Intermittency and bifurcation in SEPICs under voltage-mode control

A stroboscopic map for voltage-controlled single ended primary inductor converter （SEPIC） with pulse width modulation （PWM） is presented, where low-frequency oscillating phenomena such as quasi-periodic and intermittent quasi-periodic bifurcations occurring in the system are captured by numerical and experimental methods. According to bifurcation diagrams and nonlinear dynamical theory, the characteristics of the low-frequency oscillation and the mechanism for the appearance of the low-frequency oscillation are investigated. It is shown that as the controller parameter varies, the change in the conduction mode takes place from the continuous conduction mode （CCM） under the originally stable period one and high periodic orbits to the intermittent changes between CCM and discontinuous conduction mode （DCM）, which may be related to the losing stability of the system and brought the system to exhibiting low-frequency oscillating behaviour in the time domain. Moreover, the occurrence of the intermittent quasi-periodic oscillation reflects that the system undergoes a Neimark-Sacker bifurcation.

A Method to Obtain Complex Transfer Functions of Four Order DC-DC Converters

Two TFs （transfer functions） are needed to analyze switching DC-DC converters in control-voltage mode： the duty-cycle to output-voltage （control to output） and the input-voltage to output-voltage （line to output）. To obtain these TFs a small-signal analysis is required. The CCM （continuous conduction mode） and the DCM （discontinuous conduction mode） analysis are different. When a circuit includes the loss resistances of the components, the number of parameters increases considerably, making manual nodal-loop circuit analysis techniques impractical to obtain the TFs. Moreover, these circuits are bilinear （non-linear） and it is necessary to linearize the equations at a DC operating-point （approximate linearization）. Vorp6rian describes a PWM （pulse-width-modulated） switch model that includes all non-linear parts of the DC-DC switching converters. This model can be linearized and replaced on the switching converter schematic leading to a linear circuit. At this point it is possible to use symbolic analysis programs to obtain these TFs or to simply apply numerical values for either the Bode diagrams or the calculation of poles and zeros. Here we describe an application of Ekrem Cangeici＇s method on X DC-DC converter to obtain control to output and line to output TFs in CCM and DCM including loss resistances. The method presented in this paper is optimized to use in the online publishing platform OctaveRS. Also the control to output TF for PCC （peak current controlled） in CCM is obtained.