Simulition of a non-linear, time-variant circuit using the Haar wavelet transform

Abstract

Wavelet theory has untangled a multitude of complex problems, including those related to transient and steady-state responses of systems, when Laplace and Fourier transformations encountered obstacles. inextricable. Reactive linear components (e.g. inductors and capacitors) are typically handled in the frequency plane. Components that are nonlinear (e.g. diodes) or time variable (e.g. switches) are typically simulated in the time plane (e.g. a diode via the I– characteristic) its V) and is considered an open or short circuit in AC analysis (e.g. in circuit simulation software). Although translating circuits in an alternative plane, such as the Haar wavelet plane, greatly simplifies the process, widespread integration of wavelets into tools and education has not yet been achieved. perform; One fundamental reason is the considerable complexity of applying wavelet theory to circuits and signals. The aim of this paper is to bridge this gap, providing a new user-friendly, Laplace-like approach using models based on Haar measurements and wavelengths. The Haar wavelet transform and a numerical method for the inverse Laplace transform using the Haar operator matrix are applied to calculate the total current of a time-varying, non-linear system, that is, the total current. of a voltage source that powers a time-varying, non-linear load.