Gian Mario Maggio

Nonlinear analysis of the Colpitts oscillator and applications to design

This paper reports a methodological approach to the analysis and design of sinusoidal oscillators based on bifurcation analysis. The simple Colpitts oscillator is taken as an example to demonstrate this nonlinear approach for both the nearly sinusoidal and chaotic modes of operation. In particular, it is shown how regular and irregular (chaotic) oscillations can be generated, depending on the circuit parameters.

Nonsmooth bifurcations in a piecewise-linear model of the Colpitts oscillator

This paper deals with the implications of considering a first-order approximation of the circuit nonlinearities in circuit simulation and design. The Colpitts oscillator is taken as a case study and the occurrence of discontinuous bifurcations, namely, border-collision bifurcations, in a piecewise-linear model of the oscillator is discussed. In particular, we explain the mechanism responsible for the dramatic changes of dynamical behavior exhibited by this model when one or more of the circuit parameters are varied. Moreover, it is shown how an approximate one-dimensional (1-D) map for the Colpitts oscillator can be exploited for predicting border-collision bifurcations. It turns out that at a border collision bifurcation, a 1-D return map of the Colpitts oscillator exhibits a square-root-like singularity. Finally, through the 1-D map, a two-parameter bifurcation analysis is carried out and the relationships are pointed out between border-collision bifurcations and the conventional bifurcations occurring in smooth systems.

Bifurcations in the Colpitts oscillator: From theory to practice

This paper presents an experimental verification of the theoretical predictions, recently published in [Maggio et al., 1999; De Feo et al., 2000], about the bifurcation phenomena occurring in the Colpitts oscillator. Specifically, we performed an automated series of simulations based on the Spice model and, more importantly, a computer-assisted set of measurements on a concrete realization of the oscillator. It turns out that the bifurcation phenomena exhibited by the oscillator are relatively independent of the simplifying assumptions on the transistor model. Moreover, it is shown that the predicted behaviors can be reproduced experimentally, both qualitatively and quantitatively, in a robust way.

Devaney Chaos in an Approximate One-Dimensional Model of the Colpitts Oscillator

In this paper we consider an approximate one-dimensional model for describing the non-linear dynamics of the Colpitts oscillator. It has already been shown that this model preserves the qualitative dynamical behavior of the Colpitts oscillator. Using the theory of snap-back repellors we prove that the one-dimensional model is chaotic for certain values of its parameters.

Bifurcation phenomena in the Colpitts oscillator: a robustness analysis

A robustness assessment for the results of a bifurcation analysis of the Colpitts oscillator is presented. It is shown, by means of SPICE simulations, that the bifurcation phenomena occurring in the oscillator are relatively independent of the particular choice of the transistor model. Furthermore, the simulation results exhibit good agreement with the theoretical predictions. It is also demonstrated, through circuit experiments, that the predicted behaviors can be reproduced experimentally in a robust way.

T-CSK: A robust approach to chaos-based communications

Keywords: Non-Linear Signal Processing ; Communication a Chaos Reference LANOS-CONF-2000-010 Record created on 2004-12-03, modified on 2017-05-12