A digital automatic gain control (AGC) circuit for use in a radio frequency (RF) receiver. The AGC circuit comprises: 1) a first shifter for receiving an in-phase signal as a first series of X-bit samples and left-shifting each X-bit sample by a number of bits determined by a coarse scaling factor; 2) a first limiter for receiving the D most significant bits of the output of the first shifter and outputting a subset of the D most significant bits of the first shifter output; 3) a first multiplier for multiplying the subset of the D most significant bits of the first shifter output by a fine scaling factor to produce a first M-bit product; and 4) a gain adjustment circuit for comparing a power signal derived from the first M-bit product to a maximum threshold value and generating the coarse scaling factor and the fine scaling factor.