The gate of the access transistor of a 1 transistor 1 resistor (1T1R) type RRAM cell is biased relative to the source of the access transistor using a current mirror. Under the influence of a voltage applied across the 1T1R cell (e.g., via the bit line), the RRAM memory element switches from a higher resistance to a lower resistance. As the RRAM memory element switches from the higher resistance to the lower resistance, the current through the RRAM cell switches from being substantially determined by the higher resistance of the RRAM device (while the access transistor is operating in the linear region) to being substantially determined by the saturation region operating point of the access transistor.