Year: 2024
Author: Chunxiong Zheng, Xianwei Wen, Jinyu Zhang, Zhenya Zhou
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 4 : pp. 955–978
Abstract
Asymptotic theory for the circuit envelope analysis is developed in this paper. A typical feature of circuit envelope analysis is the existence of two significantly distinct timescales: one is the fast timescale of carrier wave, and the other is the slow timescale of modulation signal. We first perform pro forma asymptotic analysis for both the driven and autonomous systems. Then resorting to the Floquet theory of periodic operators, we make a rigorous justification for first-order asymptotic approximations. It turns out that these asymptotic results are valid at least on the slow timescale. To speed up the computation of asymptotic approximations, we propose a periodization technique, which renders the possibility of utilizing the NUFFT algorithm. Numerical experiments are presented, and the results validate the theoretical findings.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2301-m2022-0208
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 4 : pp. 955–978
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Asymptotic analysis Circuit envelope analysis Floquet theory Singularly perturbed problem.