Introduction to Electric Circuits

148 Nodal and mesh analysis

all the other nodes to it. By applying Kirchhoff's current law to each of these
other nodes in turn, a set of equations can be obtained from which the various
nodal voltages may be calculated. The node chosen as the reference can be
purely arbitrary but will normally be the one connected to an earthed or
grounded part of the circuit. Otherwise the node at the bottom of the circuit is
usually chosen.
To illustrate the method, first consider the circuit shown in Fig. 7.1.

Figure 7.1

1

I1

FII

t

i2

R3

This circuit has just two nodes which are identified as 1 and 2. Let the voltage of

nodes 1 and 2 be V 1 and V2, respectively. Applying KCL to node 1 we have

Is- I, + 12 + 13- (Vl - V2)//R1 Jr- (V 1 - V2)/R 2 Jr (V 1 - V2)/R 3

We choose the reference node to be node 2 and, since only potential differences

are important, we can make V2 = O:

Is- V~[1/R~ + 1/R2 + 1/R3]

Using conductances (G - I//R) we have

Is = VI[G1 + G: + G3]

Now let us consider the slightly more complicated circuit of Fig. 7.2 which has

three nodes. The three nodes are identified as 1, 2 and 3 and we choose node 3

as the reference. Let the node voltages be V~, V2 and V3. Applying KCL to node

1:

I- 11 Jr- 12 Jr- 13 -- (V 1 - V3)//RI + (V 1 - V3)/R 2 Jr- (V 1 - V2)/R 3

D

Figure 7.2

1 R3 " l ~ (^13) ,...- (^2) .,~
i ll I2 I I
[ ~R1^4
3
R~