Method for analysis of periodic stationary states of non-linear electric circuits on basis of Kotelnikov-Shannon series

A. O. Moskovko; O. A. Vityaz; Guy A. E. Vandenbosch

doi:10.3103/S0735272719120021

Authors

A. O. Moskovko National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Ukraine https://orcid.org/0000-0001-9432-7247
O. A. Vityaz National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Ukraine https://orcid.org/0000-0002-4252-342X
Guy A. E. Vandenbosch Catholic University of Leuven, Belgium https://orcid.org/0000-0002-5878-3285

DOI:

https://doi.org/10.3103/S0735272719120021

Keywords:

periodic steady-state, Shannon series, rectifier, oscillator

Abstract

In this paper it is represented an efficient method for calculation of periodic stationery states of non-linear electronic circuits at time domain. The method is based on application of Kotelnikov–Shannon series for approximation of derivatives of mathematic models of the circuit. Cyclic approximation form with application of Shannon kernel allows to obtain simple matrix relation for the derivatives. The coefficients matrix in obtained expressions does not depend on amount of unknown signals in the circuit and it depends on selected amount of time samples. Amount of time samples is selected considering necessary accuracy of the result and non-linearity degree of the circuit. This method allows to convert the system of differential algebraic equations into a system of non-linear algebraic equations which can be solved by means of Newton–Raphson method, for example. In this paper there are represented several examples of calculation of stationery states of non-linear electronic circuits demonstrating the method efficiency. There are also represented the experimental results of voltage rectifier proving the represented method accuracy.

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