Digital Signal Processing Reference
In-Depth Information
the theory. The discussion begins with the most intuitive method of describing a
network, which is the impedance matrix.
9.2.1
Impedance Matrix
Consider the two-port network depicted in Figure 9-4. If the voltage and current
are measured at the input and output ports, the system can be characterized in
terms of its impedance matrix. The impedance from port 1 to port 2 is calculated
by measuring the open-circuit voltage at port 2 when current is injected into
port 1:
i
port2
=
0
v
open
,
port2
i
port1
Z
21
=
(9-6a)
Similarly, the input impedance looking into port 1 is measured by injecting
current into port 1 and measuring the voltage at port 1:
i
port2
=
0
v
open
,
port1
i
port1
Z
11
=
(9-6b)
Using the definition shown in equations (9-6a) and (9-6b), a set of linear equations
can be written to describe the network in terms of its port impedances:
v
1
=
Z
11
i
1
+
Z
12
i
2
v
2
=
Z
21
i
1
+
Z
22
i
2
which is expressed more efficiently in matrix form:
v
2
=
Z
22
·
i
2
v
1
Z
11
Z
12
i
1
(9-7)
Z
21
More generally, the elements of an impedance matrix are described in equa-
tion (9-8) for an arbitrary number of ports,
v
i
i
j
=
open-circuit voltage measured at port
i
current injected into port
j
=
Z
ij
(9-8)
i
1
i
2
+
−
+
−
v
1
v
2
Port 1
Two Port Network
Port 2
Figure 9-4
Two-port network used to generate the impedance matrix.
Search WWH ::
Custom Search