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Characteristic Impedance Contnd. Air Dielectric Parallel Line Coaxial Cable. Where: D = spacings between centres of the conductors r = conductor radius. Velocity Factor. The speed at which an energy is propagated along a transmission line is always less than the speed of light.

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characteristic impedance contnd
Characteristic Impedance Contnd.
  • Air Dielectric Parallel Line
  • Coaxial Cable

Where: D = spacings between centres of the conductors

r = conductor radius

velocity factor
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).
response of line
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

open circuited line
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?
  • For what time frame do the initial conditions exist? (2T)
  • What is the relative direction of incident and reflected current?(opposite)
short circuit line
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? (V=0 and I depends on system characteristics)
  • What is the direction of incident and reflected current? (same)
pulse input to transmission line
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 line > gamma = 1

- Matched line > gamma = 0

- Short circuit line > gamma = -1

traveling waves along a line
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)
standing waves
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
standing waves contnd
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
sample question
Sample question
  • What length of RG-8/U (vf = .66) would be required to obtain a 30 degree phase shift at 100 Mhz?
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