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In this paper, we provide an analytical insight into the observed nonlinear behaviour of the buck converter and link this with the study of a wider class of piecewise-smooth systems. After introducing the buck converter model and background, we describe the most fascinating features of its dynamical behaviour. We then introduce the so-called grazing and sliding solutions and discuss their role in determining many of the buck converter's dynamical oddities. In particular, a local map is studied which explains how the grazing bifurcations cause sharp turning points in the bifurcation diagram of periodic orbits. Moreover, we show how these orbits accumulate onto a sliding trajectory through a "spiralling" impact adding scenario. The structure of such a diagram is derived analytically and is shown to be closely related to the analysis of homoclinic bifurcations. The results are shown to match perfectly with numerical simulations. The sudden jump to large-scale chaos and the fingered structure of the resulting attractor are also explained.
Original languageEnglish
Publication statusPublished - 1997

Bibliographical note

Additional information: Preprint of a paper later published by IOP Publishing (1998), Nonlinearity, 11 (4), pp.859-890, ISSN 0951-7715

Structured keywords

  • Engineering Mathematics Research Group


  • grazing and sliding solutions
  • dynamical behaviour
  • large-scale chaos
  • piecewise-smooth systems
  • homoclinic bifurcations
  • buck converter


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