299Scattering Parameters
As there is no coupling between port 1 and port 3 and between port 2 and
port 4, we have
s
13
= s
31
= 0 (8.61a)
and
s
24
= s
42
= 0 (8.61b)
In view of Equation 8.61, Equation 8.60 becomes
[ ] S
s s
s s
s s
s s
=
0 0
0 0
0 0
0 0
12 14
21 23
32 34
41 43
(8.62a)
Furthermore, in view of the symmetric property, Equation 8.62a gets mod-
ied to
[ ]S
s s
s s
s s
s s
=
0 0
0 0
0 0
0 0
12 14
12 23
23 34
14 34
(8.62b)
From unity property of S-matrix
0 0
0 0
0 0
0 0
0 0
12 14
21 23
32 34
41 43
12 14
21
s s
s s
s s
s s
s s
s
* *
*
00 0
0 0
0 0
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
23
32 34
41 43
s
s s
s s
*
* *
* *
=
(8.63)
In view of unity property, the product of the rst row of [S] and rst col-
umn of [S*] of Equation 8.63 gives
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