A two-terminal active capacitor concept is proposed recently based on an active power electronic circuit with a voltage control method and self-power scheme. It retains the convenience of use as a passive capacitor with two power terminals only without any additional required connections, and has the potential to either increased power density or reduced design cost depending on the applications. Based on the previously proof-of-concept study, this paper addresses the design constraints, impedance modeling, and start-up solutions of two-terminal active capacitors. A design method for functionality, efficiency, lifetime and cost constraints application is applied to size the active components and passive elements. A voltage feed-forward control scheme is implemented to improve its dynamic response. Two start-up solutions are proposed to overcome the issues brought by the self-power scheme. A case study of an active capacitor for the DC link of a singlephase full-bridge rectifier is presented to demonstrate the theoretical analyses.