Problem 6.26 The electric field radiated by a short dipole antenna is given in
spherical coordinates by
E(R, ;t) =
2 102
sin cos(6 108t 2 R) (V/m).
R
Find H(R, ;t).
Solution: Converting to phasor form
Chapter 5: Persuasion
Through Rhetoric
What is rhetoric?
Rhetoric
Rhetoric denotes a broad category of
linguistic techniques people use when
their primary objective is to influence
beliefs and attitud
Problem 2.17 Using a slotted line, the voltage on a lossless transmission line was
found to have a maximum magnitude of 1.5 V and a minimum magnitude of 0.6 V.
Find the magnitude of the loads reflecti
Problem 2.29 Show that the input impedance of a quarter-wavelengthlong
lossless line terminated in a short circuit appears as an open circuit.
Solution:
Zin = Z0
For l = 4 , l =
2
ZL + jZ0 tan l
Z0 +
Problem 2.64 Use CD Module 2.7 to design a quarter-wavelength transformer to
match a load with ZL = (100 j200) to a 50- line.
Solution: Figure P2.64(a) displays the first solution of Module 2.7 where
Problem 2.25 Apply CD Module 2.4 to generate plots of the voltage standingwave pattern for a 50- line terminated in a load impedance ZL = (100 j50) .
Set Vg = 1 V, Zg = 50 , r = 2.25, l = 40 cm, and f
Problem 2.35 For the lossless transmission line circuit shown in Fig. P2.35,
determine the equivalent series lumped-element circuit at 400 MHz at the input to
the line. The line has a characteristic i
Problem 2.37 A lossless transmission line is terminated in a short circuit. How
long (in wavelengths) should the line be for it to appear as an open circuit at its input
terminals?
sc = jZ tan l. If l
Problem 2.40 A 100-MHz FM broadcast station uses a 300- transmission line
between the transmitter and a tower-mounted half-wave dipole antenna. The antenna
impedance is 73 . You are asked to design a
Problem 2.15 Find and Z0 of a distortionless line whose R = 2 /m and
G = 2 104 S/m.
Solution: From the equations given in Problem 2.13,
= R G = [2 2 104 ]1/2 = 2 102 (Np/m),
r
r
1/2
L
R
2
Z0 =
=
=
=
Problem 5.12 Two infinitely long, parallel wires are carrying 6-A currents in
opposite directions. Determine the magnetic flux density at point P in Fig. P5.12.
I1 = 6 A
I2 = 6 A
P
0.5 m
2m
Figure P5.
Problem 2.11 A 50- microstrip line uses a 0.6-mm alumina substrate with r = 9.
Use CD Module 2.3 to determine the required strip width w. Include a printout of the
screen display.
Solution: According
Problem 5.24 In a certain conducting region, the magnetic field is given in
cylindrical coordinates by
4
H = [1 (1 + 3r)e3r ]
r
Find the current density J.
Solution:
4
1
3r
H = z
r [1 (1 + 3r)e ]
J
Problem 2.60 Repeat Problem 2.59 using CD Module 2.6.
Solution: In Module 2.6, after setting Z0 = 75 , and d = 0.6 , cursor is used to
move the load point so that S = 1.8 and simultaneously r = 60 . O
Problem 2.65 Use CD Module 2.7 to design a quarter-wavelength transformer to
match a load with ZL = (50 + j10) to a 100- line.
Solution: Figure P2.65 provides a summary of the two possible solutions,
Problem 1.10 An oscillator that generates a sinusoidal wave on a string completes
20 vibrations in 50 s. The wave peak is observed to travel a distance of 2.8 m along
the string in 5 s. What is the wa
Problem 2.24 A 50- lossless line terminated in a purely resistive load has a
voltage standing-wave ratio of 3. Find all possible values of ZL .
Solution:
S1 31
=
= 0.5.
S+1 3+1
For a purely resistive
Problem 1.24 If z = 3e j /6 , find the value of ez .
Solution:
z = 3e j /6 = 3 cos /6 + j3 sin /6
= 2.6 + j1.5
ez = e2.6+ j1.5 = e2.6 e j1.5
= e2.6 (cos 1.5 + j sin 1.5)
= 13.46(0.07 + j0.98)
= 0.95 +
Problem 1.23 If z = 3 j4, find the value of ez .
Solution:
ez = e3 j4 = e3 e j4 = e3 (cos 4 j sin 4),
4
e3 = 20.09,
and 4 rad = 180 = 229.18 .
Hence, ez = 20.08(cos 229.18 j sin 229.18 ) = 13.13 + j15
Problem 2.10 Use CD Module 2.3 to design a 100- microstrip transmission line.
The substrate thickness is 1.8 mm and its r = 2.3. Select the strip width w, and
determine the guide wavelength at f = 5 G
Problem 2.44 For the circuit shown in Fig. P2.44, calculate the average incident
power, the average reflected power, and the average power transmitted into the infinite
100- line. The /2 line is lossl
Problem 2.46 An antenna with a load impedance
ZL = (75 + j25)
is connected to a transmitter through a 50- lossless transmission line. If under
matched conditions (50- load) the transmitter can delive
Problem 2.47 Use the Smith chart to find the reflection coefficient corresponding
to a load impedance of
(a) ZL = 3Z0
(b) ZL = (2 j2)Z0
(c) ZL = j2Z0
(d) ZL = 0 (short circuit)
Solution: Refer to Fig.
Problem 7.1 The magnetic field of a wave propagating through a certain
nonmagnetic material is given by
H = z 30 cos(108t 0.5y) (mA/m)
Find the following:
(a) The direction of wave propagation.
(b) Th
Problem 7.5 A wave radiated by a source in air is incident upon a soil surface,
whereupon a part of the wave is transmitted into the soil medium. If the wavelength
of the wave is 60 cm in air and 20 c
Problem 7.9 For a wave characterized by the electric field
E(z,t) = x ax cos( t kz) + y ay cos( t kz + )
identify the polarization state, determine the polarization angles ( , ), and sketch
the locus
Problem 7.20 The skin depth of a certain nonmagnetic conducting material is 3 m
at 2 GHz. Determine the phase velocity in the material.
Solution: For a good conductor, = , and for any material s = 1/
Problem 7.19 Ignoring reflection at the airsoil boundary, if the amplitude of a
3-GHz incident wave is 10 V/m at the surface of a wet soil medium, at what depth will
it be down to 1 mV/m? Wet soil is