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 - <p style="text-align: justify;">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.</p>