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Unformatted text preview: Midterm EElOl
Fall, 2003 Name:
Grade: Problem #1 (25 points). A 50 Ohm lossless TEM transmission line of length L=0.5m is
connected to a 300MHz source generator. (a) If the insulating medium is air, ﬁnd the line
parameter R’, L’, G’ and C’ (5 points). (b) Find the phase constant [3 and phase velocity u p (5 points) (c) Ifwe use a pair of LC components to represent each 21/ 4 section of the transmission line, draw the lumped element model for the complete line and mark the
value of each lumped element. (5 points) ((1) If the insulating medium is with s, = 4 , redo question (a),(b),(c). (10 points) Problem #2 (20 points) A 100 Ohm lossless transmission line is terminated in a load with
impedance ZL=(60  j120) Ohm. The wavelength is 5 cm. Find the following (a) The
reﬂection coefﬁcient at the load. (4 points) (b) The standingwave ratio on the line. (4
points) (c) The positions of the voltage and current maximum nearest the load (4 points).
(d) Does the standing wave ratio change when the observation point move along the line?
why? (4 points) (e) If the incident voltage is 1 Volt, what are the values of the voltage
maximum and minimum along the line? (4 points) Problem #3 (20 points) Considering the following impedance matching circuit shown in
the ﬁgure, it is a combination of open circuit stub and a quarter wavelength transformer. (a) If the length of the open stub I, = 1/4 , characteristic impedance of the transformer
Zn1 = 809 , load impedance Z L =100£2 , ﬁnd the input impedance 231,. (5 points) (b) How
to change the value of 20.1 to realize impedance match. (5 points) (c) If the load
impedance ZL =(100— j 00)!) , how to change both 2m and I, to realize impedance
match? (10 points) Problem #4. (25 points) A lossless 50 Ohm transmission lone is terminated with
Z L = (50 — j25)Q. Use the Smith chart to ﬁnd following: (a) The reﬂection coefﬁcient 1".
(4 points) (b) The standing wave ratio. (4 points) (c) The input impedance at 0.3 A from
the load. (4 points) ((1) The input admittance at 0.3 ilfrom the load. (4 points) (6) The
shortest electrical length of the line for which the input impedance is purely resistive. (5
points) (i) The position of the voltage maximum from the load. (4 points) Problem #5. (10 points) Faraday’s Law gives {Edl=—JI%ds , (a) derive its
s differential form VxE=—% using vector calculus theorems. (5 points) (b) Similarly, derive vn = p, from Gauss’siaw jDds = jp,dv. (5 points)
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 Spring '07
 Williams

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