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 9, Problem 47P
A linear array arranged along the z axis consists of 12 equally spaced elements with d = λ/2. Choose an appropriate incremental phase delay δ so as to steer the main beam to a direction 30° above the broadside direction. Provide an expression for the array factor of the steered antenna and plot the pattern. From the pattern, estimate the beamwidth.
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If C is the circle |z|=4 evaluate ff(z)dz for each of the following
functions using residue.
Z
(a)f(z) = z²-1
Z+1
1
(b)f(z) =
=
(c)f(z)
=
z²(z+2)
z(z-2)³
z²
1
1
(d) f(z) =
=
(e) f(z) =
(f) f(z) =
(z²+3z+2)²
z²+z+1
z(z²+6z+4)
5. Answer the following questions. Take help from ChatGPT to answer these questions (if
you need). Write the answers briefly using your own words with no more than two sentences,
and check whether ChatGPT is giving you the appropriate answers in the context of our
class.
a) What is the Bode plot? What kind of input do we consider for the frequency-response-
based method?
b) What is the advantage of design using the frequency-response method?
c) Define gain margin, phase margin, gain crossover frequency, and phase crossover
frequency.
Phase (deg)
3. The Bode diagram of a system is shown below.
Magnitude (dB)
System: sys
-10
Frequency (rad/s): 0.141
Magnitude (dB): -15.6
-20
-30
40
-50
-60
0
-45
-90
-135
101
10°
Bode Diagram
System: sys
Frequency (radis): 10
Magnitude (dB): -18.9
System: sys
Frequency (rad/s): 10
Phase (deg):-52.2
101
Frequency (rad/s)
102
103
Find the steady-state output of the system for each of the following inputs.
a) u(t) = 100
b) u(t) 100 cos(10 t + 10°)
=
c) u(t) = 500 + 200 cos(10 t + 10°)
Chapter 9 Solutions
Fundamentals of Applied Electromagnetics (7th Edition)
Ch. 9.1 - What does it mean to say that most antennas are...Ch. 9.1 - What is the radiated wave like in the far-field...Ch. 9.1 - In a Hertzian dipole, what is the underlying...Ch. 9.1 - Outline the basic steps used to relate the current...Ch. 9.1 - A 1 m long dipole is excited by a 5 MHz current...Ch. 9.2 - Prob. 5CQCh. 9.2 - What is the magnitude of the directivity of an...Ch. 9.2 - An antenna has a conical radiation pattern with a...Ch. 9.2 - Prob. 3ECh. 9.3 - What is the physical length of a half-wave dipole...
Ch. 9.3 - How does the radiation pattern of a half-wave...Ch. 9.3 - How does the radiation efficiency of a...Ch. 9.3 - Prob. 4ECh. 9.3 - Prob. 5ECh. 9.5 - Prob. 6ECh. 9.5 - At 100 MHz, the pattern solid angle of an antenna...Ch. 9.6 - If the operating frequency of the communication...Ch. 9.6 - Prob. 9ECh. 9.6 - Prob. 10ECh. 9.8 - Verify that Eq. (9.86) is a solution of Eq. (9.85)...Ch. 9.8 - Prob. 12ECh. 9.8 - What condition must be satisfied in order to use...Ch. 9.8 - Derive an expression for the array factor of a...Ch. 9.8 - Prob. 15ECh. 9.11 - Prob. 11CQCh. 9.11 - Prob. 12CQCh. 9.11 - Prob. 13CQCh. 9.11 - Prob. 14CQCh. 9.11 - Prob. 15CQCh. 9 - A center-fed Hertzian dipole is excited by a...Ch. 9 - A 50 cm long center-fed dipole directed along the...Ch. 9 - Prob. 3PCh. 9 - Determine the following: (a) The direction of...Ch. 9 - Repeat Problem 9.4 for an antenna with...Ch. 9 - A 2 m long center-fed dipole antenna operates in...Ch. 9 - Repeat Problem 9.6 for a 20 cm long antenna...Ch. 9 - Prob. 9PCh. 9 - An antenna with a radiation efficiency of 90% has...Ch. 9 - Prob. 11PCh. 9 - The normalized radiation intensity of a certain...Ch. 9 - Repeat Problem 9.6 for a 1 m long half-wave dipole...Ch. 9 - Prob. 14PCh. 9 - A 50 cm long dipole is excited by a sinusoidally...Ch. 9 - Prob. 16PCh. 9 - For a dipole antenna of length l = 3/2, (a)...Ch. 9 - Prob. 18PCh. 9 - Prob. 19PCh. 9 - Prob. 20PCh. 9 - A car antenna is a vertical monopole over a...Ch. 9 - Determine the effective area of a half-wave dipole...Ch. 9 - A 3 GHz line-of-sight microwave communication link...Ch. 9 - A half-wave dipole TV broadcast antenna transmits...Ch. 9 - A 150 MHz communication link consists of two...Ch. 9 - Consider the communication system shown in Fig....Ch. 9 - The configuration shown in Fig. P9.27 depicts two...Ch. 9 - Prob. 28PCh. 9 - The configuration shown in Fig. P9.29 depicts a...Ch. 9 - Prob. 30PCh. 9 - Prob. 31PCh. 9 - A uniformly illuminated rectangular aperture...Ch. 9 - An antenna with a circular aperture has a circular...Ch. 9 - Prob. 34PCh. 9 - Prob. 35PCh. 9 - Prob. 36PCh. 9 - Prob. 37PCh. 9 - Prob. 38PCh. 9 - Prob. 39PCh. 9 - Prob. 40PCh. 9 - Find and plot the normalized array factor and...Ch. 9 - Prob. 44PCh. 9 - A three-element linear array of isotropic sources...Ch. 9 - An eight-element linear array with /2 spacing is...Ch. 9 - A linear array arranged along the z axis consists...
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- Phase (deg) 270 4. Consider a closed-loop system with unity (negative) feedback. The Bode diagram of the open-loop transfer function is given below. Magnitude (dB) -500 -150 -50 10 dB System Frequency (eds): 6.63 Magnitude (B) 0.0778 Буку Frequency(): 10.1 Magnitude ()-705 Frequency(6.63 Phase (deg): -144 Frequency (rad): 10.1 Phase (deg): -180 101 Frequency (rad) a) Find the gain margin, phase margin, gain crossover frequency, and phase crossover frequency. b) Is the closed-loop system stable? What is the steady-state error for step-input?arrow_forwardelectric plantsarrow_forwardsolve and show workarrow_forward
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