A fully digital, non-linear, wide bandwidth, current controller for DC-AC and DC-DC voltage source converters is presented in this paper. Exploiting oversampling, the controller mimics an analog hysteresis current controller, but does not employ analog comparators, digital to analog converters or any other analog signal pre-or post-processing circuitry. Indeed, it fully virtualizes the hysteresis controller's operation and, based only on a non-linear, 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 FPGA 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, micro-grid distributed energy resource (DER) controllers, laboratory battery testers, welding machines.