Digital Signal Processing Reference
In-Depth Information
ports. The conversion from
S
-to
T
-parameters is derived here for a two-port sys-
tem to demonstrate the process. To begin, the equations that relate the incoming
power waves to the outgoing are written
b
1
=
S
11
a
1
+
S
12
a
2
b
2
=
S
21
a
1
+
S
22
a
2
and equation (9-47) is expressed in algebraic form:
a
1
=
T
11
b
2
+
T
12
a
2
b
1
=
T
21
b
2
+
T
22
a
2
From the equations above, the individual
T
-parameters can be defined in terms
of the
S
-parameters:
a
2
=
0
a
1
b
2
T
11
=
b
2
=
S
21
a
1
+
S
22
(
0
)
1
S
21
T
11
=
(9-48a)
b
2
=
0
b
1
a
2
T
22
=
S
22
a
2
S
21
0
=
S
21
a
1
+
S
22
a
2
→
a
1
=−
S
12
a
2
S
11
S
22
S
21
b
1
=
S
11
a
1
+
S
12
a
2
=
−
S
11
S
22
S
21
=
S
12
−
T
22
(9-48b)
b
2
=
0
a
1
a
2
T
12
=
0
=
S
21
a
1
+
S
22
a
2
S
22
a
2
S
21
a
1
=−
S
22
S
21
T
12
=−
(9-48c)
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