Background calibration technique for pipelined A/D converters using simplified histogram-based testing

A computer-readable medium storing statements and instructions which, when executed, cause a processor to perform a calibration method for a multi-stage analog to digital (A/D) converter, each stage having an analog input, a digital output, an analog residue and a digital residue, a histogram of digital residue codes being used to correct a transfer characteristic of the stage for a given digital output, the method comprising:

• estimating a bound for a current histogram associated with a current digital output code, the estimated bound being used to estimate a discontinuity in the transfer characteristic;
• in response to a determination that a current digital residue occurs in the current histogram:
• comparing the estimated bound with a gross lock-up detection value and a fine lock-up detection characteristics;
• detecting whether a gross lock-up condition exists based on the comparison of the estimated bound with the gross lock-up detection value;
• restarting calibration in response to detection of the gross lock-up condition;
• in response to detection that there is no gross lock-up condition, detecting whether a fine lock-up condition exists by determining whether the current digital residue satisfies fine lock-up detection characteristics;
• in response to detection of that there is no fine lock-up condition, modifying the estimated bound based on a comparison of the current digital residue with a fast lock value and a bound window;
• and
• removing the discontinuity in the transfer characteristic of the A/D converter based on the estimated bound.