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Characteristic Impedance Contnd.

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- Air Dielectric Parallel Line
- Coaxial Cable

Where: D = spacings between centres of the conductors

r = conductor radius

- 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).

- 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

- 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)

- 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)

- 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

- 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)

- 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

- 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

- What length of RG-8/U (vf = .66) would be required to obtain a 30 degree phase shift at 100 Mhz?