Systems and methods for adaptive auto-calibration of Radix<2 A/D SAR converters with internally generated stimuli

A method of calibrating a charge redistribution digital-to-analog converter including a plurality of multi-valued electric components of magnitudes enabling redundant expression of electric charge values and including lesser magnitude companion components, comprising:

• producing a set of sampling bits to connect corresponding sampling components to a selected reference voltage;
• sampling the selected reference voltage with sampling components selected from said plurality of multivalued electric components;
• holding a negative of the charge sampled by the sampling components at an input of a comparator;
• producing a set of balancing bits including companion bits corresponding to balancing components selected to approximate a capacitance of the sampling components;
• approximating the charge sampled with a balancing charge from the companion bits enhanced balancing components;
• producing signed analog residue from a difference between the sampled and balancing charge amounts;
• generating digital weights corresponding to the sampling and the balancing bits and producing the difference therebetween as a signed digital residue;
• and
• correcting the generated digital weights based upon the difference between the signed analog and digital residues.

A method of calibrating a charge redistribution digital to analog converter including a set of charge carrying components, comprising:

• selecting a sampling set of charge carrying components in the charge redistribution digital-to-analog converter for sampling operation;
• sampling a reference voltage with said selected charge carrying components;
• selecting balancing sets of said charge carrying components including companion charge carrying components to cancel a charge sampled by said sampling set of charge carrying components;
• and
• determining digital weight values corresponding to said sampling and balancing sets of charge carrying components.

A companion bit system, comprising:

• a comparator having first and second inputs and an output;
• a digital-to-analog converter (DAC) connected to said comparator and comprising a digitally calibrable charge carrying component array, and adapted for sampling and balancing selected electric quantities, and including switching circuitry for connecting particular ones of the charge carrying components from said charge carrying component array, to selected individual voltages selected from a group of voltage levels including particular input, reference, and ground levels;
• logic circuitry connected to said DAC and the output of said comparator, said logic circuitry configured for connecting different ones of said charge carrying component for sampling and conversion operation to identify an analog sign residue and to establish digital calibration weights for said sampling and balancing charge carrying component sets enabling identification of a digital sign residue for comparison with said analog sign residue to enable digital weight adjustment, said logic circuitry further being configured for companion bit approximation, to provide a skew to push balancing capacitances into a redundancy region defined by the excess of the cumulative magnitude of lesser magnitude charge carrying components over a particular charge carrying component;
• a memory for storing digital sampling and balancing calibration weights;
• and
• an accumulator for determining the differences between said sampling and balancing digital weights.

A method of calibrating a plurality of multi-valued electric charge carrying components comprising elements which enable redundant expression of electric charge values with two or more subsets of said plurality, comprising:

• sampling a predetermined range of electric charge quantities;
• selecting a succession of balancing electric charge carrying components to approximate said charge samples with said electric charge carrying components being accompanied in the approximation by at least a single lesser magnitude companion component;
• and
• generating digital weights corresponding to each of said balancing electric charge carrying components.

A method of successive approximation with a plurality of electrical components of magnitudes enabling redundant expression of electric charge values and including lesser magnitude companion components in said plurality, comprising:

• sampling a selected electric value;
• comparing electric signal values of particular ones of a plurality of electrical components and at least a single associated companion component as an approximation of the sampled electric signal;
• and
• generating statistically monotonic converging digital weights to approximate the sampled electrical value.