Introduction to Electric Circuits

7 Nodal and mesh analysis

7.1 INTRODUCTION

For circuits which are more complicated than those considered in the previous

chapters, it is still possible to analyse them using the methods described there

but the working can become extremely tedious. Two of the methods devised to

make things more manageable are the nodal voltage and the mesh current

approaches. These lend themselves to matrix methods of solution, both

manually and by computer. We shall begin therefore by setting out the relevant

parts of the matrix algebra techniques.

7.2 MATRICES

A matrix is a rectangular array of numbers (or letters or functions) arranged in

rows and columns. The individual numbers are called elements of the matrix

and these are often identified by the use of double subscripts, the first part

indicating the row and the second indicating the column in which the element is

situated. Thus, for example, element a34 is an element in the 4th column of the

3rd row. Matrices are usually enclosed by square brackets so that

9

6 -1 1

is a matrix having two rows and four columns. It is said to be a matrix of order

2 • 4. In this matrix, element a13 = 9 and element a21 = -4.

Example 7.1

Write down the matrix of order 4 x 2 for which all --1; a12- O; a21---3;

a22 = 4; a31 = -6; a32 = 9; a41 = 0 and a42 = 5

Solution

A matrix of order 4 x 2 has four rows and two columns and in this case the

elements are defined numerically so we may write