Generation of chaos with simple sets of semiconductor devices

An introduction to the design of chaotic oscillators is presented from an electrical engineering point of view. Oscillators are amplifiers with unstable bias points. The basic design principle behind chaotic oscillators is the connection of two electronic circuits which are not in harmony. A number of configurations which may serve as the physical mechanisms behind chaotic behavior are listed. The behavior of an oscillator is explained by means of eigenvalue studies of the linearized Jacobian of the differential equations for the mathematical model of the oscillator. The basic design principle is demonstrated by means of different simple examples. Chaos in Circuits and Systems Downloaded from www.worldscientific.com by UNIVERSITY OF BIRMINGHAM LIBRARY -INFORMATION SERVICES on 03/20/15. For personal use only. 2 Chaotic Oscillators -Design Principles Introduction and General RemarksRadio amateurs and electronic engineers have observed chaotic performance of electronic circuits since the invention of the triode amplifier by Lee de Forest in 1906. The phenomena observed were called noise, nonlinear distortion, parasitic oscillations, intermittent operation or asynchronous heteroperiodic excitation. It was considered unwanted and impossible to investigate analytically. Edwin H. Armstrong invented the regenerative circuit for HF oscillations in 1912 (superheterodyne 1918, FM 1937. He possibly observed chaos [1,2]. Balthasar van der Pol (1889van der Pol ( -1959 reports about chaos as "an irregular noise" [3][4][5][6]. Today (year 2001) we are able to investigate the phenomena by means of computer simulation.We are interested in chaos for two reasons: we want to avoid chaos and/or we want to make use of chaos. In both cases it is necessary to study chaos in order to understand and master the phenomena. Unfortunately we still need analytical methods for the investigation of nonlinear systems in details. All our analytical design methods are based on linear approximations.Sinusoidal oscillators are normally considered second order systems. Many topologies have been proposed for sinusoidal oscillators (Colpitts, Clapp, Hartley, Pierce etc.). The design of an oscillator is normally based on the Barkhausen criteria [7] according to which an oscillator is looked upon as an ideal finite gain amplifier with a linear frequency determining feed-back circuit ( Fig. 1.5). If the poles of the whole linear circuit are placed on the imaginary axis in the complex frequency plane (s-plane) we have an ideal oscillator. In order to startup the oscillator some component values are tuned so that the complex pole pair of the circuit is placed in the right half plane (RHP) making the circuit unstable. It is then hoped that the nonlinearities of the amplifier will give rise to a limitation of the signals so that stable oscillations may occur. Possible distortion is smoothed by means of filters. Very little is reported about the mechanism behind the observed stable oscillations. Some authors even claim that the complex pole pair "is brought bac...

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“…based on nonlinear coils and/or capacitors. [29]. It is an example of coupling of two electronic circuits which are not in harmony.…”

Section: Ementioning

confidence: 99%

Chaotic Oscillators - Design Principles

Lindberg¹,

Murali²,

Tamaševičius³

2002

World Scientific Series on Nonlinear Science Series B

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“…Fig. 1 shows an ideal sinusoidal oscillator VS loaded with an RC series circuit in connection with the collector of a transistor with grounded emitter [5]. The base of the transistor is loaded with a grounded capacitor , which is charged by a constant dc voltage source VDC in series with a large resistor, i.e., integration of an almost constant dc current source.…”

Section: Introductionmentioning

confidence: 99%

The smallest transistor-based nonautonomous chaotic circuit

Lindberg

Murali

Tamaševičius

2005

IEEE Trans. Circuits Syst. II

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On the Mechanisms Behind Chaos

Lindberg

2006

Nonlinear Dyn

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Chaotic systems are observed everywhere. Electronic circuit analogues based on the differential equations of the models for the chaotic systems are often used to study the nature of chaotic systems. This tutorial is an attempt to classify electronic chaotic oscillators according to the mechanism behind the chaotic behavior, e.g. one group is based on the sudden interrupt of inductive currents, another group is based on the sudden parallel coupling of capacitors with different voltages, and a third group may be based on multiplication of signals. An example of chaos based on disturbance of integration is discussed in details.

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Generation of chaos with simple sets of semiconductor devices

Cited by 4 publications

References 9 publications

Chaotic Oscillators - Design Principles

Chaotic Oscillators - Design Principles

The smallest transistor-based nonautonomous chaotic circuit

On the Mechanisms Behind Chaos

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