Digital Signal Processing Reference
In-Depth Information
i
1
i
2
Z
1
Z
2
v
2
v
1
Port 2
Port 1
Z
3
Figure 9-28
Deriving the
ABCD
parameters for a
T
-topology equivalent circuit.
Relationship to Common Circuit Parameters
The
ABCD
parameters can be used
to create equivalent-circuit models for common circuit topologies. For example,
consider the T-circuit shown in Figure 9-28. To determine
A
, port 2 must be
open (since
i
2
=
0) while port 1 is driven with
v
1
.
i
2
=
0
v
1
v
2
A
=
Z
3
v
2
=
v
1
Z
3
+
Z
1
Z
3
+
Z
1
Z
3
A
=
(9-40a)
The term
B
is determined by shorting port 1 (since
v
2
=
0):
v
2
=
0
v
1
i
2
B
=
A current divider is used to calculate
i
2
, which is substituted into the equation
for
B
:
Z
3
i
2
=
i
1
Z
3
+
Z
2
v
1
i
1
[
Z
3
/(Z
3
v
1
i
1
Z
3
+
Z
2
B
=
=
+
Z
2
)
]
Z
3
Since
v
1
/i
1
is equal to the impedance looking into port 1,
B
can be simplified:
||
Z
3
)
Z
3
+
Z
2
Z
1
Z
2
Z
3
B
=
(Z
1
+
Z
2
=
Z
1
+
Z
2
+
(9-40b)
Z
3
To determine
C
, port 2 must be open (since
i
2
=
0) while port 1 is driven with
v
1
.
i
2
=
0
i
1
v
2
C
=
Z
3
v
2
=
v
1
Z
3
+
Z
1
Search WWH ::
Custom Search