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 pcrformancc of tlic conductor is significantly different for the converter operating on the coiitinuous coiiductioii inode (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 esscntial role for the converter opcrating on the CCM and DCM. It is known that when the load is large, the inductance for the inductor always changes. This is due lo the [act that when the current load is large, the inductance always suffers from saturation or hystersis. Because tlie inductance is nonliiiear, it very difticult lo estimate the actual value for the nonlinear inductance during large current situations. With the dual-input dcscribiiig funclion method, the nonlinear inductor can be lineariscd and the inductance can be estimated during the large current situations. It can be shown that when the induckaim of the inductor is saturated, the operating region of the discontinuous conduction inode (DCM) or the buck converter will extend drastically, which mcaiis the converter will easily operate in tlie discontinuous conduction mode. An experinicntal example verifies these results.