It is well known that single-phase pulse width modulation rectifiers have second-order harmonic currents and corresponding ripple voltages on the dc bus. The low-frequency harmonic current is normally filtered using a bulk capacitor in the bus, which results in low power density. However, pursuing high power density in converter design is a very important goal in the aerospace applications. This paper studies methods for reducing the energy storage capacitor for single-phase rectifiers. The minimum ripple energy storage requirement is derived independently of a specific topology. Based on the minimum ripple energy requirement, the feasibility of the active capacitor's reduction schemes is verified. Then, we propose a bidirectional buck-boost converter as the ripple energy storage circuit, which can effectively reduce the energy storage capacitance. The analysis and design are validated by simulation and experimental results.