Frequency dependent efficiency model of on-chip DC-DC buck converters

An analytic method to evaluate frequency dependent losses in on-chip DC-DC buck converters is presented in this paper. These converters feature high switching losses caused by the skin effect in the package inductors. The frequency dependent air-core inductor model is shown to be critical in determining the optimal switching frequency. A general RLC parameter extraction method is also described. Considering the skin effect results in a 15% reduction in overall DC-DC converter losses. The proposed approach focuses on decreasing ripple current related losses, which are dominant in the target operating condition. Consequently, to obtain optimal efficiency, the switching frequency increases as the load current decreases. An intuitive explanation for this surprising result is that switching losses rise linearly with frequency whereas ripple losses decrease as n^1.5. A SPICE based circuit model of a DC-DC converter is applied to validate the proposed analytic method.