The efficiency of methods for measuring A/D converter linearity

In this paper, the efficiency of three methods commonly used to measure the linearity characteristics of precision Nyquist-rate analog-to-digital (A/D) converters is evaluated. The efficiency of each method, which is determined by the time required to obtain linearity estimates at a specified level of accuracy, is compared to the maximum efficiency that is theoretically achievable, as given by the Cramer-Rao bound. Simulation results are presented for two open-loop measurement methods, the tally and weight method and the code density method, demonstrating that the code density method obtains an efficiency close to the theoretical optimum over a wide range of measurement times and converter noise levels, whereas the tally and weight method falls short of the optimum for converters with noise levels exceeding 1/4 LSB. The efficiency of the servo loop method, a common closed-loop method for measuring linearity, is similarly evaluated, and is found to fall short of the maximum efficiency that is theoretically achievable in the closed-loop configuration. A modified closed-loop measurement method is described that obtains an efficiency close to the theoretical optimum through the use of maximum-likelihood estimation.