The Maximum-Likelihood Noise Magnitude Estimation in ADC Linearity Measurements

Abstract

Analog-to-digital-converter (ADC) linearity measurement is recently featured as the estimation of the code-transition (CT) level. This paper carries out the maximum-likelihood (ML) estimation directly to the output sequence for a ramp input signal. The derived ML equations determine not only the CT level but also its standard deviation, i.e., noise magnitude. Our method does not necessarily assume a Gaussian noise distribution. Rather, we introduce a logistic distribution that makes ML equations simple. One solution of the ML equations for logistic noise verifies the code density method to be optimal. Another solution provides an explicit formula of the noise variance. The formula is practically important because it denotes some kind of malfunctions of the ADC that the code density method cannot inherently detect.