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Applying of differential equations with variable coefficients of Dirac δ-functions to study of series RLC-circuits with discrete-continuum characteristics

A. B. Putilin, R. E. Liberzon, V. K. Kurbanaliev

Moscow State University of Mechanical Engineering (MAMI)

FSUE "Academician A.I. Berg CNIRTI"

The paper is received on December 15, 2014

Abstract. The paper explores the effects of pulsed changes in temperature on a thermistor within a RLC circuit. The effects of temperature were represented in Dirac δ-functions. The study establishes that the solution lies in a differential equation with variable coefficients of Dirac δ-functions. An accurate dimensionless criteria solution has been obtained. An asymptotic representation of the current function in the resonance circuit at low time values has been constructed using the limit theorem. It has been proved that at certain time values the current can exceed a well-defined expected value, which may trigger the radio electronic system failure.

Key words: RLC circuit, thermistor, Dirac delta function, asymptotic representation, system failure, radio electronic system.