Journal of Circuits, Systems, and Computers Vol. 18, No. 7 (2009) 1205–1225 c  World Scientific Publishing Company GENERALIZED ANALYSIS OF ELECTRICAL CIRCUITS BY USING HYPERNION MATRICES YEFIM BERKOVICH ∗ and ARIEH SHENKMAN † Department of Electrical and Electronic Engineering, Holon Institute of Technology, 52 Golomb Str., Holon 58102, Israel ∗ Berkovich@hit.ac.il † Shenkman@hit.ac.il SAAD TAPUCHI Sami Shamoon College of Engineering, Bialic/Basel Str. Beer Sheva 84100, Israel Tapuchi@sce.ac.il Revised 15 June 2009 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. This 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.). 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 all at once by performing a parallel computation. The theoretical presentation is accompanied by numerical examples. Keywords : Electrical circuits; hyper-complex numbers; matrices; non-sinusoidal signals; circuits with changing topology. 1. Introduction As is known, complex numbers are widely used in electric circuit analysis. The symbolic method of AC circuit analysis and use of phasors, the Fourier integral and Laplace transforms are based on complex numbers. Complex numbers are actually two component (real and imaginary) numbers and therefore are appro- priate for the representation of vectors in a two-dimensional space and phasors on the complex plane, i.e., sinusoidal functions of a particular frequency. How- ever, complex numbers do not help much in the case of nonsinusoidal functions, 1205