Characteristic Impedance Contnd

Characteristic Impedance Contnd.

• Air Dielectric Parallel Line

• Coaxial Cable

r

DZo log276

d

DZ

r

O log138

Where: D = spacings between centres of the conductors

r = conductor radius

dielectric theofty permittivi relative

conductorouter ofdiameter inside d

conductorouter ofdiameter inside D :where

r

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).

Velocity Factor and Propagation Velocity

C

VV pf r

V f 1

tconsdielectricr

lightofspeedC

linetheofvelocitynpropagatiov

factorvelocityv

p

f

tan

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)

pV

LT

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

Gamma and Reflection Coefficient

ZoZl

ZoZl

ZoZl

ZoZl

V

V

V

V

i

r

i

r

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)

Length of Line/Wavelength/Phase Shift

L

fvT

f

Tv

t

dv

p

p

360

1

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?