The impact of the conversion starting threshold on the estimation of the RMS value

• Published in: Microprocessors and microsystems 2022-09, Vol.93, p.104595, Article 104595
• Main Authors: Subotin, Marina, Mirković, Stefan, Gazivoda, Nemanja, Pejić, Dragan, Urekar, Marjan, Antić, Boris
• Format: Article
• Language: English
• Subjects: Analog-to-digital conversion; Numerical integration; Rectangular method; Root mean square; Threshold; Trapezoidal rule
• ISSN: 0141-9331; 1872-9436
• DOI: 10.1016/j.micpro.2022.104595

•The selection of the conversion start threshold has a key role in the estimation of the RMS value.•The rectangular method for numerical calculation of the RMS has an optimal threshold equal to the RMS of the measured signal.•Reducing computational requirements for arithmetical units of microprocessors embedded in measurement equipment.•Improved performances of existing and future instrumentation with no or minimal investment in hardware or software. This paper presents an optimal solution for the selection of the starting instance of the analog-to-digital conversion for the purpose of the estimation of the root mean square (RMS) value of an arbitrary periodic signal when the ratio of the sampling frequency and the signal's fundamental frequency value is low and a non-integer. This selection of the optimal starting threshold is discussed in the context of the application of the two most common numerical methods used in measurement instrumentation today: the rectangular method and the trapezoidal rule. The appropriate threshold selection results in a significantly reduced measurement uncertainty of the estimated RMS value and improved measurement performances without necessitating major modifications or upgrade of the existing hardware. All theoretical results have been experimentally validated. The research is an original contribution to the field of mathematical modeling of methods implemented in microprocessor used in contemporary instrumentation.