Disclosed herein are various embodiments of power conversion systems and methods employing synchronous multi-phase AC-to-DC conversion. In one embodiment, a power converter comprises a transistor bridge and a switching controller that operates the transistor bridge in response to AC voltage threshold crossings. The switching controller may include a period counter to measure times between threshold crossings, and a delay counter to trigger a delayed state transition for the transistor bridge. One disclosed method embodiment comprises: receiving multiple phased alternating voltages; comparing each phased alternating voltage to a threshold; determining a period associated with voltage threshold crossings; triggering state transitions at some fraction of the period after each threshold crossing; and placing a transistor bridge into a configuration associated with a current state. For each state, the transistor bridge configuration is designed to couple phased alternating voltages to two output terminals in a sequence that produces a non-alternating voltage difference.