Fundamentals of Applied Electromagnetics (7th Edition)
7th Edition
ISBN: 9780133356984
Author: ULABY
Publisher: PEARSON
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Textbook Question
Chapter 2.10, Problem 22CQ
Which points on the SWR circle correspond to locations of voltage maxima and minima on the line and why?
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Students have asked these similar questions
The input reactance of an infinitesimal linear dipole of length A/60 and radius a=A/200
is given by
Xin = – 120
[In(€/a) — 1]
tan(ke)
Assuming the wire of the dipole is copper with a conductivity of 5.7 x 10' S/m,
determine at f = 1 GHz the
(a) loss resistance
(b) radiation resistance
(c) radiation efficiency
(d) VSWR when the antenna is connected to a 50-ohm line
Example
Solve the octic polynomial
2x⁸-9x⁷+20x⁶-33x⁵+46x⁴-66x³+80x²-72x+32=0
Solution
Divide by x⁴
2x⁴-9x³+20x²-33x+46-66/x + 80/x² - 72/x³ + 32/x⁴=0
Combine and bring terms
2(x⁴+16/x⁴) - 9(x³+8/x³) +20(x²+4/x²)-33(x+2/x) + 46= 0
Let use substitution
Let x+2/x =u
(x+2/x)²= u²
x²+2x*2/x + 4/x² = u²
x²+4/x²= u²-4
(x+2/x)³= x³+8/x³+3x*2/x(x+2/x)
u³= x³+8/x²+6u
x³+8/x³= u³-6u
(x²+4/x²)²= x⁴+2x²*4/x² + 16/x⁴
(u²-4)²= x⁴+16/x⁴ + 8
x⁴+16/x⁴ = (u²-4)²-8
x⁴+16/x⁴ = u⁴-8u²+8
2(u⁴-8u²+8)-9(u³-6u)+20(u²-4)-33u+46=0
Expand and simplify
2u⁴-9u³+4u²+21u-18=0
After checking
(u-1)(u-2) Are factors
Then
2u²-3u-9=0
u=3, u=-3/2
Assignment question
Solve the octic polynomial
2s⁸+s⁷+2s⁶-31s⁴-16s³-32s²-160=0 using the above example question, please explain in detail
b)
Another waveform g(t) is defined by
=0
t≥0, α>0
otherwise
g(t)= At exp(-at)
and is plotted in Figure 1 (for representative values of 4 = 1 and α = 1).
g(t)
0.4T
0.3+
0.2
0.1+
2
0
2
Figure 1
8
c)
Show that its amplitude spectrum is |G(@)| = -
A
(a²+0²)²
Describe briefly, with the aid of labelled sketches, how changing a affects
the waveform in both the time and frequency domains.
d) Deduce the Fourier transform H(@) of h(t) = g(t)+g(t+b)+g(t-b) and
calculate its DC amplitude H(0).
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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