Two Twin-T based op amp oscillators modified for chaos
01 May 1998-Journal of The Franklin Institute-engineering and Applied Mathematics (Pergamon)-Vol. 335, Iss: 4, pp 771-787
TL;DR: In this article, two complementary sinusoidal oscillator circuits based on the Twin-T network are modified for chaos using a single discrete nonlinear device with antisymmetrical current-voltage characteristics, namely a junction field effect transistor (JFET) operating in its triode region.
Abstract: Two complementary sinusoidal oscillator circuits based on the Twin-T network are modified for chaos using a single discrete nonlinear device with antisymmetrical current-voltage characteristics, namely a junction field effect transistor (JFET) operating in its triode region. The two oscillators' design equations are used as a starting point for chaos modification. Mathematical models that describe the observed behaviour in both circuits are derived. Experimental results, PSpice circuit simulations and numerical simulations of the mathematical models agree well and are included.
Citations
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TL;DR: In this paper, two generic classes of chaotic oscillators comprising four different configurations are constructed based on the simplest possible abstract models of generic second-order RC sinusoidal oscillators that satisfy the basic condition for oscillation and the frequency of oscillation formulas.
Abstract: Two generic classes of chaotic oscillators comprising four different configurations are constructed. The proposed structures are based on the simplest possible abstract models of generic second-order RC sinusoidal oscillators that satisfy the basic condition for oscillation and the frequency of oscillation formulas. By linking these sinusoidal oscillator engines to simple passive first-order or second-order nonlinear composites, chaos is generated and the evolution of the two-dimensional sinusoidal oscillator dynamics into a higher dimensional state space is clearly recognized. We further discuss three architectures into which autonomous chaotic oscillators can be decomposed. Based on one of these architectures we classify a large number of the available chaotic oscillators and propose a novel reconstruction of the classical Chua's circuit. The well-known Lorenz system of equations is also studied and a simplified model with equivalent dynamics, but containing no multipliers, is introduced.
240 citations
TL;DR: In this article, an experimental evidence of chaos in one of the simplest implicit Hartley's oscillators made simply of a junction field effect transistor (JFET) and a tapped coil is presented.
Abstract: This paper shows an experimental evidence of chaos in one of the simplest imaginable autonomous implicit Hartley’s oscillator made simply of a junction field effect transistor (JFET) and a tapped coil. The experimental setup is implemented. The variations of amplitude of the oscillations through the control element are obtained showing the domain of existence of chaos. Phase portraits of the PSpice simulation, of the numerical integration and of the experiment are displayed, confirming a good agreement between theory and praxis.
59 citations
TL;DR: In this article, a new chaotic circuit based on Gm-C integrators is presented, which realizes the double-scroll-like chaotic equation presented by Sprott (2000) and Elwakil and Kennedy (2001).
Abstract: This brief presents a new chaotic circuit based on Gm-C integrators. The circuit realizes the double-scroll-like chaotic equation presented by Sprott (2000) and Elwakil and Kennedy (2001). The mentioned equation describes double-scroll dynamics with a simple mathematical model. The proposed circuit uses a current-mode technique that is suitable for integrated circuit implementation and high-frequency operation using low supply voltage. A general block diagram is presented based on Gm-C integrators. Its realization using MOS transistors and three grounded capacitors is also given. Simulation results to demonstrate the practicality of the circuit are included.
51 citations
TL;DR: The fact that Chua’s circuit can be physically decomposed into a sinusoidal oscillator coupled to an active voltage-controlled nonlinear resistor is demonstrated and a conjecture is state which it is believed forms a basis for the design of autonomous analog chaotic oscillators.
Abstract: The fact that Chua’s circuit can be physically decomposed into a sinusoidal oscillator coupled to an active voltage-controlled nonlinear resistor is demonstrated. The sinusoidal oscillator is the beating heart of Chua’s circuit and many novel implementations can be obtained by using di!erent sinusoidal oscillator engines. In particular, inductorless realizations can be derived not by replacing the passive inductor in the classical Chua’s circuit con"guration with an active RC emulation, but rather by replacing the passive LC tank resonator by a sinusoidal oscillator. We provide several circuit-design examples and verify our results experimentally. Finally, we state a conjecture which we believe forms a basis for the design of autonomous analog chaotic oscillators. ( 2000 The Franklin Institute. Published by Elsevier Science Ltd. All rights reserved.
48 citations
Cites methods from "Two Twin-T based op amp oscillators..."
...The "rst case is when the sinusoidal oscillator is already third order [12,16], while the second case is when a hysteresis-type nonlinear device is used [11,23]....
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TL;DR: The procedure aims to transfer design issues of analog autonomous chaotic oscillators from the nonlinear domain back to the much simpler linear domain by intentionally modifying sinusoidal oscillator circuits in a semisystematic manner.
Abstract: A design procedure for producing chaos is proposed. The procedure aims to transfer design issues of analog autonomous chaotic oscillators from the nonlinear domain back to the much simpler linear domain by intentionally modifying sinusoidal oscillator circuits in a semisystematic manner. Design rules that simplify this procedure are developed and then two composite devices, namely, a diode-inductor composite and a FET-capacitor composite are suggested for carrying out the modification procedure. Applications to the classical Wien-bridge oscillator are demonstrated. Experimental results, PSpice simulations, and numerical simulations of the derived models are included.
40 citations
Cites background or methods from "Two Twin-T based op amp oscillators..."
...It should be noted that starting with a third-order sinusoidal oscillator, such as the TwinT oscillator, the above procedure simplifies to choosing a suitable position to insert a passive nonlinear element and adjusting the tuning parameters associated with the condition of oscillation [20]....
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...Other types of oscillator have also been modified for chaos [20]–[22]....
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References
More filters
01 Nov 1993
TL;DR: Strange attractors and dynamical models, L.O. Kennedy sound and music from Chua's low-level visual sensing, E.J. Elgar and M.P. Shil'nikov from the Chua circuit to the generalized Chua map.
Abstract: Strange attractors and dynamical models, L.P. Shil'nikov from the Chua circuit to the generalized Chua map, R. Brown bispectral analysis of Chua's circuit, S. Elgar and M.P. Kennedy sound and music from Chua's low-level visual sensing, E.J. Altman chaos synchronization in Chua's circuit, L.O. Chua et al controlling chaos in Chua's circuit, G.A. Johnson et al controlling of chaos in the driven Chua's circuit, K. Murali and M. Lakshmanan controlling Chua's circuit, G-R. Chen and X-N. Dong distortion control of chaotic systems - the Chua's circuit, R. Genesio and A. Tesi control of Chua's circuit, T. Hartley and F. Mossayebi reconstructing the dynamics of Chua's circuit, J. Glover and A. Mees travelling wavefront and its failure in a one-dimensional array of Chua's circuit, V. Perez-Munuzuri et al n-dimensional canonical Chua's circuit, Lj Kocarev et al. (Part contents).
694 citations
TL;DR: In this article, the authors present experimental results and SPICE simulations of chaos in a Colpitts oscillator and show that the nonlinear dynamics of this oscillator may be modeled by a third-order autonomous continuous-time circuit consisting of a linear inductor, two linear capacitors, 2 linear resistors, two independent voltage sources, a linear current-controlled current source, and a single voltage-controlled nonlinear resistor.
Abstract: In this work, we present experimental results and SPICE simulations of chaos in a Colpitts oscillator. We show that the nonlinear dynamics of this oscillator may be modeled by a third-order autonomous continuous-time circuit consisting of a linear inductor, two linear capacitors, two linear resistors, two independent voltage sources, a linear current-controlled current source, and a single voltage-controlled nonlinear resistor. The nonlinear resistor has a two-segment piecewise-linear DP characteristic. With the appropriate choice of parameters, the piecewise-linear circuit model has a positive Lyapunov exponent. >
362 citations
TL;DR: In this article, a nonlinear Wien-bridge-based circuit for chaotic oscillations is described, which contains a single opamp and a single nonlinear device displaying a current saturation characteristic.
Abstract: A nonlinear Wien-bridge based circuit generating chaotic oscillations is reported. The generator contains a single opamp and a single nonlinear device displaying a current saturation characteristic. The oscillator is described by a set of three ordinary differential equations. Experimental results are included demonstrating the circuit performance.
81 citations
TL;DR: In this article, an inductorless realisation of a Chua oscillator, which exhibits chaotic behaviour is presented, consisting of the Wien bridge oscillator coupled in parallel with the same nonlinear resistor used in the standard realisation.
Abstract: An inductorless realisation of a Chua oscillator, which exhibits chaotic behaviour is presented. This new realisation consists of the Wien bridge oscillator, coupled in parallel with the same nonlinear resistor used in the standard realisation of a Chua oscillator. This new circuit is shown experimentally to also exhibit similar chaotic behaviour.
56 citations
TL;DR: In this article, a multiloop active filter circuit of Kerwin was shown to yield a VCO whose oscillation frequency is conveniently controlled with one variable resistor, using an FET to obtain the voltage variable resistor.
Abstract: A multiloop active filter circuit of Kerwin is shown to yield a VCO whose oscillation frequency is conveniently controlled with one variable resistor. Using an FET to obtain the voltage variable resistor, experimental results are shown to agree with the theory developed.
51 citations