Fundamentals of Electromagnetics: A Two-Week, 8-Day, Intensive Course for Training Faculty in Electrical-, Electronics-, Communication-, and Computer- Related Engineering Departments

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Fundamentals of ElectromagneticsA Two-Week,
8-Day, Intensive Course for Training Faculty in
Electrical-, Electronics-, Communication-, and
Computer- Related Engineering Departments

• 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
• Amrita Viswa Vidya Peetham, Coimbatore
• August 11, 12, 13, 14, 18, 19, 20, and 21, 2008

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• Module 7
• Transmission Line Analysis in Time Domain
• Line terminated by a resistive load
• Transmission-line discontinuity
• Lines with reactive terminations and
  discontinuities
• Lines with initial conditions

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Instructional Objectives

• 30. Find the voltage and current variations at a
  location on a lossless transmission line as
  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
• 31. Design a lossless transmission line system
  by determining its parameters from information
  specified concerning the voltage and/or current
  variations on the line
• 32. Design a system of three lines in cascade
  for achieving a specified unit impulse response

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Instructional Objectives

• 33. 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
• 34. 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
• 35. 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

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• Line Terminated
• by Resistive Load
• (FEME, Sec. 7.4 EEE6E, Sec. 6.2)

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Notation
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• Excitation by Constant Voltage Source
• Semi-infinite Line, No Source Resistance

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• Example

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

B.C.
() Wave
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• Line Terminated by Resistance

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• Define Voltage Reflection Coefficient,
• Then, Current Reflection Coefficient

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• For constant voltage source,
• Actual Situation in the Steady State
• One () Wave and One () Wave

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Four equations for the four unknowns
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• Example

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• Solving, we obtain

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• Bounce Diagram Technique
• Constant Voltage Source

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• Voltage

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• Current

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• Voltage Current

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• Rectangular Pulse Source
• Use superposition.
• Example

t, ms
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t, ms
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• Transmission-Line
• Discontinuity
• (EEE6E, Sec. 6.3)

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• Transmission-Line Discontinuity

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• Current Transmission Coefficient,

Define Voltage Transmission Coefficient,
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• Note that

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• Three Lines in Cascade

d(t)
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t, ms
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w
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• Junction of Three Lines

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• Lines with
• ReactiveTerminations
• and Discontinuities
• (EEE6E, Sec. 6.4)

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• Line Terminated by an Inductor
• t T

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Using I.C.,
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Voltage
G 0
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G 0
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• Line Terminated by a Capacitor
• t T

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• Using I.C.,

t gt T
t gt T
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• Lines with
• Initial Conditions
• (FEME, Sec. 7.5 EEE6E, Secs. 6.5)

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• Line with Initial Conditions

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• Example

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• Uniform Distribution

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• t 0.5 mS
• t 1.5 mS

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• t 2.5 mS

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• Bounce Diagram Technique for
• Uniform Distribution

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

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

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• Check of Energy Balance
• Initial stored energy

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• Energy dissipated in RL

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• Another Example
• System in steady state at t 0.

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• t 0 steady state

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• t 0

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• Solving, we obtain

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• Voltage

G 0
G 0
tV 1
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• Current

G 0, tC 1
tCeff 0.5
G 0
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• t 3 ms New steady state

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• t 3 ms

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The End