Switched-Inductor DC–DC Converters: Direct Small-Signal Equivalent AC Circuit

Switched-inductor converters are ubiquitous in modern electronics. Their switching behavior makes them inherently nonlinear and unsuitable for classical linear frequency-response models, requiring linearization for stability analysis. Common approaches—such as state-space averaging, circuit averaging, and signal-flow graphs—can be algebraically intensive and may offer limited circuit-level interpretability. This paper proposes a direct small-signal AC response model for switched inductors in both CCM and DCM that preserves circuit intuition while maintaining the accuracy of conventional methods. The proposed framework enables the systematic derivation of the duty-cycle-to-output-voltage, duty-cycle-to-output-current, and duty-cycle-to-inductor-current transfer functions within a unified circuit representation. Bode plots of the duty-cycle-to-voltage and duty-cycle-to-current gains confirm that the model accurately captures the LC double pole and associated zeros, including the shift of the load-related zero in the reconstructed inductor-current gain. The resulting model remains straightforward to use, analyze, and simulate and may facilitate control-loop design as well as integration into automated synthesis or optimization tools. In DCM, the model further provides an analytical expression for the duty-cycle-to-inductor-current gain, contributing to a clearer understanding of this relationship in the literature. Results validated in SIMPLIS show excellent agreement with state-space averaging predictions.