Fundamentals of Applied Electromagnetics (7th Edition)
7th Edition
ISBN: 9780133356816
Author: Fawwaz T. Ulaby, Umberto Ravaioli
Publisher: PEARSON
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Textbook Question
Chapter 2, Problem 5P
For the parallel-plate transmission line of Problem 2.4, the line parameters are given by
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Students have asked these similar questions
1. What length of standard RG-8/U coaxial cable would be required
to obtain 45 degrees phase shift at 200 MHz? Assume that the
velocity factor is 0.66.
Hint:
Lengths of line that are not equal to a wavelength yield a phase delay
proportional to their length. Since a length A produces a phase shift of
360°, the phase delay produced by a given transmission line is
0 = (360°)
O is the phase shift
L is the Tx line length
A is the wavelength of the Tx line
Where
(3) A coaxial cable (e.g. RG-402U semirigid cable) has an inner conductor diameter of 0.91 mm and a dielectric
diameter (equal to the inner diameter of the outer conductor) of 3.02 mm. Both conductors are copper, and the
dielectric material is Teflon. Compute the R, L, G, and C parameters of this line at 1 GHz. Use the expressions
and material properties from the figure below or lecture note.
L
C
R
G
COAX
b
fe
-In
2π a
Σπε
Inb/a
Rs
+
2π a
2πTWE"
Inb/a
Material properties:
Copper:
Conductivity =
Characteristic
impedance
Teflon:
Loss tan (8) = 0.0004
€ = 2.08
€' = €0€r
Loss
Rs =
€"
Zo =
= 5.8 x 107 S/m
ιωμα
2σ
= €0€, tan(8)
R+jwL
VG+jwC
~
L
1
R
α ~
11 ( ²√² + 0 √ ² ) = ² ( 2² 6 + 0²0).
G₁
GZo
L
Zo
B≈w√LC,
Propagation
constant
Figure 2 - Coax line with the expressions and the materials properties.
Bonus: Use the results to find the characteristic impedance and attenuation(dielectric loss and conductance loss)
of the line at 1 GHz using the formula from the figure(in red box).
What is the value of the input impedance half wavelength from the load?
a.
ZL
b.
minimum
c.
maximum
d.
Zo
For an open circuit line, the location of the first maximum current is ____.
a.
at the load
b.
λ/4 from the load
c.
0.125λ from the load
d.
λ/2 from the load
What is the phase difference between two points that are half wavelength apart?
a.
90°
b.
45°
c.
180°
d.
270°
Chapter 2 Solutions
Fundamentals of Applied Electromagnetics (7th Edition)
Ch. 2.2 - What is a transmission line? When should...Ch. 2.2 - Prob. 2CQCh. 2.2 - What constitutes a TEM transmission line?Ch. 2.2 - Prob. 4CQCh. 2.2 - Prob. 1ECh. 2.2 - Calculate the transmission line parameters at 1...Ch. 2.4 - Verify that Eq. (2.26a) indeed provides a solution...Ch. 2.4 - A two-wire air line has the following line...Ch. 2.6 - The attenuation constant represents ohmic losses....Ch. 2.6 - How is the wavelength of the wave traveling on...
Ch. 2.6 - Prob. 7CQCh. 2.6 - What is a standing-wave pattern? Why is its period...Ch. 2.6 - Prob. 9CQCh. 2.6 - For a lossless transmission line, = 20.7 cm at 1...Ch. 2.6 - A lossless transmission line uses a dielectric...Ch. 2.6 - Prob. 7ECh. 2.6 - Prob. 8ECh. 2.6 - Prob. 10ECh. 2.6 - A 140 lossless line is terminated in a load...Ch. 2.8 - What is the difference between the characteristic...Ch. 2.8 - What is a quarter-wave transformer? How can it be...Ch. 2.8 - Prob. 12CQCh. 2.8 - Prob. 13CQCh. 2.8 - if the input impedance of a lossless line is...Ch. 2.8 - Prob. 12ECh. 2.8 - A 300 feedline is to be connected to a 3 m long,...Ch. 2.9 - According to Eq. (2.102b), the instantaneous value...Ch. 2.9 - Prob. 16CQCh. 2.9 - What fraction of the incident power is delivered...Ch. 2.9 - Prob. 18CQCh. 2.9 - For a 50 lossless transmission line terminated in...Ch. 2.9 - For the line of Exercise 2-14, what is the...Ch. 2.10 - The outer perimeter of the Smith chart represents...Ch. 2.10 - What is an SWR circle? What quantities are...Ch. 2.10 - What line length corresponds to one complete...Ch. 2.10 - Which points on the SWR circle correspond to...Ch. 2.10 - Prob. 23CQCh. 2.10 - Use the Smith chart to find the values of ...Ch. 2.11 - Prob. 24CQCh. 2.11 - Prob. 25CQCh. 2.12 - What is transient analysis used for?Ch. 2.12 - Prob. 28CQCh. 2.12 - What is the difference between the bounce diagram...Ch. 2 - A transmission line of length l connects a load to...Ch. 2 - Show that the transmission-line model shown in...Ch. 2 - A 1 GHz parallel-plate transmission line consists...Ch. 2 - For the parallel-plate transmission line of...Ch. 2 - In addition to not dissipating power, a lossless...Ch. 2 - For a distortionless line [see Problem 2.13] with...Ch. 2 - Prob. 15PCh. 2 - A transmission line operating at 125 MHz has Z0 =...Ch. 2 - Prob. 17PCh. 2 - Polyethylene with r=2.25 is used as the insulating...Ch. 2 - Prob. 20PCh. 2 - Prob. 21PCh. 2 - Prob. 22PCh. 2 - Prob. 23PCh. 2 - A 50 lossless line terminated in a purely...Ch. 2 - Prob. 26PCh. 2 - Prob. 27PCh. 2 - Prob. 29PCh. 2 - Prob. 30PCh. 2 - Two half-wave dipole antennas, each with an...Ch. 2 - Prob. 34PCh. 2 - For the lossless transmission line circuit shown...Ch. 2 - A lossless transmission line is terminated in a...Ch. 2 - The input impedance of a 31 cm long lossless...Ch. 2 - FM broadcast station uses a 300 transmission line...Ch. 2 - A generator with Vg=300 V and Zg = 50 is...Ch. 2 - If the two-antenna configuration shown in Fig....Ch. 2 - For the circuit shown in Fig. P2.44, calculate the...Ch. 2 - The circuit shown in Fig. P2.45 consists of a 100 ...Ch. 2 - An antenna with a load impedance ZL=(75+j25) is...Ch. 2 - Prob. 47PCh. 2 - Use the Smith chart to determine the input...Ch. 2 - Prob. 52PCh. 2 - A lossless 50 transmission line is terminated in...Ch. 2 - A lossless 50 transmission line is terminated in...Ch. 2 - Use the Smith chart to find yL if zL = 1.5 j0.7.Ch. 2 - Prob. 59PCh. 2 - Prob. 62PCh. 2 - Determine Zin of the feed line shown in Fig....Ch. 2 - Prob. 73PCh. 2 - A 25 antenna is connected to a 75 lossless...Ch. 2 - Prob. 75PCh. 2 - Prob. 76PCh. 2 - Prob. 77PCh. 2 - In response to a step voltage, the voltage...Ch. 2 - Suppose the voltage waveform shown in Fig. P2.77...Ch. 2 - For the circuit of Problem 2.80, generate a bounce...Ch. 2 - In response to a step voltage, the voltage...
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- This question is about microwave material. I need a solution as soon as possible, pleasearrow_forwardI Need the answer fastTable Provided if neededarrow_forwardIf the amplitude of the input reflection coefficient is 0.5 with an angle of 45 degrees and the length of the transmission line is I= 0.15A, find the impedance of the load. (Z0=50ohm) Zin =? SWR=? YL=? ZL=?arrow_forward
- A 500 transmission line is biased with a load with impedance ZL=100-j200n. Its wavelength is 12cm. a-The reflection coefficient in the load. b-The standing-wave ratio on the line. C-The voltage maximum position closest to the load. d-Determine the current maximum position closest to the load.arrow_forwardThe following lossless network excited with the microwave source having f 9 GHz. if Zo=74 2, 6, =5,8, then L (nH/m) =? C(pF/m)%=? fro per unit length transmission line L= nH/m C= pF/m 3λ m ZLarrow_forwardI need the answer as soon as possiblearrow_forward
- Calculate the guided intrinsic impedance at 20 GHz for the lowest-order mode of therectangular waveguide with dimensions a=0.7 in and b=0.3 in.Take relative permittivity as 2.76.arrow_forwardTn=3.14 For a Transmission line, L=6,4 nH/m, R=2,9 0/m, C=1,2 µF/m and G=8,5 S/m (f = 1 GHz). For the transmission line with 10 cm length, if Z = ZR + jZ, then ZR =? Circunt Analys of bronsmasion kinesi tett 6dz VITE Leinductonce wart lenpth_Hm por volt lenpth per Cs Copacltonce Flm for the trema 6. Condluctona " mlos lm ke comt Ri Besletonce 介arrow_forwardMicrowavearrow_forward
- The cutoff frequency is operating at 6 GHz has In an air-filled waveguide, a TE mode E. = 15 sin %3D COS TCy sin (ot-122) Vm (B) 5.973 GHz (A) 4.189 GHz ( (D) 7.946 GHz (C) 8.438 GHzarrow_forwardA 100 Q transmission line has an effective dielectric constant of 1.65. Find the shortest open-circuited length of this line that appears at its input as a capacitor of 5 pF at 2.5 GHz. Repeat for an inductance of 5 nH.arrow_forwardI want a solution for branches A and B, pleaseA) Determine the primary constants, R, L, G, and C for a distortion-less line working at 300 MHz. Given that the line has characteristic impedance, Zo=750, attenuation constant a=0.12Np/m, and wave velocity, v=1.4×10 m/sB) A lossless transmission line used in a TV receiver has a capacitance of 50 pF/m and an inductance of 200 nH/m. Find the characteristic impedance for sections of a line 10 meter long and 500 m long.arrow_forward
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