Electrical capacitance measurement by scattering ellipse approximation

Abstract

This article is devoted to the substantiation of the possibility of electrical capacitance measurement utilizing equations that are based on the approximation of scattering ellipse, formed by signals proportional to the current flowing through the capacitive tested object and voltage drop on the tested object. On the contrary, to previously developed algorithms, which were based on the approximation of the scattering ellipse by applying the least-squares method, in this case, the approximation was carried out by simply using the values of signals amplitude directly determined from current and voltage curves. The value of the phase shift between the current and voltage curves, which is also necessary to approximate the shape of the scattering ellipse, was determined by using the cross-correlation method. Besides, the article provides formulas for calculating the reactive component of voltage drop on the tested object which is based on the approximation of scattering ellipse without using the least-squares method. Formulas for calculation of the reactive component of the voltage drop on the tested object after the reduction of the quadratic form of the elliptic curve to its canonical form are also given. The results of the impact of the reduction of the quadratic form of scattering ellipse to its canonical form on the value of correlation coefficient between sine curves of current and voltage as well as on the magnitude of major semi-axis and minor semi-axis of scattering ellipse are illustrated. Also, it was shown the relationship between the values of the reactive component of voltage drop on the capacitive tested object, which were determined before the reducing of the quadratic form of scattering ellipse to its canonical form and after such reducing. Despite the rejection of the applying of the least-squares method, to simplify the calculation algorithms, and also despite the presence of a significant noise component in sampled and processed curves of current and voltage, the experimental test has shown the sufficient level of accuracy and, consequently, the possibility of measuring the electric capacitance by approximating the scatter ellipse employing parameters of the quadratic form directly calculated from previously sampled sine curves of current and voltage.