
57Fundamentals of Wave Propagation
Equations 2.76 and 2.77 can be manipulated to relate
Γ
with Z
0
and Z
R
as
Γ =
′′
′
=
+
= −
′′
′
=
+
V
V
Z Z
Z Z
I
I
Z Z
Z Z
R
R
R
R
0
0
0
0
(2.78)
2.23.2.2 Hyperbolic Form
The alternative form of solutions of Equations 2.71 and 2.72 is
V A h z B h z= +
1 1
cos sin γ γ
(2.79a)
I A h z B h z= +
2 2
cos sin γ γ
(2.79b)
These equations can be manipulated to obtain general transmission line
equations that relate the voltages and currents at the receiving and transmit-
ting ends (Figure 2.27).
For lossy line
V V h l I Z h l
S R R
= +cos sin γ γ
0
(2.80a)
I I h l
V
Z
h l
S R
R
= +cos sin γ γ
0
(2.80b)
For lossless line
V V l jI Z l
S R R
= +cos