Biomedical Engineering Reference
In-Depth Information
Notice that the system matrix is no longer symmetrical because of the dependent current
source, and two of the three nodes have a current source, giving rise to a nonzero term on the
right-hand side of the matrix equation.
Solving with MATLAB gives
>>
¼
A
[6
2
2;
29
6;
4
4 9];
>>
¼
F
[
5; 0; 3];
>>
¼
V
A\F
V
¼
1.1471
0.5294
0.4118
Thus,
V
3
¼
- 0.4118 V.
If one of the branches has an independent or controlled voltage source located between
two essential nodes, as shown in Figure 9.21, the current through the source is not easily
expressed in terms of node voltages. In this situation, we form a supernode by combining
the two nodes. The supernode technique requires only one node equation in which the
current,
I
A
, is passed through the source and written in terms of currents leaving node 2.
Specifically, we replace
I
B
þ
I
C
þ
I
D
in terms of node voltages. Because we have
two unknowns and one supernode equation, we write a second equation by applying
KVL for the two node voltages 1 and 2 and the source as
I
A
with
V
1
V
D
þ
V
2
¼
0
or
V
D
¼
V
1
V
2
V
Δ
I
B
I
A
I
C
1
2
+
+
I
D
V
1
V
2
-
-
FIGURE 9.21
A dependent voltage source is located between nodes 1 and 2.
