Abstract
This paper presents a new approach for small-signal analysis of all types of dc-dc converters with any number of topological modes within a switching cycle. So far, sampled-data modeling and sensitivity analysis are mostly used for such a purpose. In both cases, the switching conditions implicitly appear in the small-signal matrices which increases the complexity of the computation for the system with a larger number of topological modes. Here, we propose an alternative approach based on Filippov's method, which studies the effects of each switching separately. It uses a shooting method with an event detector to locate a periodic steady-state, and, when the Newton-Raphson search process of the shooting method converges, it also gives the Jacobian matrix. The algorithm can be easily implemented in a software program as an analytical tool which is expected to be useful for fast and accurate frequency-domain analysis (by small-signal transfer functions) to facilitate controller design. Moreover, since it uses the Filippov's method, this algorithm can also predict the slow- and fast-timescale instabilities.
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