Improved Matrix and Determinant Methods for Solving Networks

It is shown that a linear electrical network, which may include valves and transformers, can be represented topologically by a network composed entirely of elements of a single type. In its most general form an element of this type comprises four nodes and two directed branches. It is also shown that a linear electrical network can be represented algebraically by a matrix, termed an H-matrix. If the elements of the network are shown in the network diagram in the form of elements of the above type, the H-matrix can be written down directly from the network diagram. The value of the usual determinant of the network is equal to the value of any first co-factor of the determinant of the H-matrix. By choosing a suitable co-factor the labour of evaluating the determinant is much reduced. The transfer admittance of the network is treated as a special case of a network element. By the application of what are termed addition operators the transfer admittance can be expressed as a function of any element or elements. The calculation of equivalent networks can be considerably simplified with the aid of H-matrices.