
294 Microwave Engineering
Substitution of
11
s
13
=
1/ 2√
and in view of Equations 8.39a and
8.39b, Equation 8.32 leads to
[ ]S = −
−
1 2 1 2 1 2
1 2 1 2 1 2
1 2 1 2 0
/ / /
/ / /
/ /
(8.41)
In view of Equation 8.8
Thus,
b
b
b
a
1
2
3
1
1 2 1 2 1 2
1 2 1 2 1 2
1 2 1 2 0
= −
−
/ / /
/ / /
/ /
aa
a
2
3
(8.42)
From Equation 8.42, we get
b a a a
1 1 2 3
1
2
1
2
1
2
= + +
(8.43a)
b a a a
2 1 2 3
1
2
1
2
1
2
= + −
(8.43b)
b a a
3 1 2
1
2
1
2
= −
(8.43c)
As power is fed through port 3, a
3
≠ 0 and if a
1
= a
2
= 0
b a
1 3
2
=
(8.44a)
b a
2 3
= −
(8.44b)
and
b
3
= 0 (8.44c)
Equation 8.44 indicates that an input power fed to port 3 will be equally
divided ...