Non periodic oscillations, bistability, coexistence of chaos and hyperchaos in the simplest resistorless Op-Amp based Colpitts oscillator
R. Zebaze Nanfa'a,
R. Tchitnga,
P.H. Louodop Fotso,
R. Kengne,
F.C. Talla,
B. Nana,
F.B. Pelap
Affiliations
R. Zebaze Nanfa'a
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
R. Tchitnga
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; Institute of Surface Chemistry and Catalysis, University of Ulm, Albert-Einstein-Allee 47, 89081, Ulm, Germany; Corresponding author.
P.H. Louodop Fotso
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; São Paulo State University (UNESP), Instituto de Física Teórica, Rua Dr. Bento Teobaldo Ferraz 271, Bloco II, Barra Funda, 01140-070, São Paulo, Brazil
R. Kengne
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
F.C. Talla
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; Department of Physics, University of Bamenda, Bamenda, P.O.Box 39 Bamenda, Cameroon
B. Nana
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; Department of Physics, University of Bamenda, Bamenda, P.O.Box 39 Bamenda, Cameroon
F.B. Pelap
Laboratoire de Mécanique et de Modélisation des Systèmes, L2MS, Department of Physics, Faculty of Science, University of Dschang, P.O.Box 67, Dschang, Cameroon
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.
