Non-Standard Analysis in Electrical Engineering. Complex Circuits with Ideal Reactive Elements

Abstract

The article presents the application of concepts and methods of non-standard analysis to problems of theoreti cal electrical engineering. It is substantiated that standard methods of electrical engineering are not effective enough, because they are excessively complex or even unsuitable for calculating DC electrical circuits con taining ideal inductances and capacitances. This problem arises because for direct current (with zero frequen cy) the inductive resistance is zero, and the capacitive resistance goes to infinity. As a result, when using standard methods to calculate such electrical circuits, it is necessary to solve uncertainty expressions of the type 0 0 or ¥ ¥ , which creates difficulties within the framework of traditional mathematical analysis. Given the above difficulties, it is proposed to replace the classical mathematical analysis with a non-standard one. In this approach, the frequency of the direct current is considered not as zero, but as an infinitely small value α. This approach makes it possible to determine the reactance of inductive elements as L a 1 capacitive elements as and the reactance of . This allows to successfully apply all standard methods of theoretical electrical a C engineering and avoid the need to work with indefinite expressions. The article provides specific examples of the analysis of complex direct current circuits with ideal inductances and capacitances.