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**Unformatted text preview: **Electromagnetics II
Second Exam (10:10am—12:10m) 5/14/01 1. (10%) Consider a lossless transmission line, with characteristic impedance Zo and
propagation constant 13, that is Open circuited at the far end d = 0, as shown in Fig.
P1. Assume that a sinusoidally time—varying voltage wave, V0 sin (wt—l—ﬂd), is traveling
along the line due to a source that is not shown in the ﬁgure and that conditions have
reached steady state, where w is the angular frequency. (a) Write the expression for
the total voltage phasor 17(d). (b) Write the expression for the real (instantaneous) total voltage V(d, t). a (10%) Consider the low—loss line system shown in Fig. P2. (a) Determine the reﬁcetion
coefﬁcient at the input end at : l. (b) Determine the input impedance of the line at
d = Z. Use the notation shown in the ﬁgure. 3 (15%) Consider the structure of two parallel perfectly conducting plates separated
by a lossy medium characterized by conductivity .0, permittivity E, and permeability
n, and driven by a voltage source l/ﬁcos cut at one end, as shown in Fig. P3, where
1/5 is real. Using the quasistatic—ﬁeld approach, please derive an expression for the
magnetic ﬁeld intensity correct to the ﬁrst power in the frequency w. g1) (10%) Fig. P4 shows a magnetic circuit of square cross section with area A = W2
I and with air gaps. The magnetic core has permeability ,u. Find the relectance of this
circuit as seen by the current turns. :5. (10%) Consider an electromagnet as shown in Fig. P5. When current is passed
through the coil, the armature is pulled upward to close the air gaps. The mechanical
force Fe can be found by assuming a constant magnetic flux 11b in the core. (a) Is
there electrical energy input to the system? Please explain. (b) Drive an expression
for Fe in terms of 1b. 6. (15%) Fig. P6 shows a hybrid arrangement of a series short—circuited sub and a
parallel short-circuited stub connected at a ﬁxed distance d1 from the load in order to
achieve a match between the line and the load. (a) (10%) With the notation shown
in the figure, where 271 : 1"+ jm’, express $1 and ()2 in terms of r’ and :1," for the match to be achieved. (11)) (5%) Discuss the condition for which a solution does not exist for
a ﬁxed value of (£1, and a remedy to get around the problem. 7. (15%) Fig. P7 shows the conﬁguration of a typical problem that may be met in
practice. Say a. generator feeds an antenna by means of a coaxial transmission line
1.72 m long (with air medium); for measurement purposes a slotted section has been
inserted between the generator and the transmission line, and is tied to the line by
means of a connector. The line, the connector, and the slotted section all have a
common characteristic impedance of 50 Q. A minimum in the standing wave on the
slotted section is observed 9 cm from the connector. The generator frequency is 750
MHz, and a voltage standing wave ratio of 3 is obtained along the slotted section.
What impedance does the antenna present to the line at this frequency? (Use the
provided Smith chart to ﬁnd the solution.) ' 8. (15%) In the system shown in Fig. P8, two A / 4 line sections of characteristic impedance
50\/§ Q and 50 9, respectively, are employed. You are asked to use the Smith chart
provided to ﬁnd the locations of the two A/4 sections, that is, the values of ll and 12
to achieve a match between the IOU—Q line and the load. Use the notation shown in
the ﬁgure. (a) Mark on the Smith chart the two locations repreSenting the two solutions for 332
as P1 and P2. (b) Mark the corresponding locations as Pf and 132' representing the two solutions
for 21.
(c) Determine the corresponding values of £1 and lg. HIM) Trans'mksr‘m
II‘J’WL ...

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