Digital Signal Processing Reference
In-Depth Information
i
1
i
2
i
3
A
B
D
A
B
D
v
1
v
2
v
3
C
C
circuit
1
circuit
2
Figure 9-31
ABCD
parameters are cascaded though multiplication.
easily be written.
v
1
i
1
AB
CD
v
2
i
2
=
circuit
1
v
2
i
2
AB
CD
v
3
i
3
=
circuit
2
Note that the output of circuit 1 is
v
2
and
i
2
, which is the input of circuit 2. This
allows the simple substitution of
v
2
i
2
AB
CD
v
3
i
3
with
circuit
2
resulting in
v
1
i
1
AB
CD
AB
CD
v
3
i
3
=
circuit
1
circuit
2
Therefore, two-port S-parameters can be cascaded by converting to ABCD
parameters and multiplying
. The cascaded scattering matrix is then calculated
by converting the cascaded
ABCD
matrix back to
S
-parameters using Table 9-3.
The procedure is demonstrated in Example 9-10.
Example 9-10
Using the two independently measured values of
S
-parameters
for a via and a loss-free transmission line at 5 GHz, calculate the, equivalent
S
-parameters that would be measured if the two circuits were cascaded as shown
Figure 9-32. Assume that the termination impedance is 50
.
S
11
−
−
j
0
.
1516
S
12
0
.
1235
−
j
0
.
1516
0
.
7597
−
j
0
.
6190
via
=
S
21
S
22
0
.
7597
−
j
0
.
6190
−
0
.
1235
S
11
S
22
0
.
00325
−
j
0
.
00323
S
12
−
j
0
.
00323
−
1
.
00
−
j
0
.
003
t-line
=
S
21
−
1
.
00
−
j
0
.
003
0
.
00325
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