Transcript Velocity Factor

Characteristic Impedance Contnd.
• Air Dielectric Parallel Line
D
Zo  276log
r
Where: D = spacings between
centres of the conductors
r = conductor radius
• Coaxial Cable
138
D
ZO 
log
r d
where: D  inside diameter of outer conductor
d  inside diameter of outer conductor
 r  relative permittivity of the dielectric
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
Vp
Vf 
C
Vf 
v f  velocity factor
v p  propagation velocityof the line
C  speed of light
r  dielectriccons tan t
1
r
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)
L
T
Vp
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
Vr

Vi
Vr Zl  Zo

Vi Zl  Zo
Zl  Zo

Zl  Zo
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
d
v
t
vp 

T
1
f 
T
  360
v p  f
L

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?