Digital Signal Processing Reference
In-Depth Information
Solving for
S
2
yields
Z
n
1
Z
n
2
(
U
U
−
1
Z
n
1
Z
n
2
(
U
U
S
1
)
−
1
S
1
)
−
1
S
2
=
+
S
1
)(
U
−
+
+
S
1
)(
U
−
−
(9-59)
Example 9-11
Renormalize the following
S
-matrix measured with a 50-
ref-
erence load to 75
:
0
.
385
0
.
385
j
0
.
923
S
50
=
j
0
.
923
SOLUTION Using equation (9-59), the
S
-matrix can be manipulated so that it
looks like it was measured with a 75-
reference impedance.
50
75
10
01
0
.
385
0
.
385
10
01
0
.
385
0
.
385
−
1
j
0
.
923
j
0
.
923
S
75
=
+
−
j
0
.
923
j
0
.
923
10
01
−
1
50
75
10
01
0
.
385
0
.
385
j
0
.
923
+
·
+
j
0
.
923
01
10
01
0
.
385
0
.
385
−
1
10
0
0
j
0
.
923
−
j
×
−
−
=
j
0
.
923
−
j
Therefore, the magnitude of the renormalized
S
-matrix is
01
10
|
S
75
|=
meaning that the transmission line is loss free with a characteristic impedance
of 75
since there is no reflection (
S
11
=
0) and the insertion loss is unity
(
S
21
=
1).
9.2.7 Multimode
S
-Parameters
In Chapter 4 differential signaling was explained. Since many of the high-speed
buses being designed in modern computing systems consist of differential pairs,
it is often convenient to describe the behavior of the interconnects in terms
of multimode
S
-parameters. The multimode
S
-matrix breaks the signal on a
differential pair into terms of differential (i.e., odd mode) and common (i.e.,
even mode) signaling states. A multimode matrix for two modes can be derived
Search WWH ::
Custom Search