WOLFRAM|DEMONSTRATIONS PROJECT

Surge Propagation in a Transmission Line

​
display item
voltage
current
input pulse
input impedance
output impedance
duration:
T
i
/ T
(to transit time)
0.5
wavefront (%):
20
R
i
/
Z
0
(to surge
impedance)
0.2
R
o
/
Z
0
(to surge
impedance)
2
A lossless transmission line is characterized by the surge impedance
Z
0
and surge velocity
v
0
. When the transmission line is energized by a voltage source
V
p
, a forward surge
(1)
f
1
is created (the magnitude:
Z
0
V
p
(
R
i
+
Z
0
)
, where
R
i
is the input circuit impedance). The surge reaches the other end in the transit time
T=L/
v
0
,
L
being the line length. Then, a backward surge
(1)
f
2
is generated by the reflection factor
t
o
=(
R
o
-
Z
0
)/(
R
o
+
Z
0
)
,
R
o
being the output impedance. This wave generates another forward surge
(2)
f
1
by the factor
t
i
=(
R
i
-
Z
0
)/(
R
i
+
Z
0
)
at the initial terminal. The voltage and current in the transmission line are described by the superposition of those successive forward and backward components
(i)
f
1
and
(i)
f
2
.
This Demonstration shows the variation of voltage in space and time
V(x,t)
in a 3D graphic for a triangular-shaped input voltage, for a variety of conditions. You can vary the terminal impedances and input voltage duration. You can also display the corresponding current
I(x,t)
.