Normalized geometrical analysis: unified theory and derivation of natural trajectories for basic dc-dc topologies

This paper introduces a generalized derivation and equation that represents the behavior of the basic dc-dc topologies (namely buck, boost, and buck-boost converters) in a normalized geometrical domain. The establishment of a unified theory is an important step towards understanding the natural trajectories and physical limits of power converters. A comprehensive insight into geometrical characteristics allows for the derivation and benchmarking of high-performance controllers, which results in enhanced dynamic responses. The contribution of the normalized geometrical domain analysis relates to the understanding of the highly non-linear nature and large-signal characteristics of converters not covered by small-signal, linearized modeling around a quiescent operating point. Experimental results of buck, boost, and buck-boost converters are provided to illustrate the geometrical behavior described by a unified equation and the benefits of the state-plane analysis.