Steady-State Analysis of Series-Capacitor Buck Converters in Discontinuous Capacitor Voltage Mode

The series-capacitor buck (SCB) converter is a compact and highly-efficient alternative to the multi-phase buck converter and has recently been demonstrated in data center applications. To achieve high power density, it is desirable to reduce the total flying capacitance in this topology. However, for sufficiently small flying capacitances, a discontinuous capacitor voltage mode (DCVM) manifests, leading to an imbalance in inductor currents. This work provides a detailed derivation of the relationship between the critical capacitance describing the onset of DCVM and converter operating parameters. Moreover, the inductor current imbalance is characterized through the development of a clamped steady-state model. To recover balancing when flying capacitance below the critical value is used, a technique to drive the branches with modified duty cycles in a constant power regime is proposed. Experimental validation of the steady-state model and recovery of inductor current balancing are demonstrated on a 4-branch SCB prototype.