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Simulation of a non‐linear, time‐variant circuit using the Haar wavelet transform

Georgios Roumeliotis (UGent) , Jan Desmet (UGent) and Jos Knockaert (UGent)
(2022) IET SCIENCE MEASUREMENT & TECHNOLOGY. 16(7). p.389-399
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Abstract
Wavelet theory has disentangled numerous complexities, including those pertinent to transient and steady-state responses of systems, when Laplace and Fourier transforms face insoluble obstacles. Reactive linear components (e.g. inductors and capacitors) are typically handled in the frequency plane. Non-linear (e.g. diodes) or time-variant components (e.g. switches) are conventionally simulated in the time plane (e.g. a diode via its I-V characteristic) and are considered open or short circuits in AC analyses (e.g. in circuit simulation software). Although translating circuits in an alternative plane, such as the Haar wavelet plane, significantly simplifies the process, a wide integration of wavelets into instruments and education is not yet realised; an underlying reason is the considerate 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-alike approach, utilising measurement-based models and the Haar wavelet. The Haar wavelet transform and a numerical method for the inverse Laplace transform which uses the Haar operational matrix are applied, to calculate the total current of a non-linear, time-variant system, that is the total current of a voltage source which powers a non-linear, time-variant load.
Keywords
Electrical and Electronic Engineering, Atomic and Molecular Physics, and Optics, STATE ANALYSIS, LAPLACE TRANSFORM, VARYING SYSTEMS

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MLA
Roumeliotis, Georgios, et al. “Simulation of a Non‐linear, Time‐variant Circuit Using the Haar Wavelet Transform.” IET SCIENCE MEASUREMENT & TECHNOLOGY, vol. 16, no. 7, 2022, pp. 389–99, doi:10.1049/smt2.12112.
APA
Roumeliotis, G., Desmet, J., & Knockaert, J. (2022). Simulation of a non‐linear, time‐variant circuit using the Haar wavelet transform. IET SCIENCE MEASUREMENT & TECHNOLOGY, 16(7), 389–399. https://doi.org/10.1049/smt2.12112
Chicago author-date
Roumeliotis, Georgios, Jan Desmet, and Jos Knockaert. 2022. “Simulation of a Non‐linear, Time‐variant Circuit Using the Haar Wavelet Transform.” IET SCIENCE MEASUREMENT & TECHNOLOGY 16 (7): 389–99. https://doi.org/10.1049/smt2.12112.
Chicago author-date (all authors)
Roumeliotis, Georgios, Jan Desmet, and Jos Knockaert. 2022. “Simulation of a Non‐linear, Time‐variant Circuit Using the Haar Wavelet Transform.” IET SCIENCE MEASUREMENT & TECHNOLOGY 16 (7): 389–399. doi:10.1049/smt2.12112.
Vancouver
1.
Roumeliotis G, Desmet J, Knockaert J. Simulation of a non‐linear, time‐variant circuit using the Haar wavelet transform. IET SCIENCE MEASUREMENT & TECHNOLOGY. 2022;16(7):389–99.
IEEE
[1]
G. Roumeliotis, J. Desmet, and J. Knockaert, “Simulation of a non‐linear, time‐variant circuit using the Haar wavelet transform,” IET SCIENCE MEASUREMENT & TECHNOLOGY, vol. 16, no. 7, pp. 389–399, 2022.
@article{8756874,
  abstract     = {{Wavelet theory has disentangled numerous complexities, including those pertinent to transient and steady-state responses of systems, when Laplace and Fourier transforms face insoluble obstacles. Reactive linear components (e.g. inductors and capacitors) are typically handled in the frequency plane. Non-linear (e.g. diodes) or time-variant components (e.g. switches) are conventionally simulated in the time plane (e.g. a diode via its I-V characteristic) and are considered open or short circuits in AC analyses (e.g. in circuit simulation software). Although translating circuits in an alternative plane, such as the Haar wavelet plane, significantly simplifies the process, a wide integration of wavelets into instruments and education is not yet realised; an underlying reason is the considerate 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-alike approach, utilising measurement-based models and the Haar wavelet. The Haar wavelet transform and a numerical method for the inverse Laplace transform which uses the Haar operational matrix are applied, to calculate the total current of a non-linear, time-variant system, that is the total current of a voltage source which powers a non-linear, time-variant load.}},
  author       = {{Roumeliotis, Georgios and Desmet, Jan and Knockaert, Jos}},
  issn         = {{1751-8822}},
  journal      = {{IET SCIENCE MEASUREMENT & TECHNOLOGY}},
  keywords     = {{Electrical and Electronic Engineering,Atomic and Molecular Physics,and Optics,STATE ANALYSIS,LAPLACE TRANSFORM,VARYING SYSTEMS}},
  language     = {{eng}},
  number       = {{7}},
  pages        = {{389--399}},
  title        = {{Simulation of a non‐linear, time‐variant circuit using the Haar wavelet transform}},
  url          = {{http://doi.org/10.1049/smt2.12112}},
  volume       = {{16}},
  year         = {{2022}},
}
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