Node-Voltage Method
Special Case
Voltage source between
essential nodes
ECE 201 Circuit Theory I
1
Dependent Source between essential nodes
and Independent Source between essential
nodes
How many essential nodes are there?
ECE 201 Circuit Theory I
2
Identify the nodes and the reference
Introduce current I between nodes 2 and 3
ECE 201 Circuit Theory I
3
Write the Node-Voltage Equations
v v v

i  0
5
50
v
i 4  0
100
v v v
v


4  0
5
50 100
2
1
2
1
2
3
2
ECE 201 Circuit Theory I
3
4
The Algebra
v v v
v


4  0
5
50 100
v  50
v  v  10i  v  10
5
2
3
1
2
2
3

2
ECE 201 Circuit Theory I

2

5
Solving
v  50V
1
v  60V
2
v  80V
3
ECE 201 Circuit Theory I
6
Is there an easier way?
• Introduce a “supernode”
Consider nodes 2 and 3 to be one node
Sum the currents away from the node
ECE 201 Circuit Theory I
7
Write the equations
v v v
v


4  0
5
50 100
v  v  10i
2
3
1
2
2
3

ECE 201 Circuit Theory I
8
Solving
v  50V
1
v  60V
2
v  80V
3
ECE 201 Circuit Theory I
9
MultiSim Simulation
V
R2
5
V1
50 V
R1
40
+
-
50.000
V2
V DC 10M
10
R3
50
+
-
60.000
U1
V DC 10M
ECE 201 Circuit Theory I
R4
100
I1 + 80.000
4A -
V3
V DC 10M
10