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

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Maggio, Gian Mario
Di Bernardo, Mario
Kennedy, Michael Peter
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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
Border-collision bifurcations , Colpitts oscillator , Grazing , Nonsmooth systems , One-dimensional map , Sliding mode
Maggio, G.M., di Bernardo, M., Kennedy, M.P., 2000. Nonsmooth bifurcations in a piecewise-linear model of the Colpitts oscillator. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 47(8), pp.1160-1177. doi: 10.1109/81.873871
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