Biomedical Engineering Reference
In-Depth Information
Solution
Notice that this circuit has three essential nodes and a dependent current source. We label the
essential nodes 1, 2, and 3 in the redrawn circuit, with the reference node at the bottom of
the circuit and three node voltages
V
1
,
V
2
, and
V
3
, as indicated.
1/4
Ω
2I
d
1/4
Ω
2
3
1
1/2
Ω
+
+
+
I
d
5 A
V
1
V
2
1/3
Ω
3 A
V
3
1
Ω
-
-
-
Note that
I
d
¼
V
3
according to Ohm's law. Summing the currents leaving node 1 gives
5
þ
2
ð
V
1
V
2
Þ þ
2
I
d
þ
4
ð
V
1
V
3
Þ ¼
0
which reduces to
6
V
1
2
V
2
2
V
3
¼
5
Summing the currents leaving node 2 gives
2
I
d
þ
2
ð
V
2
V
1
Þ þ
3
V
2
þ
4
ð
V
2
V
3
Þ ¼
0
which simplifies to
2
V
1
þ
9
V
2
6
V
3
¼
0
Summing the currents leaving node 3 gives
4
ð
V
3
V
2
Þ
3
þ
V
3
þ
4
ð
V
3
V
1
Þ ¼
0
reducing to
3
The three node equations are written in matrix format as
4
V
1
4
V
2
þ
9
V
3
¼
2
4
3
5
2
4
3
5
¼
2
4
3
5
6
2
2
V
1
V
2
V
3
5
0
3
29
6
4
49
