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Average-value modeling of dc-dc converters has been an area of active research for many years. Developing accurate average-value models of higher order converters is further complicated by the presence of parasitics and waveform nonlinearity. This paper extends the numerical state-space averaging to the fourth-order capacitor-based switching stages. The proposed model takes into account conduction losses associated with switching-stage components and is seamlessly functional in all operational modes. The proposed model is validated with a hardware prototype and detailed simulation and is shown to accurately predict large-signal time-domain transients as well as small-signal frequency-domain characteristics.