## Dartmouth College Ph.D Dissertations

2022

Thesis (Ph.D.)

#### Department or Program

Engineering Sciences

Jason T. Stauth

Charles R. Sullivan

Minh Q. Phan

#### Abstract

Efficient power delivery is increasingly important in modern computing, communications, consumer and other electronic systems, due to the high power demand and thermal concerns accompanied by performance advancements and tight packaging. In pursuit of high efficiency, small physical volume, and flexible regulation, hybrid switched-capacitor topologies have emerged as promising candidates for such applications. By incorporating both capacitors and inductors as energy storage elements, hybrid topologies achieve high power density while still maintaining soft charging and efficient regulation characteristics. However, challenges exist in the hybrid approach. In terms of reliability, each flying capacitor should be maintained at a nominal `balanced' voltage for robust operation (especially during transients and startup), complicating the control system design. In terms of implementation, switching devices in hybrid converters often need complex gate driving circuits which add cost, area, and power consumption.

This dissertation explores techniques that help to mitigate the aforementioned challenges. A discrete-time state space model is derived by treating the hybrid converter as two subsystems, the switched-capacitor stage and the output filter stage. This model is then used to design an estimator that extracts all flying capacitor voltages from the measurement of a single node. The controllability and observability of the switched-capacitor stage reveal the fundamental cause of imbalance at certain conversion ratios. A new switching sequence, the modified phase-shifted pulse width modulation, is developed to enable natural balance in originally imbalanced scenarios. Based on the model, a novel control algorithm, constant switch stress control, is proposed to achieve both output voltage regulation and active balance with fast dynamics. Finally, the design technique and test result of an integrated hybrid switched-capacitor converter are reported. A proposed gate driving strategy eliminates the need for external driving supplies and reduces the bootstrap capacitor area. On-chip mixed signal control ensures fast balancing dynamics and makes hard startup tolerable. This prototype achieves 96.9\% peak efficiency at 5V:1.2V conversion and a startup time of 12$\mu s$, which is over 100 times faster than the closest prior art.

With the modeling, control, and design techniques introduced in this dissertation, the application of hybrid switched-capacitor converters may be extended to scenarios that were previously challenging for them, allowing enhanced performance compared to using traditional topologies. For problems that may require future attention, this dissertation also points to possible directions for further improvements.

#### Original Citation

[1] Z. Xia, B. L. Dobbins, J. S. Rentmeister and J. T. Stauth, "State Space Analysis of Flying Capacitor Multilevel DC-DC Converters for Capacitor Voltage Estimation," 2019 IEEE Applied Power Electronics Conference and Exposition (APEC), 2019, pp. 50-57.

[2] Z. Xia, B. L. Dobbins and J. T. Stauth, "Natural Balancing of Flying Capacitor Multilevel Converters at Nominal Conversion Ratios," 2019 20th Workshop on Control and Modeling for Power Electronics (COMPEL), 2019, pp. 1-8.

[3] Z. Xia and J. Stauth, "17.1 A Two-Stage Cascaded Hybrid Switched-Capacitor DC-DC Converter with 96.9% Peak Efficiency Tolerating 0.6V/μs Input Slew Rate During Startup," 2021 IEEE International Solid- State Circuits Conference (ISSCC), 2021, pp. 256-258.

[4] Z. Xia and J. T. Stauth, "A Cascaded Hybrid Switched-Capacitor DC–DC Converter Capable of Fast Self Startup for USB Power Delivery," in IEEE Journal of Solid-State Circuits, vol. 57, no. 6, pp. 1854-1864, June 2022.

[5] Z. Xia and J. T. Stauth, "Constant Switch Stress Control of Hybrid Switched Capacitor DC-DC Converters," 2022 IEEE Applied Power Electronics Conference and Exposition (APEC), 2022, pp. 1214-1221.

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