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Unformatted text preview: ECE PILD. PRELIMINARY EXAMINATION
SPRING 2001 pm = no, where no is the permeability of a vacuum, an a permeability We and conductivity Ufe. (a) In terms of the total current I sol
current density J in each region. ( as a function of r. (c) Solve for the magnetic ﬂux density B in each region. Code Number: shown below. The voltage V recorded by the TDR is shown for a source voltage VS that ZL is the impedance of the load. The transit times “[1 and 1 wave to travel the are the characteristic impedances of the transmission lines, and a length of transmission line 1 and 2, respectively. Determine the
impedances Z], 23, and _ZL_and the transit times 1'1 and 1:2. 2. = o
22 = (2
2L = Q
1'] "—' HS
12 = ns gc = 0.02 Siemens; bm = 0.0325 Siemens (3) 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. (b) Find the magnitude of the primary input voltage and the percentage voltage regulation when the transformer is delivering 75 kVA at a voltage of 108 volts to a load which has a power factor of
0.8 lagging. (c) For the load condition in (b) ﬁnd the core loss, the resistance loss (or copper loss), and the
efﬁciency of the transformer. PROBLEM 4 Code Number: mamon I'.'otor Assume ideal voltage source CABLE:
Per phase (positive sequence) impedance: 0.69+j0.69 ohms Power Rating: 500 kVA Voltage rating: 480 Volts, Line to Line Per Phase Stator resistance: 0.0046 ohms Per Phase Rotor resistance: 0.0092 ohms referred to stator
Per Phase Stator leakage reactance: 0.0138 ohms Per Phase Rotor leakage reactance: 0.0184 ohms referred to stator
Core loss, magnetizing reactance: neglect PROBLEM 5 Code Number: Fig. 2 a) (2 pts) Derive the differential equation that governs the behavior of v00), equating
the time constant to circuit element values. b) (2 pts) Determine the general form of the homogeneous (natural response)
solution to the above differential equation. the circuit with v50) = e'm no), where the decay constant of the source is
a=1000 sec". d) (4 pts) If va(t=0) = O, compute values for all unknown coefﬁcients and determine
an eXpression for of v00). PROBLEM 6 Code Number: (10 pts total) Refer to the following diffamp circuit for parts (a) through (d). Let VDD
= 5V, V55 = 5V, RD = 10 kg R5 = 22 1:12 The devices are of equal size, and gm = 10
HIS, F0 = a) (3 pts) Calculate the small signal voltage gain Avg from v; to v0.
b) (3 pts) Calculate the common mode rejection ratio. c) (4 pts) Suppose v; = v; + v,. Derive an expression for the output signal v0 in terms
of A a}, and CMRR. VDD VDD SS Si material parameters to use: ni= IOIocm'3, un=1360 cmst, up=460 cmZ/Vs, Eg=l .11 eV, Tn: 'cp =100 us. illumination? (c) What is the change in conductivity of the sample due to illumination?
(d) Is this low level injection? LO LS— fL Mm) PROBLEM 8 Code Number: h Use the following constants in your calculations: (21:1.6x10'19 C, c=3x108 m/s,
h=6.63x10'34 Js, kT/q=0.026 v. Si material parameters to use: ni= lomcm'3, un=1360 cmst, up=460 cmZ/Vs, Eg=1 .11
eV, Tn: I], =100 us. A Si pn junction has a current of l uA under a 0.4 V forward bias. The dOping on the p
side of the junction is 4 times that on the 11 side of the junction. (3) What is the reverse saturation current (10)? (b) What is the deping on the 11 side and the p side? (0) Assuming that the diode is not in reverse bias breakdown, what is the reverse current
when an applied reverse bias of 1.2 V is applied to this pn junction diode? ((1) Draw roughly the current density as a function of position for this diode under a forward bias of 0.4 V on the graph below. Draw the total, hole, and electron current
densities as a function of position in the diode. if u Code Number: PROBLEM I 1 Code Number: “ Consider a 2way setassociative Writethrough cache with 4word 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 Inltlally empty and LRU replacement IS used. Assume that the data stored in each PROBLEM 12 Code Number: (Part ‘1) Consider the circuit shown below. When the output of the inverter is HIGH. the LED shown turns on. We desire that the LED remain ON even when the output of the inverter is LOW. To solve this problem, the following data is given: (a) the "ON" resistance of an NMOS transistor is 100 ohms (b) for the LED to turn "ON" (emit light), 1 milliampere of current must flow through it when it is forward—biased and in this
condition, the voltage drop across the LED is 1.5V It is easily seen that for very small values of R. the LED will turn "OFF". What is the minimum value of R that guarantees that the LED will be "ON" when the output of the inverter is LOW ? Show all your calculations and any equations that you
use to get your answer. Vdd=5V Vdd = 5v
100 ohms
1.5V
100 ohms LED v V; R I 7 7 1 mAl 500 ohms [77 (Part 2) Using the implication chart method or any other technique that you know, reduce the state transition table of the following synchronous ﬁnite state machine. Identify all equivalent states and give the reduced state transition table. The
machine has a single input line. PRESENT STATE 2
rn XT STATE. OUTPUT NPUT=0 N [Tl XT STATE, OUTPUT INPUT=1 B.
B.
C.
D.
E.
B Dommmm
b __. C) —I C) C) PROBLEM 13 Code Number: A continuoustime system is described in statevariable format by 2":(t) = i7 0 1 ]x(t)+[0]u(t)
—100 —20 1 W) = [1 0 ]I(t) :r
Compute )‘(IL for r 2 0, assuming that 12(0) = [ 1 0 ] and 11(1) = 0, PROBLEM 14 Code Number: m The schematic below shows a closed loop ﬂuid flow system where a ﬂoat level sensor and value
as shown, are used to close the 100p. The Open 100p transfer function ofthis system (without the sensor/valve combination) can be
written as: A 3
6(5) 2 Q(5) = 1
AQI(5) 5+1
u here ' = RC R IS a constant equn alent to the re515tance offered bx the onﬁce so that (a) Draw a closedloop flow graph or block diagram.
(b) Write the closed100p transfer function (c) Determine and compare the openloop and closedloop system for sensitivity to changes in
the equivalent coefﬁcient R and the feedback coefﬁcient K .. (d) Determine the steadystate error of the level (head) for a step change of the input 130I D .... (e) Determine the necessary loop gain, KR , in order to maintain the steadystate error of the
head less than 5% of the magnitude of a step change in the input AQl .. PROBLEM 15 Code Number: In an analog communication system that uses amplitude modulation (AM),
C(t) = sin(2:r10r +ﬂ' / 4) is being used as the carrier wave. The modulated wave is given as: 30') = 2 [1 + 0.55in(2m)]c(r).
Find and plot , the spectrum of 50‘). Label all quantities in the plot. PROB LEM 16 Let
12(t) = 6—2:
23(15) 2 33(t + 1) (In other words, :z:(t) is periodic with period 1.) Code Number: I— PROBLEM 17 Code Number: * 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. 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. 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)? PROBLEM 18 Code Number: “I It is wellknown to photographers that stepping down a camera lens (using a smaller lens aperture
or effective diameter) increases the depth of ﬁeld, or range of object distances that yield images
that appear to be in focus. Using words or diagrams as appmpriate, explain how this happens. ...
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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.
 Fall '10
 DDAA

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