Download Name_____________________ 55:070 Final exam May 17, 2002

Name_____________________
55:070
Final exam
May 17, 2002
1. _____________________
2. _____________________
3. _____________________
4. _____________________
5. _____________________
6. _____________________
Total_____________________
1.
a) The relative dielectric constant of the material that separates the two
conductors of a coaxial cable is increased by a factor of 4. If the original
characteristic impedance of the transmission line was 50, calculate the
characteristic impedance of the new transmission line.
_____________________
b) In part (a), calculate the ratio of the velocity of propagation for a signal
in the new transmission line divided by the velocity of propagation in the old
transmission line.
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c) Assume that a signal is launched on the old transmission line that exists
from - < z < 0 and the new transmission line exists in the region 0 < z < +. A
wave whose amplitude is 10 V is launched at z = - , calculate the amplitude of
the wave that is transmitted into the region z > 0.
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d) In part (c), calculate the amplitude of the wave that is reflected from the
interface at z = 0.
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e) Assuming that the signal generator were placed at z = + , would you
expect that the magnitude of the wave which is transmitted into the region z < 0
be (1) greater than; (2) equal to; or (3) less than the incident wave?
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2.
a) On the impedance Smith chart,
clearly indicate the point that represents a
normalized load impedance that is an open
circuit.
b) On this Smith chart, clearly indicate
the point that represents a matched
transmission line.
c) Using the Smith chart, clearly
demonstrate the procedure that allows you to
convert a normalized load impedance zL = +j1
into a normalized load admittance yL.
d) Calculate the impedance of a 1  resistor that is in parallel with a /4
transmission line that is terminated in a short circuit.
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e) A quarter wave transmission line is terminated with a short circuit.
Would you expect that the input impedance of this transmission line to be:
(1) greater than; (2) equal to; or (3) less than zero?
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ct
3. A 2V battery is connected
via a switch to a transmission
line whose characteristic
impedance is Zc = 2. The
switch is closed at a time t =
0. The values of the voltages
of the resulting waves are
plotted on the “bounce”
diagram. From this diagram,
2ascertain the following
values.
0
2L
+1
L
L
+1
0
L
a) The value of the load impedance.
_____________________
b) The value of the battery impedance.
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c) Carefully plot the expected
amplitude that would appear on the
oscilloscope that is located at the load.
+2
V
0
-2
0
d) Carefully plot the expected
amplitude that would appear on the
oscilloscope that is located at the
switch.
2
3
2
3
2
3
L/c
+2
V
0
-2
0
e) Carefully plot the expected
amplitude that would appear on the
oscilloscope that is located at the
midpoint between the switch and the
load.
1
1
L/c
+2
V
0
-2
0
1
L/c
4.
a) Carefully plot the amplitude of
the electric field as a function of
distance from an electric charge that is
concentrated into a point. The value at
one location is indicated.
100
E
1
0.01
0.01
b) Carefully plot the amplitude of
the voltage as a function of distance
from an electric charge that is
concentrated into a point. The value at
one location is indicated.
.
c) Electric charge is uniformly
distributed in the radial direction of a
cylinder. Carefully plot the amplitude of
the electric field within this cylinder.
The value at one location is indicated.
1  100
100
V
1
0.01
0.01
1  100
100
E
1
0.01
0.01
1
r
100
d) The repulsive electric force between two charges that are separated
from each other by a distance of one meter is 10 N. Calculate this repulsive
force if the same two charges are separated by a distance of two meters.
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e) A current I flows in the same direction through two parallel wires. Will
there be a magnetic force that will: (1) cause the wires to move together; (2)
cause the wires to move apart; or (3) not affect the location of the wires?
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5.
a) Assume that a current density j = jouz exists in space. State the
direction of the magnetic vector potential created by this current.
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b) In part (a), state the direction of the magnetic field intensity caused by
this current.
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c) The electric field in the vacuum region x < 0 is E = 5ux + 5uif. Calculate
the normal component of the electric field in the dielectric region x > 0. The
relative dielectric constant of the dielectric is equal to 4 and there is no surface
charge at the interface.
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d) In part (c), calculate the tangential component of the electric field in the
dielectric.
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e) If a surface charge density of s = 5 C/m2 exists at the interface in part
(c), calculate the tangential component of the electric field in the dielectric.
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6.
a) In terms of fundamental units: mass M, length L, time T, and charge Q;
state the units of the displacement flux density.
.
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b) The magnetic flux density exponentially increases in time. Will the
electric field in a hypothetical loop that encloses this magnetic field: (1) increase
in time; (2) decrease in time; or (3) be unaffected by this change in the magnetic
field? You may assume that the vector direction of the loop and the magnetic
field are in the same direction.
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c) A plane wave propagates in a
vacuum. The electric field is specified
with the following equation
E = Eo cos(t + ky)ux.
Clearly indicate the vector direction of
the magnetic field intensity on the
coordinate system.
z
y
x
d) In part (c), state the phase velocity of the wave.
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e) Is a vacuum (1) a dispersive media or (2) a nondispersive media?
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