A fully digital, nonlinear, wide-bandwidth current controller for dc-ac and dc-dc voltage source converters is presented in this paper. Exploiting over-sampling, the controller mimics an analog hysteresis current controller, but it does not employ analog comparators, digital-to-analog converters, or any other analog signal pre- or postprocessing circuitry. Indeed, it fully virtualizes the hysteresis controller's operation and, based only on a nonlinear, efficient current error processing algorithm, drives the power converter at almost constant switching frequency. Overall, it offers the same excellent dynamic performance of the analog hysteresis controller and, at the same time, solves most of the related problems. Because the current error sample processing algorithm is inherently parallel in structure, the controller is suited for VHDL synthesis and field-programmable gate-array implementation, which guarantees flexibility and low cost, together with minimum computation and signal conversion delays. Its intended application areas include active filters, uninterruptible power supplies, microgrid distributed energy resource controllers, laboratory battery testers, and welding machines.