Biomedical Engineering Reference
In-Depth Information
Nodes 2 and 3 are connected by an independent voltage source, so we form a supernode 2
þ
3.
Summing the currents leaving the supernode 2
þ
3 gives
4
ð
V
2
V
1
Þ þ
3
V
2
1
þ
2
V
3
þ
5
ð
V
3
V
1
Þ ¼
0
Simplifying yields
1
The second supernode equation is KVL through the node voltages and the independent source,
giving
9
V
1
þ
7
V
2
þ
7
V
3
¼
V
2
þ
1
þ
V
3
¼
0
or
V
2
þ
V
3
¼
1
The two node and KVL equations are written in matrix format as
2
4
3
5
2
4
3
5
¼
2
4
3
5
11
4
5
2
1
V
1
V
2
V
3
977
0
11
1
Solving with MATLAB gives
¼
A
[11
4
5;
9 7 7; 0
1 1];
¼
F
[2;1;
1];
¼
V
A\F
¼
V
0.4110
0.8356
0.1644
Thus,
V
3
¼
- 0.1644.
9.6 LINEARITY AND SUPERPOSITION
If a linear system is excited by two or more independent sources, then the total response
is the sum of the separate individual responses to each input. This property is called the
principle of superposition. Specifically for circuits, the response to several independent
sources is the sum of responses to each independent source with the other independent
sources dead, where
A dead voltage source is a short circuit.
A dead current source is an open circuit.
In linear circuits with multiple independent sources, the total response is the sum of each
independent source taken one at a time. This analysis is carried out by removing all of
