Digital Signal Processing Reference
In-Depth Information
TABLE 9-3. Relationships Between Two-Port
S
and
ABCD
Parameters
a
B
−
Z
n
(D
−
A
+
CZ
n
)
B
+
Z
n
(D
+
A
+
CZ
n
)
2
Z
n
(AD
−
BC)
B
+
Z
n
(D
+
A
+
CZ
n
)
S
11
S
12
S
21
S
22
2
Z
n
B
+
Z
n
(D
+
A
+
CZ
n
)
B
−
Z
n
(A
−
D
+
CZ
n
)
B
+
Z
n
(D
+
A
+
CZ
n
)
(
1
+
S
11
)(
1
−
S
22
)
+
S
12
S
21
2
S
21
Z
n
(
1
+
S
11
)(
1
+
S
22
)
−
S
12
S
21
2
S
21
AB
CD
−
S
11
)(
1
−
S
22
)
−
S
12
S
21
2
S
21
−
S
11
)(
1
+
S
22
)
+
S
12
S
21
2
S
21
1
Z
n
(
1
(
1
a
Z
n
is the termination impedance at the ports.
L
barrel
Port 1
Port 2
Barrel
Port 1
C
pad
C
pad
Port 2
Via pad
(a)
(b)
Figure 9-30
Via and equivalent circuit for Example 9-9.
Example 9-9
Extract an equivalent circuit for the via shown in Figure 9-30a from
the following
S
-parameter matrix measured at 5 GHz assuming port impedance
values (
Z
n
)of50
:
S
11
S
22
−
−
j
0
.
1516
S
12
0
.
1235
−
j
0
.
1516
0
.
7597
−
j
0
.
6190
=
−
j
0
.
6190
−
S
21
0
.
7597
0
.
1235
SOLUTION
Step 1:
Transform the
S
-matrix into
ABCD
parameters using the relations in
Table 9-3.
AB
CD
0
.
790
0
.
790
j
22
.
22
=
j
0
.
01686
Step 2
: Choose the form of the equivalent circuit. A signal propagating through
the via will experience the capacitance of the via pad, the inductance of the barrel,
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