Generalized analysis of electrical circuits by using hypernion matrixes

In this paper a novel method for circuit analysis is proposed. It is based on using symbolic analysis in matrix form, which is especially appropriate for repetitive similar calculations of the same circuit. The method, which applies hyper-complex numbers (hypernions), was first developed by the authors for analyzing the non-sinusoidal operation of electrical circuits. Now, the method has been extended to the analysis of electronic/switching circuits in which the sources and/or the parameters are step-wisely changed as a result of switching. Such circuits are common in different kinds of DC-DC converters (such as Buck, Boost, Cuk, etc. converters). The proposed method gives a new approach to the analysis of the above circuits by opening the possibility of treating them in a general-analytical form, just like in regular electrical circuits having a constant configuration and constant parameters. The computation of such kinds of circuits by using the proposed method becomes very simple, since the circuit does not have to be analyzed many times, each time for a different configuration, but at once by performing a parallel computation. The theoretical presentation is accompanied by numerical examples.