ABSTRACT
An electrical network is describable by a system of algebraic and differential equations known as the primary
system of equations obtained by applying the Kirchhoff ’s current and voltage laws and the element v-i
relations. In the case of linear networks, these equations can be transformed into a system of linear algebraic
equations by means of the Laplace transformation, which is relatively simple to manipulate. The main
drawback is that it contains a large number equations. To reduce this number, three secondary systems of
equations are available: the nodal system, the cutset system, and the loop system. If a network has n nodes, b
branches, and c components, there are n – c linearly independent equations in nodal or cutset analysis and
b – nþ c linearly independent equations in loop analysis. These equations can then be solved to yield the
Laplace transformed solution. To obtain the final time-domain solution, we must take the inverse Laplace
transformation. For most practical networks, the procedure is usually long and complicated and requires an
excessive amount of computer time.
