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EE361Midterm Exam
October 19, 2009
Please answer all questions.
Include proper units in all your answers.
Start each question on a new page.
Be sure to put yourname andstudent ID on your exam book.
1. [56 points] A coaxial cable whose insulator is perfect (no
leakage current) carries an underwater
acoustic-sensor signal whose total phasor voltage is given by
the following sum of two terms:
8 2 8 2( ) 2exp( 10 ) exp( 10 )V y cy j y dy j y = + +% Volts.
(Eq. 1)
Here is angular frequency (radians/sec), y is a space variable
in meters, and c and d are realnumbers (though not necessarily
positive ones).
a. What is the direction of propagation of the first
phasor-voltage term (the first of two) in Eq. 1?
b. What physical phenomenon in the transmission line does the
parameter c in (Eq. 1) represent?
(Its not the speed of light.) Which lumped line parameter (R, L,
G, C) is responsible for it?
c. Write an expression for the instantaneous voltage associated
with just the first term of Eq. 1.
(keep c and as unknowns. Include proper units.)d. State clearly
the definition of a dispersive transmission line. (1 sentence
should suffice. You
must be clear.)
e. Is the above line dispersive? State why or why not. (1
sentence.)
f. What are the units of the constant d, in Eq. 1?
g. In Eq. 1, is the constant c zero, positive, or negative?
(Explain your thinking in 1 sentence.)
h. In Eq. 1, is the constant d zero, positive, or negative? (No
explanation required.)
i. Is the imaginary part Im(Z0) of the characteristic impedance
of this line zero or nonzero? State
your reasoning (1 sentence.)j. The above line is excited by a
sinusoidal signal at a very low angular frequency of 1
radian/sec.
You sit on a peak of the sine wave. How fast are you traveling
in m/s? (Your answer should
contain no unknowns.)
k. If the load is at position y=0, what is the lines voltage
reflection coefficient at the load?
l. Let =104 radians/sec. If the load were replaced by a matched
load and the line was extremely
long, qualitatively sketch the magnitude ( )V y% of the total
phasor voltage on the line. (Nocalculations or numbers required,
but your sketch must clearly show the general behavior.)
m. Let =1 radian/sec. If the load were again replaced by a
matched load but the line was only 10meters long, qualitatively
sketch the total instantaneous voltage on the line at an instant
when the
voltage at the load is a maximum.
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2. [25 points] A two-wire lossless transmission line
transporting a video signal at 1.3 GHz has a measured
phasor voltage magnitude ( )V z% that varies between 2.1V and
8.4V, as shown below.
a. Starting with the fact that
0 0( )j z j z
LV z V e V e + += + % ,
show that the voltage reflection coefficient lmeters from the
load is2( ) j lLl e
= .(You must clearly show your reasoning.)
b. What is this lines voltage standing-wave ratio?c. What is the
magnitude of the voltage reflection coefficient at the load?
d. What is the phase of the lines voltage reflection coefficient
at a position 0.092 from the load?e. What is the phase of the
backward traveling voltage minus the phase of the
forward-traveling
voltage at the load?
2
(Phasor voltagemagnitude
~ Volts
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3. [20 points] Over all of space, including the region in the
figure below, the electric field has curl
4
3E y = V/m2 ,
and divergence
3E = g V/m2 ,
where y is the unit vector in the y-direction.
Paths C1, C2 , and C3 are square oriented paths, 1 meter on a
side, that reside in the x-y, y-z, and x-zplanes, respectively.
Surface S is the box shown with one corner at the origin and
oriented with surface-normals pointing out of the box.
a. You place a curl-meter (paddlewheel) at position
(x,y,z)=(1,1,1) and search orientations to find
the curl of E, which is algebraically stated above. When the
curl-meters axis points in two
distinct directions, the curl-meter undergoes maximum
circulation (max rotation). What are
those two directions?
b. Find the fluxS
E ds of E through box S, including proper units. (Youll find it
easiest to use afundamental theorem of vector calculus here.)
c. Find the circulation3C
E dl of E around path C3, including proper units.
d. Are there any sinks or drains of this E-fieldregions into
which the field flows? If not, state
why not; if so, state exactly where they are. (1 sentence).
3
x(coming out of page)
y
z
Path C2
1
1
Path C1
11
Path C3
1
1
1
1
S
ds
ds
