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This paper describes a fast digital calibration scheme for pipelined analog-to-digital converters (ADCs). The proposed method corrects the nonlinearity caused by finite opamp gain and capacitor mismatch in multiplying digital-to-analog converters (MDACs). The considered calibration technique takes the advantages of both foreground and background calibration schemes. In this combination calibration algorithm, a novel parallel background calibration with signal-shifted correlation is proposed, and its calibration cycle is very short. The details of this technique are described in the example of a 14-bit 100 Msample/s pipelined ADC. The high convergence speed of this background calibration is achieved by three means. First, a modified 1.5-bit stage is proposed in order to allow the injection of a large pseudo-random dithering without missing code. Second, before correlating the signal, it is shifted according to the input signal so that the correlation error converges quickly. Finally, the front pipeline stages are calibrated simultaneously rather than stage by stage to reduce the calibration tracking constants. Simulation results confirm that the combination calibration has a fast startup process and a short background calibration cycle of 2 × 221 conversions.