PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

118 Practical MATLAB® Applications for Engineers

R.2.74 Nodal analysis is more powerful than mesh analysis in the sense that it applies
equally well to both planar and nonplanar networks.
For any arbitrary node x, the structure (and format) of the node equation is given by

∑[]current sources at xx
[admittances connected between annd yV

xyV

x

y

]*

[]*

∑

∑admittances between and for all possiblle sy

where the current sources (left side of equation) are considered positive if its polar-
ity points towards x and negative otherwise, and y is a node connected to x through
an element (or group of elements) for any y, 1 < y ≤ n – 1.

R.2.75 The following example, a network consisting of three nodes as shown in Figure 2.9,
is analyzed using node equations.

ANALYTICAL Solution

The node equations are

For node V 1

I

RR

V

R

1 
 V

11 1

13

1

3

2







**



For node V 2

I

R

V

RR

2 V

3

1

23

2

111


**









R.2.76 Source transformation refers to the fact that any voltage source V in series with a
resistor Rs can be replaced by a current source I = V/Rs, in parallel with the same
resistor Rs and vice versa as illustrated in Figure 2.10.

R.2.77 An example of source transformation is shown in Figure 2.11, where a voltage
source V = 10 V, in series with a resistance Rs = 5 Ω, can be transformed into an
equivalent current source I = (10/5) = 2 A in parallel with Rs = 5 Ω.

R.2.78 The superposition theorem states that in a linear DC network, the current through,
or voltage across any element is given by the algebraic sum (contributions) of the

FIGURE 2.9
Electrical network requiring two node equations.

V 1

R 1

R 3

R 2

V 2

I 1 I 2