A resistive random access memory (RRAM) circuit and related method limits current, or ramp voltage, applied to a source line or bitline of an RRAM array. The RRAM array has one or more source lines and one or more bitlines. A control circuit sets an RRAM cell to a low resistance state in a set operation, and resets the RRAM cell to a high resistance state in a reset operation. A voltage applied to a bitline or source line is ramped during a first time interval, held to a maximum voltage value during a second interval, and ceased after the second time interval.