response over an appropriate range of frequencies. Label the plot carefully
to show all essential features of the magnitude response. (c) If the LTI system has a system function given by the z—transform:
H (z) = 1 + 2‘5 determine the Fourier Series of the output signal, y(t), when the input is :r(t) above.
In other words, if give the numerical values of Q the Fourier Series coefﬁcients {bk}, as well as the
fundamental frequency (we). PROBLEM 16 Code Number: 'Il—III— The following analog communication system is used. If m(t) = 2Wsinc(2Wt) , then ﬁnd an Ideal
Lowpass Filter Cut0% 2W Hz Ideal Channel
v0) 2 cos(7rWt) 2 005(71'Wt) PROBLEM 17 Code Number: A glass isosceles prism of refractive index n has an apex angle qb as shown. With the prism in air,
light enters the front surface at angle on to the normal, where on < ¢. The light exits the back surface at angle 04. a. Derive an expression for :14 in terms of a1, qb, n, and no other variables. Useful formulas may
include Snell‘s law, 1:; sin 61 = 112 sin 92, and the identity, sin(a :l: b) = sin 0. cos b i cos asin b. b. Using your result of part a, or simply by using your knowledge of how refractive index varies
with wavelength, will (14 increase or decrease as the wavelength is increased? Explain. PROBLEM 18 Code Number: The 1’ number of a lens is deﬁned as the ratio of the focal length to the lens diameter. Suppose we
have a diffractionlimited lens of a known f number, and a point source at inﬁnity is to be imaged
by this lens. Derive an expression for the radius of the image of the point source that is formed by
the lens. Your result should be only in terms of the f number and the wavelength, A. Possibly useful formula: Airy disk halfangle: A6", = 1.22A/d ...
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 Virtual memory, code number

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