Analysis and performance trade-offs of linearity calibration for stochastic ADCs

Stochastic flash analog-to-digital converters (ADCs) have been proposed as a solution to the scalability problems encountered by a standard flash ADC. Instead of generating comparator references with a well-matched resistor ladder, it generates randomly distributed thresholds using either the comparator offsets or a separate noise-generating circuit. This allows all devices to be minimum size without matching problems; consequently the stochastic ADC becomes an attractive solution for a synthesizable ADC design. This work achieves two goals: first, it derives the relationship between the number of comparator decisions and effective resolution of a stochastic ADC with an arbitrary probability distribution function (PDF) of comparator thresholds. Second, this work identifies the conditions under which linearity calibration will improve performance. Monte-Carlo simulations demonstrate that for high signal amplitude or numbers of comparisons, calibration significantly improves resolution. For low amplitudes or numbers of comparisons, the ADC performs better without linearity calibration.