Circuit Simulation of Any Time-Domain Source on Fractional-Order Impedances by Use of the Haar Wavelet Transform, Case Study of the Skin Effect

Abstract

An application of the ability of the Haar wavelet operational matrix to perform the numerical inverse Laplace transform as combined with the intrinsically convenient Haar wavelet transform of any time-domain signal is presented in this paper. A case study of the transient- and steady-state behavior of the input impedance of a short-circuited transmission line showcases a method to perform the numerical inverse Laplace transform of fractional-order approximative expressions of the skin effect. Furthermore, an improved skin effect approximation is presented.