Universal Approach for Estimating the RMS Measurement Error Caused by ADC Nonlinearity
Andrey Nikolayevich Serov · 2021
Currently, the root mean square value (RMS) is one of the most informative parameter of electrical power networks. To measure the RMS, digital measurement methods are applied, which are based on the processing of the signal samples. Analog-to-digital converters (ADCs) are used to obtain signal samples and the transfer function of which are not ideal. In most cases, the greatest contribution to ADC measurement error produced by ADC nonlinearity, which cannot be eliminated by zero-adjusting or calibration of the measurement channel. The ADC nonlinearity form is individual for each specific ADC chip, however, it has some general patterns in accordance with ADC architecture. Sigma-delta ADCs are characterized by a smooth nonlinearity form, while successive approximation register (SAR) and pipelined ADCs characterizes a nonlinearity form close to stochastic. This paper proposes an approach for describing the ADC nonlinearity conversion function, based on the application of sinusoidal function. By varying of the nonlinearity oscillation number, the ADC nonlinearity curve of sigma-delta, SAR or pipelined architectures can be effectively modeled. The influence of the ADC parameters and the input signal parameters on the RMS measurement error is investigated. Analytical relationships have been obtained that make it possible to estimate the RMS measurement error by applying the ADC and input signal parameters for the considered method of nonlinearity describing. A method is proposed for choosing the parameters of harmonic function applied for ADC nonlinearity approximation, based on an analysis of the ADC parameters and a nonlinearity typical form. Simulation modeling was performed by Matlab software package. The comparison of the proposed method for describing ADC nonlinearity and existing methods is performed.