Dynamical Modeling and Multi-period Behavior Analysis of Voltage-mode Bi-frequency Controlled Switching Converter

Dynamical model and the corresponding characteristics equation of volt-age-mode bi-frequency controlled switching converter operating in discontinu-ous conduction mode are derived. According to the dynamical model, its bor-der-collision bifurcation and multi-period behaviors, such as period-2, period-3, period-4, and so on, are studied by bifurcation diagram with the variation of circuit parameters. It is found that the converter behaves the bifurcation route of period-1, multi-period, and period-1, and the change of period state is induced by border-collision bifurcation. Based on the characteristics equation, its stabil-ity is investigated by Lyapunov exponent. It is shown that Lyapunov exponent is always smaller than zero with the variation of circuit parameters and the con-verter operates in stable period state all the time. Also, it is validated that pe-riod-3 behavior of voltage-mode bi-frequency controlled switching converter does not predicate its inevitable chaos. Time-domain waveforms, phase portraits, and fre-quency spectrums of voltage- mode bi-frequency controlled switching converter are analyzed by circuit simulation, which validates the feasibility of dynamical model and the correctness of theoretical analysis. Simulation results are verified by experimental ones in this paper.