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

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.

A 5G mm-wave compact voltage-controlled oscillator in 0.25 µm pHEMT technology

“…The architecture of the proposed VCO is based on the Colpitts structure studied in the references [16][17][18] and the structure proposed by the authors in [12] as shown in Figure 2. The active part of this oscillator consists of two transistors pHEMT 1 and pHEMT 2: each one has 4 fingers and a gate length and width of 0.25 µm and 20 µm, respectively.…”

Logistic Curve Modeling of the Germination of Beans Seeds Phaseolus Vulgaris Previously Exposed to Multi-Periodic and Chaotic Electromagnetic Fields

“…These authors used an electronic circuit of a few components Tchitnga [23] out of a family of simple chaotic circuits comprising a coil Tchitnga Talla & Zebaze Nanfa'a [24][25][26] to generate electromagnetic signals of various periods (period-1, period-2, period-4) as well as a chaotic signal. These various signals were applied to the bean plants during their evolution 24 hours a day and 7 days a week.…”

Experimental Study on Colpitts Chaotic Oscillator-Based Communication System Application for the Internet of Things

“…Simpler analog chaos oscillators can replace digital chaotic communication for resourceconstrained IoT sensors and nodes. Various chaotic oscillators, including Colpitts [36], have been extensively studied [37][38][39][40][41]. Colpitts chaos oscillators, in particular, have garnered attention for their simple schematic.…”