Transient Responses to Relaxation Oscillations in Multivibrators
The multivibrator is an electronic circuit that has three oscillation states: astable, monostable, and bistable; these circuits typically contain opamps. These states are often modeled using hybrid systems, which contain characteristics of both continuous and discrete time. While an ideal opamp poss...
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| Format: | Article |
| Language: | English |
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IEEE
2024-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/10371294/ |
| _version_ | 1797366824576221184 |
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| author | Seiya Amoh Tetsushi Ueta Hiroshi Kawakami |
| author_facet | Seiya Amoh Tetsushi Ueta Hiroshi Kawakami |
| author_sort | Seiya Amoh |
| collection | DOAJ |
| description | The multivibrator is an electronic circuit that has three oscillation states: astable, monostable, and bistable; these circuits typically contain opamps. These states are often modeled using hybrid systems, which contain characteristics of both continuous and discrete time. While an ideal opamp possesses both continuous and discrete characteristics, actual opamps exhibit continuous properties, which necessitate in-depth modeling. The relaxation oscillations produced by the multivibrator, characterized by periodic, rapid state changes, are typically modeled by considering slow–fast dynamical systems. In these systems, the phenomenon whereby the amplitude of the signal changes rapidly is referred to as a “canard explosion”. By considering this phenomenon, it is possible to understand the process of relaxation oscillations in the multivibrator. In this work, we model the multivibrator by considering a slow-fast dynamical system and observe canard explosions through numerical experiments. This study indicates that the oscillatory changes in the multivibrator are continuous, which explains the onset of relaxation oscillations. Additionally, circuit experiments are conducted using affordable opamps; in this experimental work, canard explosions are observed. |
| first_indexed | 2024-03-08T17:10:10Z |
| format | Article |
| id | doaj.art-cd6f0668db2f4116b45ca55b19f7fada |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-03-08T17:10:10Z |
| publishDate | 2024-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-cd6f0668db2f4116b45ca55b19f7fada2024-01-04T00:02:34ZengIEEEIEEE Access2169-35362024-01-011247148210.1109/ACCESS.2023.334584010371294Transient Responses to Relaxation Oscillations in MultivibratorsSeiya Amoh0https://orcid.org/0000-0003-2423-9625Tetsushi Ueta1https://orcid.org/0000-0001-5810-437XHiroshi Kawakami2https://orcid.org/0000-0002-8083-8174Graduate School of Advanced Technology and Science, Tokushima University, Tokushima, JapanCenter for Administration of Information Technology, Tokushima University, Tokushima, JapanFaculty of Engineering, Tokushima University, Tokushima, Japan (Retired)The multivibrator is an electronic circuit that has three oscillation states: astable, monostable, and bistable; these circuits typically contain opamps. These states are often modeled using hybrid systems, which contain characteristics of both continuous and discrete time. While an ideal opamp possesses both continuous and discrete characteristics, actual opamps exhibit continuous properties, which necessitate in-depth modeling. The relaxation oscillations produced by the multivibrator, characterized by periodic, rapid state changes, are typically modeled by considering slow–fast dynamical systems. In these systems, the phenomenon whereby the amplitude of the signal changes rapidly is referred to as a “canard explosion”. By considering this phenomenon, it is possible to understand the process of relaxation oscillations in the multivibrator. In this work, we model the multivibrator by considering a slow-fast dynamical system and observe canard explosions through numerical experiments. This study indicates that the oscillatory changes in the multivibrator are continuous, which explains the onset of relaxation oscillations. Additionally, circuit experiments are conducted using affordable opamps; in this experimental work, canard explosions are observed.https://ieeexplore.ieee.org/document/10371294/Bifurcation analysiscanardmultivibratorsingular perturbationslow–fast dynamical systems |
| spellingShingle | Seiya Amoh Tetsushi Ueta Hiroshi Kawakami Transient Responses to Relaxation Oscillations in Multivibrators IEEE Access Bifurcation analysis canard multivibrator singular perturbation slow–fast dynamical systems |
| title | Transient Responses to Relaxation Oscillations in Multivibrators |
| title_full | Transient Responses to Relaxation Oscillations in Multivibrators |
| title_fullStr | Transient Responses to Relaxation Oscillations in Multivibrators |
| title_full_unstemmed | Transient Responses to Relaxation Oscillations in Multivibrators |
| title_short | Transient Responses to Relaxation Oscillations in Multivibrators |
| title_sort | transient responses to relaxation oscillations in multivibrators |
| topic | Bifurcation analysis canard multivibrator singular perturbation slow–fast dynamical systems |
| url | https://ieeexplore.ieee.org/document/10371294/ |
| work_keys_str_mv | AT seiyaamoh transientresponsestorelaxationoscillationsinmultivibrators AT tetsushiueta transientresponsestorelaxationoscillationsinmultivibrators AT hiroshikawakami transientresponsestorelaxationoscillationsinmultivibrators |