Unified average and small-signal modeling of direct-on-time control

A unified and consistent method for the average and small-signal modeling of switched-mode converters under direct-on-time (DOT) or voltage mode (VM) control applicable to fixed- and variable-frequency operation in discontinuous (DCM) and continuous (CCM) modes of operation is proposed. The method is based on the direct estimation of the state-variable derivatives using their physical and circuit theoretical dependence on the corresponding circuit elements. This has been the first time that it has been explicitly recognized that the time-varying local average value of the inductor current is the state variable instead of the instantaneous current being also continuous within a cycle regardless of the operation mode. The method provides a common basis for the average modeling of VM control and leads eventually to the well-recognized results obtained using state-space averaging (SSA) in CCM or its modified version in DCM under fixed-frequency operation as well as accurate full-order models also in the variable-frequency operation. In addition, the method known as unterminated modeling is introduced, providing a useful tool for the dynamic analysis of switched-mode converters.