Problem 7.19 Ignoring reection 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 characterized by r = 1, r = 9, and = 5 104
S/m.
Solution:
Family Name:
Given name:
Student number
Signature
Faculty of Applied Science and Engineering
ECE357 Electromagnetic Fields
First Test, February 16, 2006
Examiners M. Mojahedi
Only Calculators approved by Registrar allowed
Answer the questions in the space
UNIVERSITY OF TORONTO
FACULTY OF APPLIED SCIENCE AND ENGINEERING
The Edward S. Rogers Sr. Department of
Electrical and Computer Engineering
ECE320H1F FIELDS AND WAVES
PROBLEM SET 9
Topics: Plane-Wave Propagation, Propagation in lossy media, electromagneti
Problem 8.1 A plane wave in air with an electric eld amplitude of 20 V/m is
incident normally upon the surface of a lossless, nonmagnetic medium with r = 25.
Determine the following:
(a) The reection and transmission coefcients.
(b) The standing-wave rati
Problem 7.1 The magnetic eld 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) The phase velocity.
(c) The wavelength in the material.
(d)
Problem 3.41 Evaluate the line integral of E = x x y y along the segment P1 to P2
of the circular path shown in the gure.
y
P1 = (0, 3)
x
P2 = (3, 0)
Solution: We need to calculate:
P2
P1
E d .
Since the path is along the perimeter of a circle, it is bes
Problem 6.1 The switch in the bottom loop of Fig. P6.1 is closed at t = 0 and
then opened at a later time t1 . What is the direction of the current I in the top loop
(clockwise or counterclockwise) at each of these two times?
R2
I
t = t1
t=0
R1
Figure P6.
UNIVERSITY OF TORONTO
FACULTY OF APPLIED SCIENCE AND ENGINEERING
The Edward S. Rogers Sr. Department of
Electrical and Computer Engineering
ECE320H1F FIELDS AND WAVES
PROBLEM SET 5
Topics:
diagrams
Impedance matching, transient response of transmission li
UNIVERSITY OF TORONTO
FACULTY OF APPLIED SCIENCE AND ENGINEERING
The Edward S. Rogers Sr. Department of
Electrical and Computer Engineering
ECE320H1F FIELDS AND WAVES
PROBLEM SET 5
Topics:
Review of vector calculus
Reading:
Chapter 3
1.
2.
3.
4.
5.
6.
Ula
UNIVERSITY OF TORONTO
FACULTY OF APPLIED SCIENCE AND ENGINEERING
The Edward S. Rogers Sr. Department of
Electrical and Computer Engineering
ECE320H1F FIELDS AND WAVES
PROBLEM SET 4
Topics:
Time-harmonic behaviour of transmission lines, standing waves, Smi
UNIVERSITY OF TORONTO
FACULTY OF APPLIED SCIENCE AND ENGINEERING
The Edward S. Rogers Sr. Department of
Electrical and Computer Engineering
ECE320H1F FIELDS AND WAVES
PROBLEM SET 2
Topics:
Time-harmonic behaviour of transmission lines, standing waves
Read
ECE320 Quiz # 3 ' ' Page 1
PROBLEM #1. [10 POINTS]
A step function is launched onto a transmission line as shown in Figure 1. THe step function is
generated at t = O by the arrangement of the battery, resistor R5, and switch. The wave velocity of
the li
Family Name:
Given name:
Student number
Signature
Faculty of Applied Science and Engineering
ECE357 Electromagnetic Fields
First Test, February 4, 2005
Examiners M. Mojahedi
Only Calculators approved by Registrar allowed
Answer the questions in the spaces
Question 2 (35 marks)
A 75 lossless transmission line, with r = 2.25, is connected to a 40 V pulse generator with a
source impedance of 125 . The line is 200 m long and is terminated in a 25 load. At time
t = 0, a single rectangular pulse of width 1 s is
Assignment #1
ECE357 Electromagnetic Fields
Spring 2005 / University of Toronto
1. Show that e j cos j sin .
2. The current through a circuit is found to be I 6-40. What is the expression
for the time dependent current with 60 Hz?
Partial answer:
3. Prove
Transmission Lines Smith Chart &
Impedance Matching
(Intensive Reading)
1 The Smith Chart
Transmission line calculations such as the determination of input impedance using equation
(4.30) and the reflection coefficient or load impedance from equation (4.3
ECE 134
Introductory Electromagnetics
Prof. York
Review of Transmission-Line Theory
The term transmission-line in electromagnetics is commonly reserved for those structures which are capable of guiding TEM waves. Transmission-lines are a special class of
ECE320 Quiz # 4 Page 1
PROBLEM #1. [10 POINTS]
A stationary square loop of wire is placed in the cry-plane centred at the origin, as shown in Fig-
ure 1. The dimensions of the loop are 2 cm X 2 cm. A magnetic ux density passes through the
loop and is
ECE320 Quiz # 2 Page 1
PROBLEM #1. [10 POINTS]
A lossless transmission line with a length of K = 0.2 m is left opencircuited, as shown in Figure 1.
A travelling voltage wave with a frequency of 2 GHZ and an amplitude of V5 2 3 V is launched
onto the tra
ECE320H1F Fields and Waves
Problem Set 1 Solution
1.
Calculate the current phasor:
.
Convert to time domain:
0.6
0.6 cos
67
.
2. a) First convert from sin to cos, then convert into a phasor:
4 cos
90
3 cos
30
3 30
4 90
Transform back into time domain:
3 3
UNIVERSITY OF TORONTO
FACULTY OF APPLIED SCIENCE AND ENGINEERING
The Edward S. Rogers Sr. Department of
Electrical and Computer Engineering
ECE320H1F FIELDS AND WAVES
PROBLEM SET 3
Topics:
Time-harmonic behaviour of transmission lines, standing waves,
imp
ECE320H1F-Fields and Waves
Problem Set 3 Solutions
Fall 2010
1)
L 2
C 2
) (1 j
)
( R jL )(G jC ) RG (1 j
R
G
1
1
Now, use the following relation: (1 x) 2 1 x for x 1
2
L
C
(Note that
1 and
1 )
R
G
L
C
j L C
1 L C
j L C
RG (1 j
)(1 j
) RG 1
( ) (
)(
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