New Solution Technique for the Frequency and Transient Response of Transformer Windings with All Inter-Turn Mutual Inductances and Capacitances Included

Abstract

The paper suggests a Laplace-domain technique for analyzing the transient response of non-uniform transmission lines with arbitrarily varying characteristic impedance. A mathematical model based on a distributed parameter Laplace-domain representation will be derived taking into account the waveform of the current and/or voltage sources initiating the transients, as well as the circuit constants of the non-uniform line. From the location dependence of the line’s characteristic impedance and the application of a recursive circuit reduction technique, s-domain expressions for the line’s input impedance for any loading condition will be determined. The voltage and current distributions along the line can then be obtained. These expressions, followed by numerical Laplace inversion, will be utilized for finding the line’s transient response in the time domain.