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EM2_2001_Mid2.pdf

# EM2_2001_Mid2.pdf - Electromagnetics II Second...

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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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