Digital Signal Processing Reference
In-Depth Information
S
dd
21
is a measure of the differential energy transmitted across the network from
port 1 to port 2.
Identical analysis can be used to calculate the common-mode
S
-parameters,
where the energy is being transmitted in the even mode, by driving the four-port
network with
+
v
on port 3 when ports 2 and 4 are not being
driven. This allows (9-60) to be simplified where
b
c
1
+
v
on port 1 and
=
b
1
+
b
3
,
b
c
2
=
b
2
+
b
4
,
=
a
1
+
a
3
=
v
+
v
=
and
a
c
1
2
v
.
b
1
b
2
b
3
b
4
S
11
S
12
S
13
S
14
0
0
=
S
21
S
22
S
23
S
24
(9-63)
S
31
S
32
S
33
S
34
S
41
S
42
S
43
S
44
The common-mode
S
-parameters are easily obtained algebraically from (9-63):
a
2
=
a
4
=
0
=
b
c
1
a
c
1
1
S
cc
11
=
2
(S
11
+
S
33
+
S
13
+
S
31
)
(9-64a)
a
2
=
a
4
=
0
=
b
c
2
a
c
1
1
2
(S
21
S
cc
21
=
+
S
23
+
S
41
+
S
43
)
(9-64b)
Equations (9-64a) and (9-64b) describe how much energy is being reflected and
transmitted when the four-port system is being driven with a common-mode
source (i.e., the system is being driven in the even mode).
As described in Chapter 4, for a system with two signal conductors, the volt-
ages at the ports are combinations of odd and even modes. Consequently, for a
perfectly symmetric system (where each leg of the differential pair is electrically
identical), if the system is driven differentially, all the energy will be contained
within the odd mode. However, if the pair exhibits any asymmetry, a portion of
the energy will be flowing in the even mode. The multimode matrix also accounts
for the
differential-to-common mode conversion
, which describes the amount of
energy being transformed into the even mode when the system is being driven
differentially and the
common mode-to-differential conversion
, which tells how
much energy is being converted to the odd mode when driven commonly. Since
most high-speed buses are driven differentially, the
differential-to-common mode
conversion
is the most important parameter of the two.
The
differential-to-common mode S
-
parameters
, where the energy is being
transmitted in the odd mode and received in the even mode, are calculated by
driving the four-port network differentially at the driver and sensing in common
mode at the receiver. The differential-to-common mode coefficients are
b
c
1
=
b
1
+
b
3
,
b
c
2
=
b
2
+
b
4
, and
a
d
1
=
a
1
−
a
3
=
v
−
(
−
v)
=
2
v
.
b
1
b
2
b
3
b
4
S
11
S
12
S
13
S
14
v
0
−
v
0
=
S
21
S
22
S
23
S
24
(9-65)
S
31
S
32
S
33
S
34
S
41
S
42
S
43
S
44
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