Fast calculation of signal delay in RC-circuits based on Laguerre functions

摘要

Linear systems of ordinary differential and algebraic equations modelling passive integral circuits consisting of resistors and capacitors (RC-circuits) are considered. A method for the fast calculation of signal delay is such circuits is proposed. For this purpose, the input signal is approximated by several first Laguerre functions and the output of the system is obtained in the form of a sum of several Laguerre functions and one of the eigenvalues of the matrix pencil corresponding to the system (spectral correction of the solution). For the case of approximation of the input and output signals by two Laguerre functions, criteria are proposed for a priori determination whether sufficiently good approximation is guaranteed for the particular system. Results of numerical experiments with industrial design tests are presented and discussed.