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ELEC 390
Theory and Applications of Electromagnetics
Spring 2011
Homework Assignment #4 – due in class Friday, Feb. 18, 2011
Instructions, notes, and hints:
You may make reasonable assumptions and approximations in order to compensate for missing
information, if any. Provide the details of all solutions, including important intermediate steps.
You will not receive credit if you do not show your work.
Prob. 2.33: Impedances Zin1 and Zin2 are the input impedances measured at the inputs of the upper
and lower lines, respectively.
Prob. 2.39: A visual depiction of the system is shown in Fig. 2-22 on p. 83 of the text.
Prob. 2.41: The easiest way to find the time-domain current is first to find the phasor
representation of the current and then convert that expression to the time-domain expression.
Assignment:
Probs. 2.31abc, 2.33, 2.39 (CD module part not required), and 2.41 (CD module part not
required) in the textbook, plus the following additional problems:
1. Recall that the impedance at the location of a voltage maximum on a lossless transmission
line is purely real. As shown below, a resistor R has been connected between the two
conductors of a line at the location of a maximum. If it has an appropriately selected value,
then there will be no reflected waves propagating along the line to the left of the resistor.
a. Find the value of R that results in no reflected waves.
b. Find the VSWR along the line between the resistor and the load.
c. Find the VSWR along the line to the left of the resistor.
Zo = 52 
ZL = 40 + j20 
R
no reflections
dmax
2. Recall that the attenuation constant for low-loss lines can be approximated as

R
2Z o
where R′ is the resistance per unit length, and Zo can be considered to be purely real. RG-58A
coaxial cable has a copper inner conductor with a radius of 0.47 mm, an outer copper
conductor with a radius of 1.71 mm, polyethylene insulation, and a characteristic impedance
very close to 52 . The attenuation constant at 400 MHz is 0.0216 Np/m. What is the
attenuation constant at 30 MHz? Note that there is a quick way and a cumbersome way to
solve this problem.
(continued on next page)
3. As shown in the diagram below, a 47-pF capacitor is attached to the end of a 21.9-cm-long
RG-58A coaxial cable that has a characteristic impedance of 52 . The loaded line forms a
wave trap that is designed to eliminate interference from WVBU in the EE labs. WVBU’s
operating frequency is 90.5 MHz. Recall that the wave trap was originally designed by
assuming that the line is perfectly lossless. In that case, the input impedance is very close to
0  at 90.5 MHz. In reality, the cable is slightly lossy, and its attenuation constant at
90.5 MHz is approximately 0.01 Np/m. Find the input impedance of the wave trap at
90.5 MHz taking into consideration the loss. The input impedance of a lossy line is given by
Z in  l   Z o
Z L  jZ o tanh  l 
Z o  jZ L tanh  l 
where “tanh” is the hyperbolic tangent function;  =  + j; and  can be assumed to be equal
to the value obtained for the lossless line case.
Zo = 52 
Zin
l = 21.9 cm
47 pF