28.5 A 94.1%-Efficiency Parallel-SC Hybrid Buck Converter Designed Using VCR-Aware Topology Optimizer for a 4.2A/mm² Current-Density FoM

Increasing power density—delivering more power in a smaller footprint—stands as a pervasive trend across multiple markets, including the sector for buck DC-DC converters. One of the cardinal challenges in achieving optimized power density is navigating the intrinsic trade-off between an inductor's volume and its parasitic DC resistance (DCR); miniaturizing the inductor invariably leads to elevated DCR. To enhance efficiency even when using compact inductors, many hybrid buck converter topologies have been investigated [1–4]. These hybrid inductor-capacitor innovations aim to mitigate inductor current (IL) by means of additional capacitive power delivery. A straightforward method for designing hybrid converters involves substituting one switch in a switched-capacitor (SC) converter with an inductor. As illustrated in the upper-left of Fig. 28.5.1, employing this design methodology enables the derivation of four distinct hybrid designs (H 1 to H 4) from a basic 2:1 SC converter. In most hybrid converters, the flying capacitor (CF) is charged by IL during the on-duty cycle (D × TS) and discharges its capacitive current, IC, to the output (V₀) during the off-duty cycle [(1-D) × TS]. Accordingly, the duty-cycle ratio $(D)$ is critical in determining both IL and IC. As exemplified in the H 3 and H 4 topologies (top right of Fig. 28.5.1), a low D leads to a negligible reduction in IL, thereby losing the benefits of a hybrid converter. Conversely, when D is too high, IC is prone to excessive surges because of the overcharging of CF during an extended D · TS, which in turn makes IC ²-related conduction loss dominant. Optimal balance in the delivery of IL and IC can thus be achieved when D ≈ 0.5. It is worth noting that D also influences the voltage conversion ratio (VCR). The bottom right of Fig. 28.5.1 shows the H 1 to H4's conduction losses, normalized to those in a typical buck converter. Herein, the optimal VCR at which $D(=0.5)$ is balanced is denoted as V C Ropt.. Interestingly, it can be seen that the minimum loss point for each hybrid design closely aligns with V C R0 p t. Therefore, for maximum efficacy of a hybrid converter, the topology should be designed such that the target VCR (.V C RTarget) matches V C R0 p t.