Maximum likelihood estimation of ADC Parameters

Dynamic testing of analog-digital converters (ADC) is a complex task. A possible approach is using a sine wave because it can be generated with high precision. However, in the sine wave fitting method for the test of ADC's, all the available information is extracted from the measured data. Therefore, the estimated ADC parameters (ENOB, linearity errors) are not always accurate enough, and not detailed information is gained about the nonlinearity of the ADC. Generally, maximum likelihood (ML) estimation is a powerful method for the estimation of unknown parameters. However, currently it is not used for the processing of such data, because of the difficulties of formulating it, furthermore because of the numerically demanding task of the minimization of the ML cost function. We have succeeded in formulating the maximum likelihood function for a sine wave excitation, and in minimizing it. The number of parameters is frightening (all comparison levels of the ADC plus parameters of the sine wave plus variance of an additive input noise), but proper handling allows to determine the best values based on the data. The proper definition of the ML function and formulation of the numerical method are presented, with results using simulation and measurement data. To our knowledge, this is the first case to solve the full maximum likelihood problem.