CALCULATION OF TRANSIENTS IN ELECTRICAL CIRCUITS WITH «INCORRECT» INITIAL CONDITIONS WITH THE HELP OF THE DUHAMEL INTEGRAL AND DISCONTINUOUS FUNCTIONS

Abstract

A technique for calculating transients using the Duhamel integral and discontinuous functions is presented. On specific examples, the procedure for calculating «incorrect» problems with respect to differential equations, compiled according to Kirchhoff laws, and using the Duhamel integral is presented. In this case, the Kirchhoff law and the transition characteristic in the Duhamel integral are written using unitary discontinuous functions for the electrical circuit as a whole (before and after commutation). It is shown that the application of discontinuous functions for describing piecewise continuous input signals and switching in an electric circuit extends the domain of applicability of the Duhamel integral.

Keywords

• transients
• Duhamel integral
• discontinuous functions