Small-signal modeling of switched-mode converters under direct-on-time control-a unified approach

Small-signal modeling of switched-mode converters has been developed in early 70s, when the state-space averaging (SSA) method was introduced for assessing the dynamics of direct-duty-ratio controlled converters in continuous conduction mode (CCM). It turned out that the direct circuit theoretical approach could not be applied to get accurate models also for discontinuous operation mode (DCM). We present in this paper a unified and consistent method for the modeling of switched-mode converters under direct-on-time control applicable to fixed-frequency and variable-frequency operation in DCM and CCM. 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.