A method of accelerated nodal analysis of electrical circuits with changing element parameters

A method of accelerated node analysis of electrical circuits is proposed, which provides a significant reduction in com-putational costs when studying the effect of changes in the parameters of elements on the operating modes of circuits. Linear electric circuits in direct current or alternating current mode are considered. A significant reduction in the amount of calculations was achieved by using a new modification of the Gauss elimination method for solving systems of linear algebraic equations and taking into account the features of the structure of the nodal conductivity matrix, as well as the specifics of the algorithm for reshaping this matrix when changing the parameters of the elements. A theorem defining the condition for the existence of a single solution to the problem of circuit reanalysis is formulated and proved, as well as a theorem defining the condition for the occurrence of the phenomenon of potential transition from one node to an-other when the parameter of one element changes. It is shown that for sufficiently complex circuits, the ratio of the number of scalar multiplication or division operations required to calculate all new values of nodal potentials after changing the parameter of one circuit element to the number of circuit nodes is close to unity. The method is character-ized by a small error, which does not accumulate as the number of new node potential values increases. The corresponding software in C++ was developed and numerical experiments were performed, the results of which confirmed the high efficiency of the method.