Digital Signal Processing Reference
In-Depth Information
a
2
=
a
4
=
0
=
b
c
1
a
d
1
1
S
cd
11
=
2
(S
11
−
S
13
+
S
31
−
S
33
)
(9-66a)
a
2
=
a
4
=
0
=
b
c
2
a
d
1
1
2
(S
21
S
cd
21
=
−
S
23
+
S
41
−
S
43
)
(9-66b)
The
common mode-to-differential S-parameters
, where the energy is being trans-
mitted in the even mode and received in the odd mode, are calculated by driving
the four-port network in the common mode and sensing differentially at the
receiver. The derivation is left to the reader.
The multimode
S
-parameters for a four-port system can be combined to create
the
multimode matrix
b
d
1
b
d
2
b
c
1
b
c
2
S
dd
11
S
dd
12
S
dc
11
S
dc
12
a
d
1
a
d
2
a
c
1
a
c
2
=
S
dd
21
S
dd
22
S
dc
21
S
dc
22
(9-67a)
S
cd
11
S
cd
12
S
cc
11
S
cc
12
S
cd
21
S
cd
22
S
cc
21
S
cc
22
Note that each quadrant of the multimode matrix represents unique parameters.
For example, the upper left quadrant is the differential
S
-parameter matrix,
b
d
1
b
d
2
S
dd
11
S
dd
22
a
d
1
a
d
2
S
dd
12
=
S
dd
21
(9-67b)
[
S
dd
]
a
d
1
a
d
2
=
which assumes that all the energy is sourced and sensed in a differential manner.
Consequently, the multimode matrix takes the form
b
d
1
b
d
2
b
c
1
b
c
2
a
d
1
a
d
2
a
c
1
a
c
2
[
S
dd
]
S
dc
]
[
S
cd
]
S
cc
]
=
(9-67c)
where each matrix describes a specific driving and receiving configuration:
S
dd
: Driver and receiver are differential.
S
cc
: Driver and receiver are common mode.
S
dc
: Driver is common mode and receiver is differential.
S
cd
: Driver is differential mode and receiver is common mode.
The format of (9-67c) allows the four-port
S
-parameters to be reduced to an
equivalent simple two-port system for specific circumstances. For example, in
high-speed differential buses, each pair is driven and received assuming that all
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