Modeling and Analysis of MHz-Frequency PRC-$LCLC$ Resonant Converter Utilizing Only Parasitic Capacitance From Planar Transformer and Cockcroft–Walton Voltage Multiplier as Parallel Capacitor

High-frequency planar transformers and Cockcroft–Walton (CW) rectifiers are essential for developing miniaturized and high-power-density high voltage generators. Parallel resonant converters (PRCs) are commonly used for parasitics integration and high-efficiency operation. However, modeling and designing PRC-$LCLC$resonant converters with planar transformers and CW voltage multipliers are challenging due to the significant nonlinear parasitics from rectifier diodes and the compensation effects in the resonant tank caused by the discontinuity of rectifier current. To address these challenges, this work proposes a model incorporating nonlinear parasitic capacitance based on the rectified-compensation fundamental mode approximation (RCFMA) method. A novel normalized analysis is conducted on the basis of the resonant frequency of the parallel branch of the RCFMA model, which separates the series-branch-based PRC-$LCLC$resonant characteristics from the compensation effect of rectifier and nonlinear parasitic capacitance. Furthermore, a voltage-oriented design methodology is introduced. The methodology utilizes the components of the series branch to achieve the step-up voltage gain and zero voltage switching condition for the PRC-$LCLC$resonant tank. Simultaneously, the parallel branch effectively manages compensation effects and nonlinear parasitic parameters without external capacitors. The proposed design methodology enhances the high-frequency design feasibility, improves the parasitics integration and resolves the conflict between the characteristics design, compensation effects, and the nonlinear parasitic parameters utilization compared to traditional analysis-based designs of PRC-$LCLC$resonant converters. Finally, the RCFMA model and design methodology are verified through experiments with a gallium nitride-based 25-V/1000-V MHz-frequency PRC-$LCLC$resonant converter.