Oscillators And Oscillator Systems

Many dynamical systems in physics, chemistry and biology exhibit complex be­ haviour. The apparently random motion of a fluid is the best known example. How­ ever also vibrating structures, electronic oscillators, magnetic devices,lasers, chemical oscillators, and population kinetics can behave in a complicated manner. One can find irregular oscillations, which is now known as chaotic behaviour. The research field of nonlinear dynamical systems and especially the study of chaotic systems has been hailed as one of the important breaktroughs in science this century. The sim­ plest realization of a system with chaotic behaviour is an electronic oscillator. The purpose of this book is to provide a comprehensive introduction to the application of chaos theory to electronic systems. The book provides both the theoretical and experimental foundations of this research field. Each electronic circuit is described in detail together with its mathematical model. Controlling chaos of electronic oscilla­ tors is also included. End of proofs and examples are indicated by •. Inside examples the end of proofs are indicated with O. We wish to express our gratitude to Catharine Thompson for a critical reading of the manuscript. Any useful suggestions and comments are welcome. Email address of the first author: MVANWYK@TSAMAIL. TRSA. AC. ZA Email address of the first author: WHS@RAU3. RAU. AC. ZA Home page of the authors: http://zeus. rau. ac. za/steeb/steeb. html xi Chapter 1 Introduction 1.

"Pseudochaotic Kicked Oscillators: Renormalization, Symbolic Dynamics, and Transport" presents recent developments in pseudochaos, which is concerned with complex branching behaviors of dynamical systems at the interface between orderly and chaotic motion.

The design and optimization of electronic systems often requires appraisal an of the electrical noise generated by active devices, and, at a technological level, the ability to properly design active elements in order to minimize, when possible, their noise. Examples of critical applications are, of course, receiver front-ends in RF and optoelectronic transmission systems, but also front-end stages in sensors and, in a completely different context, nonlinear circuits such as oscillators, mixers, and frequency multipliers. The rapid de­ velopment of silicon RF applications has recently fostered the interest toward low-noise silicon devices for the lower microwave band, such as low-noise MOS transistors; at the same time, the RF and microwave ranges are be­ coming increasingly important in fast optical communication systems. Thus, high-frequency noise modeling and simulation of both silicon and compound­ semiconductor based bipolar and field-effect transistors can be considered as an important and timely topic. This does not exclude, of course, low­ frequency noise, which is relevant also in the RF and microwave ranges when­ ever it is up-converted within a nonlinear system, either autonomous (as an oscillator) or non-autonomous (as a mixer or frequency multiplier). The aim of the present book is to provide a thorough introduction to the physics-based numerical modeling of semiconductor devices operating both in small-signal and in large-signal conditions. In the latter instance, only the non-autonomous case was considered, and thus the present treatment does not directly extend to oscillators.

Shape your perfect sound leveraging the powerful Dual oscillators, LFO, Sample and Hold, Ring-mod, high-pass and low pass filters. Take inspiration from the built-in library and start your own sonic odyssey of discovery with endless tweakability. You can use Odyssey as mono, duophonic or as a polyphonic synth with up to 4 simultaneous voices to take your project to the next level.