A precision sigma-delta A/D converter having a desired number of cascaded stages is disclosed herein. The multi-stage sigma-delta analog-to-digital converter (10) of the present invention is operative to convert an analog input signal X(z) to an output sequence of digital words. The converter (10) of the present invention includes a first sigma-delta converter stage (14) for generating a first sequence of digital words and a quantization error signal in response to the analog input signal X(z). An interstage amplifier (34) then amplifies the quantization error signal by a first gain factor G. The present invention further includes a second sigma-delta converter stage (18) for generating a second sequence of digital words in response to the amplified quantization error signal. The first and second sequences are next filtered by a digital noise cancellation network (31, 32) and the filtered second sequence is divided by the first gain factor G via a divider circuit (38). A summing circuit (40) provides the output sequence of digital words by summing the filtered first sequence and the divided second sequence. The digital noise cancellation network (32) is also used to compensate for errors due to analog component imperfections, e.g., capacitor mismatches and finite operational amplifier gain.