Two key techniques necessary to digitally calibrate multistep or pipelined converters are demonstrated in a differential 5-V, 13-b, 10-Msample/s analog-to-digital converter (ADC). One technique, called code-error calibration, is to linearize the transfer characteristic of digital-to-analog converters (DAC's) while the other, called gain-error proration, is to evenly distribute interstage gain errors over the full conversion range. The core of the former technique is an oversampling delta-sigma ratio calibrator working synchronously with the converter. This digital calibration process constantly tracks and updates the code errors without interfering with the normal operation. The prototype converter fabricated using a 1.4-µm BiCMOS process consumes 360 mW with a 5-V single supply and exhibits a signal-to-noise ratio of 71 dB and a maximum end-point integral nonlinearity of 1.8 LSB at a 13-b level. The proposed techniques can be incorporated into general multistep or pipelined ADC's without sacrificing the conversion speed.