A Novel Approach to Transient Fourier Analysis for Electrical Engineering Applications
This paper presents a detailed investigation into the application of transient Fourier analysis in select electrical engineering contexts. Two novel approaches for addressing transient analysis are introduced. The first approach combines the Fourier series with the Laplace–Carson (<inline-formula...
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2024-10-01
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| author | Mariana Beňová Branislav Dobrucký Jozef Šedo Michal Praženica Roman Koňarik Juraj Šimko Martin Kuchař |
| author_facet | Mariana Beňová Branislav Dobrucký Jozef Šedo Michal Praženica Roman Koňarik Juraj Šimko Martin Kuchař |
| author_sort | Mariana Beňová |
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| description | This paper presents a detailed investigation into the application of transient Fourier analysis in select electrical engineering contexts. Two novel approaches for addressing transient analysis are introduced. The first approach combines the Fourier series with the Laplace–Carson (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">L</mi><mtext>-</mtext><mi>C</mi></mrow></semantics></math></inline-formula>) transform in the complex domain, utilizing complex time vectors to streamline the computation of the original function. The inverse transformation back into the time domain is achieved using the Cauchy-Heaviside (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><mtext>-</mtext><mi mathvariant="script">H</mi></mrow></semantics></math></inline-formula>) method. The second approach applies the Fourier transform (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">F</mi><mtext>-</mtext><mi>Τ</mi></mrow></semantics></math></inline-formula>) for the transient analysis of a power converter circuit with both passive and active loads. The method of complex conjugate amplitudes is employed for steady-state analysis. Both contributions represent innovative approaches within this study. The process begins with Fourier series expansions and the computation of Fourier coefficients, followed by solving the system’s steady-state and transient responses. The transient states are then confirmed using the Fourier transform. To validate these findings, the analytical results are verified through simulations conducted in the Matlab/Simulink R2023b environment. |
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| issn | 2076-3417 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | MDPI AG |
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| series | Applied Sciences |
| spelling | doaj-art-cccefba6e90a445888698b5ac7816a8e2025-08-20T02:14:22ZengMDPI AGApplied Sciences2076-34172024-10-011421988810.3390/app14219888A Novel Approach to Transient Fourier Analysis for Electrical Engineering ApplicationsMariana Beňová0Branislav Dobrucký1Jozef Šedo2Michal Praženica3Roman Koňarik4Juraj Šimko5Martin Kuchař6Department of Electromagnetics and Biomedical Engineering, Faculty of Electrical Engineering and Information Technology, University of Žilina, 010 26 Žilina, SlovakiaDepartment of Mechatronics and Electronics, Faculty of Electrical Engineering and Information Technology, University of Žilina, 010 26 Žilina, SlovakiaDepartment of Mechatronics and Electronics, Faculty of Electrical Engineering and Information Technology, University of Žilina, 010 26 Žilina, SlovakiaDepartment of Mechatronics and Electronics, Faculty of Electrical Engineering and Information Technology, University of Žilina, 010 26 Žilina, SlovakiaDepartment of Mechatronics and Electronics, Faculty of Electrical Engineering and Information Technology, University of Žilina, 010 26 Žilina, SlovakiaDepartment of Mechatronics and Electronics, Faculty of Electrical Engineering and Information Technology, University of Žilina, 010 26 Žilina, SlovakiaDepartment of Applied Electronics, Faculty of Electrical Engineering and Computer Science, Technical University of Ostrava, 708 00 Ostrava, Czech RepublicThis paper presents a detailed investigation into the application of transient Fourier analysis in select electrical engineering contexts. Two novel approaches for addressing transient analysis are introduced. The first approach combines the Fourier series with the Laplace–Carson (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">L</mi><mtext>-</mtext><mi>C</mi></mrow></semantics></math></inline-formula>) transform in the complex domain, utilizing complex time vectors to streamline the computation of the original function. The inverse transformation back into the time domain is achieved using the Cauchy-Heaviside (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><mtext>-</mtext><mi mathvariant="script">H</mi></mrow></semantics></math></inline-formula>) method. The second approach applies the Fourier transform (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">F</mi><mtext>-</mtext><mi>Τ</mi></mrow></semantics></math></inline-formula>) for the transient analysis of a power converter circuit with both passive and active loads. The method of complex conjugate amplitudes is employed for steady-state analysis. Both contributions represent innovative approaches within this study. The process begins with Fourier series expansions and the computation of Fourier coefficients, followed by solving the system’s steady-state and transient responses. The transient states are then confirmed using the Fourier transform. To validate these findings, the analytical results are verified through simulations conducted in the Matlab/Simulink R2023b environment.https://www.mdpi.com/2076-3417/14/21/9888Fourier transformLaplace–Carson transformtransient phenomenastate-space variableselectrical circuitspower electronic system |
| spellingShingle | Mariana Beňová Branislav Dobrucký Jozef Šedo Michal Praženica Roman Koňarik Juraj Šimko Martin Kuchař A Novel Approach to Transient Fourier Analysis for Electrical Engineering Applications Applied Sciences Fourier transform Laplace–Carson transform transient phenomena state-space variables electrical circuits power electronic system |
| title | A Novel Approach to Transient Fourier Analysis for Electrical Engineering Applications |
| title_full | A Novel Approach to Transient Fourier Analysis for Electrical Engineering Applications |
| title_fullStr | A Novel Approach to Transient Fourier Analysis for Electrical Engineering Applications |
| title_full_unstemmed | A Novel Approach to Transient Fourier Analysis for Electrical Engineering Applications |
| title_short | A Novel Approach to Transient Fourier Analysis for Electrical Engineering Applications |
| title_sort | novel approach to transient fourier analysis for electrical engineering applications |
| topic | Fourier transform Laplace–Carson transform transient phenomena state-space variables electrical circuits power electronic system |
| url | https://www.mdpi.com/2076-3417/14/21/9888 |
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