Characteristic Impedance Contnd'

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Characteristic Impedance Contnd.

• Air Dielectric Parallel Line
• Coaxial Cable

Where D spacings between centres of the
conductors r conductor radius
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Velocity Factor

• The speed at which an energy is propagated along
  a transmission line is always less than the speed
  of light.
• Almost entirely dependant upon the dielectric
  constant
• Propagation velocity of signal can vary from 66
  (coax with polyethylene dielectric) to 95(air).

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Velocity Factor and Propagation Velocity
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Response of Line

• CONDITIONS
• Step Impulses
• Assume lossless line and infinite length with Zo
  equal to characteristic impedance of the line
• Discuss
• -Reflections along a line of finite length
  that is
• a.) Open at point of termination (end of
  line)
• b.) Shorted at point of termination
• c.) Matched load at point of termination

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Open Circuited Line

• Switch is closed and followed by a surge down
  line.
• How much of the source voltage appears across the
  source? (V/2)
• What is the state of voltage and current at the
  end of the line?
• - equals the incident voltage (V)
• For what time frame do the initial conditions
  exist? (2T)
• What is the relative direction of incident and
  reflected current?(opposite)

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Short Circuit Line

• What is the state of voltage at the source prior
  to 2T? (V/2)
• What is the state of voltage and current when the
  surge reaches the load? (V0 and I depends on
  system characteristics)
• What is the direction of incident and reflected
  current? (same)

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Pulse Input To Transmission Line

• With a matched line the load absorbs energy and
  there is no reflection
• Open circuit has positive reflections
• Short Circuit has negative reflections
• REFLECTION COEFFICIENT(Gamma)
• - Open circuit linegt gamma 1
• - Matched line gt gamma 0
• - Short circuit line gt gamma -1

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Gamma and Reflection Coefficient
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t0
Ri50 ohm 1 V
RL25 ohm
Zo50 ohm vf0.7
10 m
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Traveling Waves Along A Line

• Assume a matched line and a sinusoidal signal
  source.
• Traveling wave
• After initial conditions a steady state situation
  exists.
• Signal will appear the same as the source at any
  point on the line except for time delay.
• Time delay causes a phase shift ( one period
  360 degrees)

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Length of Line/Wavelength/Phase Shift
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Standing Waves

• Assume a transmission line with an open
  termination, a reasonably long line and a
  sinusoidal source
• After initial reflection the instantaneous values
  of incident and reflected voltage add
  algebraically to give a total voltage
• Resultant amplitude will vary greatly due to
  constructive and destructive interference between
  incident and reflected waves

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Standing Waves contnd.

• Reminder A sine wave applied to a matched line
  develops an identical sine wave except for phase.
• If the line is unmatched there will be a
  reflected wave.
• The interaction of the two travelling waves (vr
  and vi) result in a standing wave.
• SWR Vmax/Vmin

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Sample question

• What length of RG-8/U (vf .66) would be
  required to obtain a 45 degree phase shift at 100
  Mhz?

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