Constant output characteristics, zero phase angle (ZPA), and coupler voltage stresses as low as possible are practical requirements for high power and large air-gap capacitive power transfer (CPT) applications. This article derives conditions of load-independent constant voltage output, ZPA, and minimum coupler voltages for general CPT systems, respectively. Minimum degrees of freedom (DOF) for the above performance are analyzed. Given performance requirements, a systematic circuit design method based on DOF analysis is proposed to design compensation circuits with fewer components to simplify complexity and decrease costs. The proposed method can predict feasible topologies, and application considerations are provided to guide topology selection. A 3 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> -compensated CPT system is proposed to realize the constant voltage output with ZPA, minimum coupler voltages, and efficiency optimization. A 2.2 kW CPT prototype has been prepared with a 250 mm air-gap distance and dc–dc efficiency is 87.2%. Rms values of coupler voltages are about 5 kV at the rated power.