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.

A new method for analysing the stability of dc-dc converters in closed-loop operation is developed. A generalized discrete model is proposed consisting of two nonlinear vector equations: the state equation and the nondynamic constraint. After model linearization, the classical technique of using characteristic multipliers can be applied. Several problems were solved regarding: the nondynamic constraint derivation; the steady-state operation point calculation; verifying that the parameters defining the steady-state operation point are located in the linear region and are not in the proximity of a saturated vicinity; partial derivatives determination and Jacobian calculation. The above concepts have been easily implemented in Matlab, allowing: determination of the parameter value for which instability occurs; to demonstrate that instability is installed with a Neimark-Sacker bifurcation; to prove that the proposed exact method predicts a much larger stable region, 327% higher compared to that predicted by the traditional approach. The theoretical considerations were accurately validated by computer simulation.