A New Exact Mathematical Approach for Studying Bifurcation in DCM Operated dc-dc Switching Converters

Abstract

A bifurcation study for dc-dc converters operated in DCM is performed using an accurate method. When applying classical techniques significant difficulties are encountered in the calculations. For example, using the averaging method the validity of the result is limited to half the switching frequency and higher order effects are neglected Another approach is to perform a Taylor expansion of the state transition matrices. However, this is somehow also an averaging but the fact that the Taylor series is truncated leads to unacceptable inaccuracy. A new mathematical technique for discontinuous conduction mode (DCM) analysis of dc-dc switching converters is proposed in order to predict bifurcation and chaos. The proposed technique is based on exact calculation of the state transition matrices and of the Jacobian thus providing higher accuracy of the results compared to other previously reported approaches. Beside the fact the new technique allows for exact diagnosis of instability, it is also highly general, in the sense that it can be applied to any dc-dc DCM operated converter employing any type of control. The good agreement between theoretical, simulation and experimental results, with an error lower than 0.94%, confirms the validity of the proposed method.

Keywords

• mathematical model
• bifurcation
• chaos
• state-space model
• discontinuous conduction mode
• eigenvalues
• nonlinear circuits