Metrological analysis of integrated analog RMS converters described by explicit and implicit functions

Abstract

The paper presents a metrological analysis of RMS converters described by explicit and implicit functions. The following function circuits are analyzed: a converter described by the explicit function, consisting of a squaring circuit, a square rooter and an integrator, and a converter described by the implicit function, consisting of an absolute value circuit, a multiplier–divider and an integrator. The errors of the converters are of the same order for voltages above 4.86V and sinusoidal waveforms and depend on the multiplicative errors of the function circuits. Since for lower voltages the converter errors depend on the additive errors of the function circuits, the errors of the converter described by the implicit function are incomparably smaller. The results of the analysis indicate that for the same converter errors the measurement range of the converter described by the implicit function is by one order higher than the measurement range of the converter described by the explicit function and the differences increase with the accuracy of the function circuits.