This paper introduces the design procedure for a class of bidirectional zero fundamental ripple or zero first-order ripple (ZFR) dc-dc converters. ZFR topologies eliminate the first-order switching ripples by utilizing a coupled inductor. As a result, these converters require smaller inductive and capacitive filtering elements. After introducing the modes of operation, the average model of a ZFR converter is derived. Using this model, a scheme for optimal design of the damping circuitry is introduced. Also, the overall design procedure for a ZFR converter is introduced using an example. The designed ZFR converter is experimentally evaluated to demonstrate the effectiveness of the design procedure.