
289Scattering Parameters
Thus
s
13
= s
31
s
12
= s
21
s
23
= s
32
= s
13
(8.13)
The refection coefcient s
33
= 0 as port 3 is perfectly matched.
In view of the above properties, [S] matrix can be modied to
[ ] S
s s s
s s s
s s
=
11 12 13
12 22 13
13 13
0
(8.14)
In view of unity property
[s
ij
] [s
ij
*
] = [I] (8.15)
s s s
s s s
s s
s s s
s s s
11 12 13
12 22 13
13 13
11 12 13
12 22 13
0
* * *
* * **
* *
s s
13 13
0
1 0 0
0 1 0
0 0 1
=
(8.16)
This leads to the following set of equations:
s
11
s
11
*
+ s
12
s
12
*
+ s
13
s
13
*
= 1 (8.17a)
s
12
s
12
*
+ s
22
s
22
*
+ s
13
s
13
*
= 1 (8.17b)
s
13
s
13
*
+ s
13
s
13
*
= 1 (8.17c)
Using zero property,
s
13
s
11