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基于最简单的无电阻运算放大器的考毕兹振荡器中的非周期振荡、双稳性、混沌与超混沌共存。

Non periodic oscillations, bistability, coexistence of chaos and hyperchaos in the simplest resistorless Op-Amp based Colpitts oscillator.

作者信息

Nanfa'a R Zebaze, Tchitnga R, Fotso P H Louodop, Kengne R, Talla F C, Nana B, Pelap F B

机构信息

Unité de Recherche de Matière Condensée d'Electronique et de Traitement du Signal (URMACETS), Department of Physics, Faculty of Science, University of Dschang, P.O. Box 67 Dschang, Cameroon.

Research Group on Experimental and Applied Physics for Sustainable Development, Department of Physics, Faculty of Science, University of Dschang, P.O.Box 412 Dschang, Cameroon.

出版信息

Heliyon. 2020 Feb 27;6(2):e03482. doi: 10.1016/j.heliyon.2020.e03482. eCollection 2020 Feb.

DOI:10.1016/j.heliyon.2020.e03482
PMID:32140597
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC7047204/
Abstract

In the framework of a project on simple circuits with unexpected high degrees of freedom, we report an autonomous microwave oscillator made of a CLC linear resonator of Colpitts type and a single general purpose operational amplifier (Op-Amp). The resonator is in a parallel coupling with the Op-Amp to build the necessary feedback loop of the oscillator. Unlike the general topology of Op-Amp-based oscillators found in the literature including almost always the presence of a negative resistance to justify the nonlinear oscillatory behavior of such circuits, our zero resistor circuit exhibits chaotic and hyperchaotic signals in GHz frequency domain, as well as many other features of complex dynamic systems, including bistability. This simplest form of Colpitts oscillator is adequate to be used as didactic model for the study of complex systems at undergraduate level. Analog and experimental results are proposed.

摘要

在一个关于具有意外高自由度的简单电路的项目框架内，我们报告了一种由科尔皮茨型CLC线性谐振器和单个通用运算放大器（运放）制成的自主微波振荡器。谐振器与运放并联耦合以构建振荡器所需的反馈回路。与文献中基于运放的振荡器的一般拓扑结构不同，后者几乎总是存在负电阻来解释此类电路的非线性振荡行为，我们的零电阻电路在GHz频域中呈现出混沌和超混沌信号，以及复杂动态系统的许多其他特征，包括双稳性。这种最简单形式的科尔皮茨振荡器足以用作本科阶段研究复杂系统的教学模型。文中给出了模拟和实验结果。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/2bb1/7047204/a098634ab024/gr17.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/2bb1/7047204/8648eff4a421/gr1.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/2bb1/7047204/56735b7fc9fa/gr2.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/2bb1/7047204/87cfd74cc0a7/gr3.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/2bb1/7047204/74d85725ea07/gr4.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/2bb1/7047204/d8142f612095/gr5.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/2bb1/7047204/d3546db32570/gr6.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/2bb1/7047204/1663ad9b9c9e/gr7.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/2bb1/7047204/40b4c4857345/gr8.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/2bb1/7047204/aaf1f276b769/gr9.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/2bb1/7047204/985026bf53ef/gr10.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/2bb1/7047204/63961014881a/gr11.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/2bb1/7047204/dcfc0e244390/gr12.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/2bb1/7047204/37e7d4cc2a90/gr13.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/2bb1/7047204/300596455f43/gr14.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/2bb1/7047204/fba1d812fb2c/gr15.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/2bb1/7047204/c4a4a12dc0d3/gr16.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/2bb1/7047204/a098634ab024/gr17.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/2bb1/7047204/8648eff4a421/gr1.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/2bb1/7047204/56735b7fc9fa/gr2.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/2bb1/7047204/87cfd74cc0a7/gr3.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/2bb1/7047204/74d85725ea07/gr4.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/2bb1/7047204/d8142f612095/gr5.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/2bb1/7047204/d3546db32570/gr6.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/2bb1/7047204/1663ad9b9c9e/gr7.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/2bb1/7047204/40b4c4857345/gr8.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/2bb1/7047204/aaf1f276b769/gr9.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/2bb1/7047204/985026bf53ef/gr10.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/2bb1/7047204/63961014881a/gr11.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/2bb1/7047204/dcfc0e244390/gr12.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/2bb1/7047204/37e7d4cc2a90/gr13.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/2bb1/7047204/300596455f43/gr14.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/2bb1/7047204/fba1d812fb2c/gr15.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/2bb1/7047204/c4a4a12dc0d3/gr16.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/2bb1/7047204/a098634ab024/gr17.jpg

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本文引用的文献

1
Didactic model of a simple driven microwave resonant T-L circuit for chaos, multistability and antimonotonicity.用于研究混沌、多稳定性和反单调性的简单驱动微波谐振T型L电路的教学模型。
Heliyon. 2019 Nov 1;5(10):e02715. doi: 10.1016/j.heliyon.2019.e02715. eCollection 2019 Oct.
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