ECE 3025C
--
Electromagnetics
Homework Assignment
#2
September 6, 2007
Problem 1.
Consider the following circuit consisting of a generator, transmission line, and a resistive load at
the end of the transmission line:
The switch is thrown at
0
t
=
and
T
is the one way propagation time in the transmission line.
For times much greater than 10 reflections, the transmission line effects diminish and the
resultant equivalent circuit is:
For this equivalent circuit
L
V
is related to
g
V
,
g
R
and
L
R
by:
L
L
g
g
L
R
V
V
R
R
⎛
⎞
=
⎜
⎟
⎜
⎟
+
⎝
⎠
(2.1)
If all line reflections are considered as
t
→ ∞
,
then
L
V
, the steady state voltage on the line and
across the load, may be expressed in terms of reflection coefficients
L
Γ
and
G
Γ
as:
1
1
O
L
L
g
O
G
L
G
Z
V
V
Z
R
⎛
⎞
+ Γ
=
⎜
⎟
+
− Γ Γ
⎝
⎠
(2.2)
Use equations
L
O
L
L
O
R
Z
R
Z
−
Γ
=
+
and
G
O
G
G
O
R
Z
R
Z
−
Γ
=
+
to show that Equation 2.2 reduces to the
equivalent circuit described by Equation 2.1.

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