A Design of High-Speed-Sampling Stochastic Flash Analog-to-Digital Converter Utilizing Device Mismatch

Estimation of Number of Comparators Required in N‐Bit Stochastic Flash AD Converters

“…However, according to our analysis for a uniform distribution, 6‐bit resolution can be achieved by using about 20 times fewer comparators. In fact, there have also been simulations in which 6‐bit resolution was obtained with comparators , which is close to our estimate.…”

“…Another approach was taken in Ref. : namely, two normal distributions were parallel‐shifted symmetrically to the positive and negative sides so as to flatten the central portion of the PDF.…”

“…Another approach was taken in Ref. [3]: namely, two normal distributions were parallel-shifted symmetrically to the positive and negative sides so as to flatten the central portion of the PDF. Aiming at a combination of the above approaches, a method was proposed [6] in which the PDF is flattened by setting the reference voltages for multiple comparator groups as a downward-convex quadratic function (U-quadratic function).…”

“…As regards clues to the determination of the required number of comparators, Weaver and colleagues published their analytic results indicating that in case of a uniform distribution of the offset voltage between the utilized comparators, the expected SQNR (Signal‐to‐Quantization Noise Ratio) is , where n is the total number of comparators. However, the target SQNR was obtained with much fewer comparators in other numerical experiments as well as in the prototypes of Weaver and colleagues themselves , and thus the required number of comparators remains unclear.…”

“…For example, denoting the standard deviation of the offset voltage by σ, the input must be within 0.6σ to provide 6‐bit linearity in the case of normally distributed variation, which means that only 46% of the comparators are utilized. Some methods have been proposed to solve this problem, such as using inverse functions to cancel nonlinearity , or linearization by dividing the comparators into two groups and specifying a fixed reference voltage for each group ; however, comparator utilization remains low.…”