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Volume 42, Issue 4
Asymptotic Theory for the Circuit Envelope Analysis

Chunxiong Zheng, Xianwei Wen, Jinyu Zhang & Zhenya Zhou

DOI: 10.4208/jcm.2301-m2022-0208

J. Comp. Math., 42 (2024), pp. 955-978.

Published online: 2024-04

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  • 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.

  • Keywords

Asymptotic analysis, Circuit envelope analysis, Floquet theory, Singularly perturbed problem.

  • AMS Subject Headings

94C05, 35C20, 35B25, 35B40, 34C25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-42-955, author = {Zheng , ChunxiongWen , XianweiZhang , Jinyu and Zhou , Zhenya}, title = {Asymptotic Theory for the Circuit Envelope Analysis}, journal = {Journal of Computational Mathematics}, year = {2024}, volume = {42}, number = {4}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2301-m2022-0208}, url = {http://global-sci.org/intro/article_detail/jcm/23042.html} }
TY - JOUR T1 - Asymptotic Theory for the Circuit Envelope Analysis AU - Zheng , Chunxiong AU - Wen , Xianwei AU - Zhang , Jinyu AU - Zhou , Zhenya JO - Journal of Computational Mathematics VL - 4 SP - 955 EP - 978 PY - 2024 DA - 2024/04 SN - 42 DO - http://doi.org/10.4208/jcm.2301-m2022-0208 UR - https://global-sci.org/intro/article_detail/jcm/23042.html KW - Asymptotic analysis, Circuit envelope analysis, Floquet theory, Singularly perturbed problem. AB -

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.

Chunxiong Zheng, Xianwei Wen, Jinyu Zhang & Zhenya Zhou. (2024). Asymptotic Theory for the Circuit Envelope Analysis. Journal of Computational Mathematics. 42 (4). 955-978. doi:10.4208/jcm.2301-m2022-0208
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