Theoretical and Experimental Aspects About the RMS Estimation Based on Signal Samples

The RMS value is used in large number of applications. Since the digital technologies got more popular and microprocessor technology became cheaper and powerful the RMS value of a signal is more often calculated using the signal samples. Usually the sampling frequency is neither synchronized with the signal frequency, nor multiple of it. This is reflected in getting different sample location on consecutive periods. This is reflected in the error affecting the estimation of the RMS value. The present paper is presenting a study on how the position of the first sample relative to the signal zero crossing is affecting the RMS value and how a coherent sampling improve the result. The theoretical study is performed for different resolutions and different number of samples per period, while the experimental one is performed for a single resolution and different number of samples per period. Since the power network applications are the most frequent, the signal frequency is varied from 40 Hz to 60 Hz. The study reveals that when the first sample is located at 55 or 110 degrees gives the best result for the estimated RMS, while the coherent sampling keeps the error constant and about an order of magnitude lower than the non-coherent frequency sampling.