# Characteristic Impedance Contnd. - PowerPoint PPT Presentation

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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.

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### Characteristic Impedance Contnd.

• Air Dielectric Parallel Line

• Coaxial Cable

Where: D = spacings between centres of the conductors

### 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

• 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

• 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

• 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

• 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

• 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

• 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.

• 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

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