An accurate small-signal model of a low-side active clamp forward converter and stability assessment in hard- and soft-switching operations

This article examines the internal stability of an active clamp forward converter (ACFC) from a non-linear system and arbitrary changes in the state variable's point of view. The analysis is based on the Lyapunov direct method in conjunction with the operating theory of the ACFC. The equivalent circuit with the state equations is established and their stability is assessed in consideration of the hard- and soft-switching operations using the Lyapunov energy function approach in a piecewise manner. In addition, averaged switch modelling is applied explicitly to derive a more accurate small-signal model of a low-side ACFC. The study revealed the presence of a non-minimum phase problem as the major adverse effect on the stability feature of the ACFC predesigned with soft-switching capability. The instability of ACFC is related to the magnetising inductance ($L_m$) value (core loss resistance) which influences/determines the hard- or soft-switching operations of the ACFC. Hardware prototype was developed with two different transformers having distinct values of $L_m$ for hard- and soft-switching operations. From the experimental frequency measurement, the model accurately predicts the movement of the complex zeros from the left-half-plane (LHP) to the right-hand-plane (RHP) as the ACFC changes from the hard-switching to a soft-switching operation.