Calibration apparatus for systems such as analog to digital converters

A calibration circuit for a recirculation of remainder analog-to-digital (A/D) converter heuristically solves a multiple variable conversion equation. Input analog calibration and analog reference signals are compared in a comparator, and when the two signals have a predetermined relationship, the comparator generates an indicator signal. A microprocessor determines a first pattern of digital reference signals that, together with digital calibration signals generated by the microprocessor, causes the comparator to generate the indicator signal and a second pattern of digital reference signals that, together with the input analog calibration signals, causes the comparator to generate the indicator signal. The difference between the first and second patterns of digital reference signals is stored as conversion coefficients.