Abstract: Currently, to measure the root mean square values (RMS) are commonly used digital methods. The implementation of these methods involves the use of analog-to-digital converters (ADC) for receiving input signal samples in digital code. Transform function (DFT) of a real ADC contains additive, multiplicative and nonlinear components of the error. These elements have different coefficients of influence on RMS measurement error. It is shown that the additive component virtually does not affect the accuracy of the RMS measurement, and a multiplicative component of the ADC error is linearly related to the RMS measurement error. For the case of polyharmonic and sinusoidal input signals derived the analytical expression showing the effects of the ADC nonlinearity to the RMS measurement error. The reliability of the expressions for the case of sinusoidal input signal is confirmed by results of mathematical simulation performed in the software package Matlab. The research of the influence of the amplitude value of the input signal and the initial phase of the RMS measurement error caused by the nonlinearity of the ADC is performed. To assess the effectiveness of the proposed method by mathematical simulation the estimates of RMS measurement error for the case of ADC ADS8372 (built on the architecture of successive approximation) and ADS1610 (built on the Sigma-Delta architecture). The manufacturer of both the considered ADC is the company Texas Instruments. Analyzed the additive, multiplicative and nonlinear components of the error of the considered ADC. It is shown that the proposed method of estimation of RMS measurement error caused by the nonlinearity of the ADC allows the top to assess the RMS measurement error caused by the nonlinearity of the ADC. However, this error estimate is overstated relative to the simulation results.
Index terms: analog-to-digital Converter, root mean square value, measurement error, integral nonlinearity, quantization error.