Applications of describing functions to estimate the continuous and discontinuous conduction mode for a DC-to-DC buck converter

For a DC-to-DC buck converter, the performance of the conductor is significantly different for the converter operating on the continuous conduction mode (CCM) or discontinuous conduction mode (DCM). The operating condition on the CCM and DCM is addressed for a saturated inductor. It is shown that the inductor plays an essential role for the converter operating on the CCM and DCM. It is known that when the load is large, the inductance for the inductor always changes. This is due to the fact that when the current load is large, the inductance always suffers from saturation or hysteresis. Because the inductance is nonlinear, it is very difficult to estimate the actual value for the nonlinear inductance during large current situations. With the dual-input describing function method, the nonlinear inductor can be linearised and the inductance can be estimated during the large current situations. It can be shown that when the inductance of the inductor is saturated, the operating region of the discontinuous conduction mode (DCM) of the buck converter will extend drastically, which means the converter will easily operate in the discontinuous conduction mode. An experimental example verifies these results