Conventional Power Factor Correction (PFC) converters require high DC-bus capacitances to cope with the double-line frequency power pulsation. This affects the cost and size of the converter, and it creates high inrush currents. With the ongoing high-power-density trends in GaN-based converters, it is crucial to reduce the size of components, including DC-bus capacitors. This paper introduces a fast-transient geometric PFC controller on a GaN-based modified bridgeless converter capable of operating at $1$ MHz switching frequency. The proposed controller is based on large-signal state-plane modeling and it addresses the sluggish dynamic performance of the conventional DC-bus voltage controller, enabling the utilization of a significantly reduced DC-bus capacitor. As a result, the inrush current is reduced and ceramic DC-bus capacitors can be employed, which increases the reliability, and it offers rapid response to load transients. The analysis of this paper is supported by mathematical derivations and validated via simulations and preliminary experimental results.
