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Unformatted text preview: Name: ‘< E Problem 1. (20 points, 5 points/answer, 2 points/answer deduced if answer is correct by no work is shown) A lossless transmission line has a characteristic impedance of Z0 = 80 Q , and the propagation time for a
10 meter length of this cable is measured as 48.34 x 10'9 seconds, i.e. 48% nanoseconds. 3.34 3
A. Find the velocity of propagation in the cable. (f VI, = «Q. 06 7X /0 M/g
/ 0 '8’
Alg= =2.069X/0’"'/<
9‘8 . 3 1/ x M“?
B. Assume that the cable dielectric is nonmagnetic. 8R = 2. . / Calculate the relative permittivity of the cable. /U'=I'——I——=C'o"('—'
Pﬁzré: V8? 2. ’2.
w? ’ (91.0637 >003)z C. Find the capacitance and inductance per unit length. C = Q 0 e 7 8 F4 ”H '2. L. _ '2 L
2': —:> LC2)C—— 5' 2.. 2" L= QMZZé7ALH/m ‘3 70 ‘7 '
WE Z.oé9)</0$ /m _./_.. ’  _._L_.,_LQ;8__.__.= , as! X/o‘gF
6’ 45,1; " c Pz~>C 270’; " ?o(z.069) G‘OOé % D. For the circuit shown below, V1; is measured as 5 (V), RL = $1? .  3) Q— and the voltage on the line aﬁer this wave reﬂects once from
the load is 4.25 (V). What is the resistance value of the load? 55+ng #325
T" ”'Zg’5=—O.IS’$‘Q‘—%o o. g Eur80
QLonOlSEL’lZSD ”5.25% $RL=§$l3IL February 8, 2005 2 ECE 3025D Exam #1 Name; K55: Problem 2. (30 points, 2 points/answer, 1 points/answer deduced if answer is correct by no work is shown) Consider the following circuit which consists of two lossless transmission lines joined at an intermediate junction. The propagation time in the cable 1 is T , and the propagation time in cable 2 is 2 T. All cable impedances and
resistor values are listed on the circuit diagram Assume both cables have the same propagation velocity. son can m2 20:”n,r Z.=759,ZT IOU) '— 339 A. What is the reﬂection coefﬁcient at the 3 3 Q , load end of the line? FL = "" O :52 8 q B. What is the reﬂection coefﬁcient at the 5 0 Q , generator end of the line, PG = O
assume that the switch is in the closed position for this calculation? {7 ={bf—LSD 2. O
&' \O'D C. What is the reﬂection coefﬁcient at the junction between the cables FF = O n 2
for forward going waves from cable 1 to cable 2? 75,90 ' ZS"
(1 ; a—(___=O.Z 7 S‘+§o \‘L‘S D. What is the reﬂection coefﬁcient at the junction between the cables FR = ’ 0 c 2
for reverse going waves from cable 2 to cable 1? February 8, 2005 3 ECE 3025D Exam #1 Name: K E Y ’ Problem 2. (Continued) ‘ 2.
E. What is the transmission coefﬁcient at the junction for forward I}; = '
going waves from cable 1 to cable 2? ‘1”..=!+F'F=4+o.2= :.2_ F. What is the transmission coefﬁcient at the junction for reverse TR = O o 3
going waves from cable 2 to cable 1? i}; ~l+72= (—0.2 = 0.? G. What is the amplitude of the forward going wave that is launched VI; = S V into cable 1 immediately after the switch is closed at t = 0 ? V+ WPLO J“ S’v
It] ’ 5'04'9'0
H. What is the eventual steady state voltage across the load for t >> 10 T ? Vss = 3 o a 7 g \/ s3  1s; ..
V53 = m[s‘o+’33]’ lei g3  3.97Sv I. What is the eventual steady state current across the load for t>> 10 T ? Iss = I 20 o S/M A‘ 155: V53 .'~. 3973: 0.1205" A
R 33 J. If it is desired to eliminate cable reﬂections at the load end of the line, R1. = 7 g—(Z—
what value must R'L = 33 Q be changed to?
g .—
' ’7 5+7 9 February 8, 2005 4 7 pm: 2m<n pvom m Name: KEY Problem 2. (Continued) K. What is the amplitude of the ﬁrst wave that arrives at RL = 33 9 V =
atatime of t=3T ? L. When does the next wave arrive at RL after at time of t = 3T ? t = M. What is the amplitude of the lSt reﬂection received at the generator V =
end of the cable? N. What is the amplitude of the 2“d reﬂection received at the generator V =
end of the cable? 0. What is the amplitude of the 3rd reﬂection received at the generator V =
end of the cable? Cable 1 Cable 2 February 8, 2005 +ev '7T
+«v ~LQG7V HT ECE 3025D Exam #1 Name; KEY Problem 3. (30 points) Consider the following circuit. At time t = 00 the switch was set to position B to completely discharge the transmission line. The switch is placed in position A at time t = 0. Next, the switch is placed in position B at time
t = 4T. Plot the reﬂection diagram for the time interval 0 S t S IOT. son A Z.=son.r 5/4 oat <‘/T ‘ (70:2 t>>T)' \ésao
V*,~,m¢= 9v, v$$= 6v Foe 2:2 97; g: 1/3
lg: 0) ‘1: 0‘1 Tl‘fEL/ENM/ EQUIV
c/ILCUIT Fan; zﬁr§ 1:46P.
go.“— ‘1 ,i , February 8, 2005 5 nnn ﬁnnrn : Name: K5 Y Problem 3. (Graph paper for a Bergeron Plot if you care to try it, but it is not required.) D ("501?— ’€&, waxes
V Axis ,A'T 10V o.‘ EN EN TU M,“
511:.ka CFKT'E. FOP. t>>T February 8, 2005 , 7 ECE 3025D Exam #1 KEY Problem 4. (20 points) Name: Consider the following circuit which contains a nonlinear load. At time t = 0 the switch is closed. Graphically, construct a currentvoltage plot, i.e. Bergeron Plot, that will result from the nonlinear load curve plotted below.
Show all distinct state voltage points on the generator and load curves that correspond to the cable reﬂections for the time interval 0 S t S 5 T . Plot your answers on the supplied graph. 209 zo=7sn,T’ VazY I
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I 100m 200m. February 8, 2005 8 ECE 3025D Exam #1 ...
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 Spring '08
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