
190 Microwave Engineering
The substitution of Equation 6.2 in Equation 6.4 results in
Z
V
I
V e V e
I e I e
R jX
j l j l
j l j l
= =
′
+
′′
′
+
′′
= +
−
−
γ γ
γ γ
(6.14)
In view of Equations 6.3, 6.5 and 6.14
Z
V e e
I e e
Z
e e
e e
j l j l
j l j l
j l j l
j l j l
=
′
+
′
−
=
+
−
=
−
−
−
−
( )
( )
γ γ
γ γ
γ γ
γ γ
Γ
Γ
Γ
Γ
0
ZZ
e e e e
e e e e
Z
j l j l j l j l
j l j l j l j l
0
0
( )( )
( )( )
γ γ γ
γ γ γ
+ −
− −
=
− −
− −
Γ Γ
Γ Γ
γ
γ
(( ) ( )
( ) ( )
( )
1
1
1 2
2
2 2
2
2 2
0
2
− − −
+ − +
=
− −
−
−
Γ Γ
Γ Γ
Γ Γ
e e
e e
Z
j
j l j l
j l j l
γ γ
γ γ
ssin
( ) cos
2
1 2 2
2
γ
γ
l
l+ −Γ Γ
(6.15)
In view of the normalisation of impedance (z), Equation 6.15 leads repre-
senting normalised resistance (r) and reactance (x) which can be written as
r
l
=
−
+ −
1
1 2 2
2
2