Fundamentals of Electromagnetics for Teaching and Learning: A Two-Week Intensive Course for Faculty in Electrical-, Electronics-, Communication-, and Computer- Related Engineering Departments in Engineering Colleges in India - PowerPoint PPT Presentation

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Fundamentals of Electromagnetics for Teaching and Learning: A Two-Week Intensive Course for Faculty in Electrical-, Electronics-, Communication-, and Computer- Related Engineering Departments in Engineering Colleges in India

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Title: Fundamentals of Electromagnetics for Teaching and Learning: A Two-Week Intensive Course for Faculty in Electrical-, Electronics-, Communication-, and Computer- Related Engineering Departments in Engineering Colleges in India


1
Fundamentals of Electromagnetics for Teaching and
Learning A Two-Week Intensive Course for Faculty
in Electrical-, Electronics-, Communication-, and
Computer- Related Engineering Departments in
Engineering Colleges in India
  • by
  • Nannapaneni Narayana Rao
  • Edward C. Jordan Professor Emeritus
  • of Electrical and Computer Engineering
  • University of Illinois at Urbana-Champaign, USA
  • Distinguished Amrita Professor of Engineering
  • Amrita Vishwa Vidyapeetham, India

2
Program for Hyderabad Area and Andhra Pradesh
Faculty Sponsored by IEEE Hyderabad Section, IETE
Hyderabad Center, and Vasavi College of
Engineering IETE Conference Hall, Osmania
University Campus Hyderabad, Andhra Pradesh June
3 June 11, 2009 Workshop for Master Trainer
Faculty Sponsored by IUCEE (Indo-US Coalition for
Engineering Education) Infosys Campus, Mysore,
Karnataka June 22 July 3, 2009
3
  • Module 7
  • Transmission Line Analysis in Time Domain
  • 7.1 Line terminated by a resistive load
  • 7.2 Transmission-line discontinuity
  • 7.3 Lines with reactive terminations and
    discontinuities
  • 7.4 Lines with initial conditions
  • 7.5 Lines with nonlinear elements

4
Instructional Objectives
  • 49. Find the voltage and current variations at a
    location on a
  • lossless transmission line a functions of
    time and at an
  • instant of time as functions of distance,
    and the steady
  • state values of the line voltage and
    current, for a line
  • terminated by a resistive load and excited
    by turning on a
  • constant voltage source, by using the
    bounce-diagram
  • technique
  • 50. Design a lossless transmission line system by
    determining
  • its parameters from information specified
    concerning the
  • voltage and/or current variations on the
    line
  • 51. Design a system of three lines in cascade for
    achieving a
  • specified unit impulse response

5
Instructional Objectives (Continued)
  • 52. Compute the reflected power for a wave
    incident on a
  • junction of multiple lossless transmission
    lines from one
  • of the lines and the values of power
    transmitted into each
  • of the other lines, where the junction may
    consist of lines
  • connected in series, parallel, or
    series-parallel, and
  • include resistive elements
  • 53. Find the solutions for voltage and current
    along a
  • transmission-line system excited by a
    constant voltage
  • source and having reactive elements as
  • terminations/discontinuities
  • 54. Find the voltage and current variations at a
    location on a
  • lossless transmission-line system as
    functions of time and
  • at an instant of time as functions of
    distance, for specified
  • nonzero initial voltage and/or current
    distributions along
  • the system

6
Instructional Objectives (Continued)
  • 55. Analyze a transmission line terminated by a
    nonlinear
  • element by using the load line technique
  • 56. Understand the effect of time delay in
    interconnections
  • between logic gates

7
  • 7.1 Line Terminated
  • by Resistive Load
  • (EEE, Sec. 6.2 FEME, Sec. 7.4)

8
Notation
9
(No Transcript)
10
Assuming Z0 50 O,
11
Assuming Z0 50 O,
12
  • Excitation by Constant Voltage Source
  • Semi-infinite Line, No Source Resistance

13
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14
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15
  • E7.1

t, ms
t, ms
16
t 1 ms
17
  • Effect of Source Resistance

B.C.
() Wave
18

19
  • Line Terminated by Resistance

20
7-19
21
  • Define Voltage Reflection Coefficient,
  • Then, Current Reflection Coefficient

22

23

24
7-23
25
7-24

26
(No Transcript)
27
  • For constant voltage source,
  • Actual Situation in the Steady State
  • One () Wave and One () Wave

28

Four equations for the four unknowns
29
  • E7.2

30
  • Solving, we obtain

31
7-30
7-30
  • Bounce Diagram Technique
  • Constant Voltage Source
  • E7.3

32
7-31
  • Voltage

33
7-32
  • Current

34
7-33
  • Voltage Current

35

36

37

38

39
7-38
  • Rectangular Pulse Source
  • Use superposition.
  • E7.4

t, ms
40
7-39
t, ms
41
Review Questions
  • 7.1. Discuss the general solutions for the line
    voltage and
  • line current and the notation associated
    with their
  • interpretation in concise form.
  • 7.2. What is the fundamental distinction between
    the
  • occurrence of the response in one branch
    of a lumped
  • circuit to the application of an
    excitation in a different
  • branch of the circuit and the occurrence
    of the response
  • at one location on a transmission line to
    the application of
  • an excitation at a different location on
    the line?
  • 7.3. Describe the phenomenon of the bouncing back
    and forth
  • of transient waves on a transmission line
    excited by a
  • constant voltage source in series with
    internal resistance
  • and terminated by a resistance.

42
Review Questions (Continued)
  • 7.4. What is the nature of the formula for the
    voltage
  • reflection coefficient? Discuss its
    values for some
  • special cases.
  • 7.5. What is the steady state equivalent of a
    line excited by a
  • constant voltage source? What is the
    actual situation in
  • the steady state?
  • 7.6. Discuss the bounce diagram technique of
    keeping track
  • of the bouncing back and forth of
    transient waves on a
  • transmission line for a constant voltage
    source.
  • 7.7. Discuss the bounce diagram technique of
    keeping track
  • of the bouncing back and forth of
    transient waves on a
  • transmission line for a pulse voltage
    source.

43
Problem S7.1. Plotting line voltage and line
current on a transmission-line system involving
two lines
44
Problem S7.2. Finding several quantities
associated with a transmission-line system from
given observations
45
Problem S7.3. Time-domain analysis of a
transmission- line system using the bounce
diagram technique
46
Problem S7.4. Time-domain analysis of a
transmission- line system for a sinusoidal
excitation
47
  • 7.2 Transmission-Line
  • Discontinuity
  • (EEE, Sec. 6.3)

48
  • Transmission-Line Discontinuity

49
(No Transcript)
50

51
7-50
  • Current Transmission Coefficient,

Define Voltage Transmission Coefficient,
52
7-51
  • Note that

53
7-52
  • Three Lines in Cascade
  • E7.5

54
7-53
55
(No Transcript)
56
7-55
7-55
57
7-56
58

59

w
60
  • Junction of Three Lines
  • E7.6

61
7-60
62
7-61
63
7-62
7-62
64
Review Questions
  • 7.8. Discuss the phenomenon of reflection and
    transmission
  • for a wave incident on a junction
    between two
  • transmission lines.
  • 7.9. How are the voltage and current
    transmission
  • coefficients at a junction between two
    lines related to
  • voltage reflection coefficient?
  • 7.10. Explain how it is possible for the
    transmitted voltage or
  • current at a junction between two
    transmission lines to
  • exceed the incident voltage or current,
    respectively.
  • 7.11. Discuss the determination of the unit
    impulse response
  • of a system of three lines in cascade.
  • 7.12. Outline the procedure for the determination
    of the
  • frequency response of a system of three
    lines in cascade
  • from its unit impulse response.

65
Review Questions (Continued)
  • 7.13. Discuss the determination of the reflection
    and
  • transmission coefficients at a junction
    connecting a
  • transmission line to two lines in
    parallel.
  • 7.14. How would you determine the reflection and
  • transmission coefficients at a junction
    connecting a
  • transmission line to two lines in
    series?

66
Problem S7.5. Finding three parameters for a
system of three media from unit impulse response
67
Problem S7.5. Finding three parameters for a
system of three media from unit impulse response
(Continued)
68
Problem S7.6. Analysis of a system of three
transmission lines excited by a pulse voltage
source
69
Problem S7.6. Analysis of a system of three
transmission lines excited by a pulse voltage
source (Continued)
70
Problem S7.7. A system of three transmission
lines with a resistive network at the junction
71
  • 7.3 Lines with
  • Reactive Terminations
  • and Discontinuities
  • (EEE, Sec. 6.4)

72
  • Line Terminated by an Inductor
  • E7.7
  • t T

73
7-72

Using I.C.,
74
7-73

75

Voltage
G 0
76
G 0
77

78

79
  • Line Terminated by a Capacitor
  • E7.8
  • t T

80
7-79

81
7-80
  • Using I.C.,

t gt T
t gt T
82
Review Questions
  • 7.16. Discuss the transient analysis of a line
    driven by a
  • constant voltage source in series with a
    resistance equal
  • to Z0 of the line and terminated by an
    inductor.
  • 7.17. Why is the concept of reflection
    coefficient not useful
  • for studying the transient behavior of
    lines with reactive
  • terminations and discontinuities?
  • 7.18. Outline the transient analysis of a line
    driven by a
  • constant voltage source in series with a
    resistance equal
  • to Z0 of the line and terminated by a
    capacitor.

83
Problem S7.8. Transient analysis of a
transmission line terminated by a capacitive
network
84
Problem S7.9. Finding the nature of a
discontinuity in a transmission line system
85
  • 7.4 Lines with
  • Initial Conditions
  • (EEE, Sec. 6.5 FEME, Sec. 7.5)

86
  • Line with Initial Conditions

87

88
  • E7.9

89
7-88
90
7-89
91
7-90
7-90

92
(No Transcript)
93
7-92
7-92
94
7-93
  • Uniform Distribution
  • E7.10

95

96
(No Transcript)
97
(No Transcript)
98
  • Bounce Diagram Technique for
  • Uniform Distribution

99

100

101
  • Energy Storage in Transmission Lines
  • we, Electric stored energy density
  • We, Electric stored energy

102
  • wm, Magnetic stored energy density
  • Wm, Magnetic stored energy

103
  • Check of Energy Balance
  • Initial stored energy

104
  • Energy dissipated in RL

105
7-104
  • E7.11
  • System in steady state at t 0.

106
  • t 0 steady state

107
  • t 0

108
  • Solving, we obtain

109
7-108
  • Voltage

G 0
G 0
tV 1
110
7-109
  • Current

G 0, tC 1
tCeff 0.5
G 0
111
7-110
  • New steady state

112
7-111
113
Review Questions
  • 7.19. Discuss the determination of the voltage
    and current
  • distributions on an initially charged
    line for any given
  • time from the knowledge of the initial
    voltage and
  • current distributions.
  • 7.20. Discuss with the aid of an example the
    discharging of an
  • initially charged line into a resistor.
  • 7.21. Discuss the bounce-diagram technique of
    transient
  • analysis of a line with uniform initial
    voltage and
  • current distributions.
  • 7.22. How do you check the energy balance for the
    case of a
  • line with initial voltage and/or current
    distribution(s)
  • and discharged into a resistor?

114
Problem S7.10. For the analysis of an
initially-charged transmission line discharging
into a resistor
115
Problem S7.10. For the analysis of an
initially-charged transmission line discharging
into a resistor (Continued)
116
Problem S7.11. Analysis of a system of an
initially-charged line connected to another
initially-charged line
117
Problem S7.12. For the analysis of an initially
charged transmission line connected to a
capacitor
118
  • 7.5 Lines with
  • Nonlinear Elements
  • (EEE, Sec. 6.6 FEME, Sec. 7.6)

119
Nonlinear Termination Load line Technique E7.12
120
(No Transcript)
121
(No Transcript)
122
(No Transcript)
123
(No Transcript)
124
(No Transcript)
125
Interconnection Between Logic Gates
126
(No Transcript)
127
(No Transcript)
128
(No Transcript)
129
(No Transcript)
130
(No Transcript)
131
Review Questions
  • 7.23. Discuss the load-line technique of
    obtaining the time
  • variations of the voltages and currents
    at the source and
  • load ends of a line from the knowledge
    of the terminal
  • V-I characteristics.
  • 7.24. Discuss the analysis of interconnection
    between logic
  • gates, using transmission line.

132
Problem S7.13. Application of load-line
technique for an initially charged line
discharging into a nonlinear resistor
133
The End
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