Radix-based digital calibration techniques for multi-stage recycling pipelined ADCs

This work describes a digital-domain self-calibration technique for multistage pipelined analog-to-digital converters (ADCs). By making the signal paths of both the input and the reference voltage the same, all error factors within a stage are merged into a single term which represents the equivalent radix number. The initially estimated radix for each stage mathematically iterates to the final correct value via an incremental update algorithm, after foreground calibration measurements are obtained during ADCs recycling mode of operation. In this way, an accurate calibration is achieved using a modified radix-based calculation. Two different single-bit-per-stage ADC adaptation/calibration methods are presented as examples. The proposed technique compensates for linear errors such as capacitor mismatches as well as finite opamp gain.