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

This paper dears with the implications of considering a first-order approxi mation of the circuit nonlinearities in circuit simulation and design. The Colpitts oscillator is taken as a case study and the occurrence of disconti nuous bifurcations, namely, border-collision bifurcations, in a piecewise-l inear model of the oscillator is discussed. In particular, we explain the m echanism responsible for the dramatic changes of dynamical behavior exhibit ed by this model when one or more of the circuit parameters are varied. Mor eover, it is shown how an approximate one-dimensional (1-D) map for the Col pitts oscillator can be exploited for predicting border-collision bifurcati ons. It turns out that at a border-collision bifurcation, a I-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.