Abstract: Digital measurement methods are used to measure the root mean square value (RMS) now. One of the most popular
measurement methods is an approach based on filtering squares of samples. This method has several advantages, including: the
ability to measure both sinusoidal and polyharmonic signals, high accuracy, ease of analysis of the methodological error. It is known
that the methodological measurement error mainly depends on the frequency characteristics of the filters. That is why the problem
arises of determining the analytical dependence, which allows us to put forward filter requirements for a given marginal error of
measuring the RMS. Another task is to find a filter that allows you to provide the smallest error in measuring the RMS with the least
order and complexity of implementation on a real element base. Analytical relations are obtained in this work, that allow us to
estimate the methodological error of measuring the RMS for the case of a sinusoidal input signal. An analysis is made of the
influence of the frequency deviation of the input signal on the measurement error of the RMS. Various types of IIR and FIR digital
filters were considered, including Butterworth, Chebyshev filters, also a filter with a Kaiser window and a Moving Average filter.
The case of the Moving Average filter was analyzed in more detail. Also a method for determining the order of a filter and methods
for reducing the final measurement error were proposed. Estimates of the error of the RMS measurements were obtained by
simulation in the software packages Matlab and Simulink. The obtained analytical relationships are confirmed by the coincidence of
the results of simulation and analytical modeling at control points.
Index terms: root mean square, measurement error, digital filtration, frequency spectrum.