Approximation of the ADC Aperture Jitter by the Sinusoidal Function to Estimate the RMS Measurement Error

The root mean square value of voltage and current is one of the most important parameters in the electric power industry. Among the sources of error, one can single out the ADC aperture jitter as one of the sources that cannot be compensated by zero adjusting and calibrating. In practice, random functions are used to approximate aperture jitter. This approach has a number of disadvantages: the resulting analytical expressions for estimating the error are empirical in nature. In this work, sinusoidal functions are used to estimate the aperture jitter. The influence of the signal frequency, the maximum value of the aperture jitter, the sampling frequency, the observation time on the measurement error of the mean square value and apparent power is considered. Analytical expressions are obtained that allow estimating this effect on the RMS measurement error. With the application of Matlab software, simulation modeling was performed, which makes it possible to evaluate the correctness of the obtained analytical expressions. An estimation of the RMS measurement error ratios for the case of performing the approximation by a sinusoidal function and pseudo-random functions is performed. The paper shows that the nature of the dependence of the error when performing the approximation of sinusoidal functions and pseudo-random functions is the same. For this reason, the dependences obtained can be used to estimate the error and for other approaches to approximation. This technique is proposed in the materials of this publication.