Research of the Error of the RMS Measurement Method Based On Low-Pass Filtration

Abstract

For the modern measurement transducers of root mean square (RMS), digital measurement methods are usually implemented. This paper discusses a digital RMS measurement method based on application of a low-pass digital filter. The high measurement speed and the possibility of application for sinusoidal and non-sinusoidal periodic input signals are main advantages of this technique. The finite implementation of all RMS digital measurement techniques involves the application of an analog to digital converter (ADC). Real ADCs have a large number of error sources including offset (additive component), conversion coefficient deviation (multiplicative component), nonlinearity, and quantization error. It is shown that for the considerate measurement method the offset error approximately does not affect to the RMS error. It was researched that the multiplicative component is proportional to the RMS error for the considerate measurement method. The nonlinearity and quantization error of applied ADC influence on the RMS error is discussed. This influence can be calculated by signal spectral components which are not equal to zero. For the nonlinearity influence calculation, the analytical expressions are obtained. The case of nonlinearity representation by second and third order polynomials, the “worst case” method and stochastic function is considerate. The model of RMS digital measurement transducer is designed by Simulink software.