# ELECTRICAL CAPACITANCE MEASUREMENT BY SCATTER ELLIPSE APPROXIMATION

2020;
: pp. 41-46
Authors:
1
National Technical University “Kharkiv Polytechnic Institute”, Ukraine

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.

[1] J. Garcia-Martin, J. Gomez-Gil, E. Vazques-Sqnchez, “Non-destructive techniques based on eddy current testing”, Sensors, 17: 2525-2565.

https://doi.org/10.3390/s110302525

[2] O. Naumovich, Y. Pokhodylo, M. Dovhan, “Modeling of human body tissues impedance components in frequency range”, Measuring Equipment and Metrology, no. 80, p. 49-53, 2019.

https://doi.org/10.23939/istcmtm2019.04.049

[3] A. Arshad, R. Tasnim, A. H. M. Zahirul Alam, Sheros Khan,  “Low value capacitance measurement system for the application of monitoring human body”, ARPN Journal of Engineering and Applied Science, no. 11 (1), p. 327-330, 2016.

[4] D .Trushakov, S. Rendzinyak, I. Vasylchyshyn, “Determining of complex magnetic permeability of the ferromagnetic material by complex impedance of inductance coil with ferromagnetic core”, Przeglad Elektrotechniczny, no. 4, p. 221-223, 2014. doi:10.12915/pe.2014.04.53

[5] J-E. Sigdell, “A principle for capacitance measurement, suitable for linear evaluation of capacitance transducers”, IEEE Transaction on Instrumentation and Measurement,  no. 1, p. 21-223, 1972.

https://doi.org/10.1109/TIM.1972.4313959

[6] B. Bezprozvannych, I. Mirchuk, “The evaluation of possibility of normal operation of cables based on twisted pairs with PVC jacket under the conditions of high humidity and temperature”, Electrical Engineering & Electromechanics, no. 5, p. 49-53, 2017.

https://doi.org/10.20998/2074-272X.2017.5.08

[7] B. Bezprozvannych, A. Roginskiy, “Dielectric spectroscopy of casing thermosetting composite electrical insulation system of induction traction electric machines”, Electrical Engineering & Electromechanics, no.1, p. 49-53, 2018.

https://doi.org/10.20998/2074-272X.2018.5.02

[8] M. Gutten, D. Korenciak, M. Sebok, et. al. “Diagnostics of transformer with insulation oil-paper”, Przeglad Elektrotechniczny, no. 4, p. 69-72, 2015.

https://doi.org/10.15199/48.2015.08.18

[9] L. Callegaro, “Electrical impedance: principles, measurement, and applications”, Publishing House “CRC Press”, Boca Raton, USA, p. 92-138, 2013.

https://doi.org/10.1201/b13069

[10] M. Raven, D. Raven, “New approaches to the direct measurement of capacitance”, Electrocomponent Science and Technology, no. 4, p. 37-42, 1977.

https://doi.org/10.1155/APEC.4.37

[11] A. Cichy, “Methods of synthesis of quasi-balanced circuits for measuring of impedance components”, Elektronika ir Elektrotechnika, no.22 (2), p. 38-42, 2016.

https://doi.org/10.2478/v10178-010-0022-8

[12] G. Lentka, “Using a particular sampling method for impedance measurement”, Metrol. Meas. Syst., no. 21 (3), p. 497-508, 2014.

https://doi.org/10.2478/mms-2014-0042

[13] K. Chabowski, T. Piasecki, A. Dzierka, et. al., “Simple wide frequency range impedance meter based on AD5933 integrated circuit”, Metrol. Meas. Syst., no. 22 (1), p. 13-24, 2015.

https://doi.org/10.1515/mms-2015-0006

[14] P. Ramos, F. Janiero, A. Cruz Serra, et. al., “Recent developments on impedance measurements with DSP-based ellipse-fitting algorithms”, IEEE Transactions on Instrumentation and Measurement, no. 58 (5), p. 1680-1689, 2009.

https://doi.org/10.1109/TIM.2009.2014512

[15] P. Ramos, F. Janiero, “Implementation of DSP based algorithms for impedance measurement”, in Proc. IEEE International Conference on Signal Processing and Communications, United Arab Emirates, 2007.

https://doi.org/10.1109/ICSPC.2007.4728444

[16] P. Ramos, F. Janiero, T. Radil, “DSPIC-based impedance measuring instrument”, Metrol. Meas. Syst., no. 18 (2), p. 185-198, 2011.

https://doi.org/10.2478/v10178-011-0002-0

[17] P. Ramos, F. Janiero, T. Radil, “Comparative analysis of three algorithms for two-channel common frequency sinewave parameter estimation: ellipse fit, seven parameters sine fit and spectral sinc fit”, Metrol. Meas. Syst., no. 17 (2), p. 250-270, 2010.

https://doi.org/10.2478/v10178-010-0022-8

[18] R. Halir, J. Flusser, “Numerically stable direct least squares fitting of ellipses”, in Proc. Conference in central Europe on computer graphics, visualization and interactive digital media, Czech Republic, 1998.

[19] E. Ventcel, Probability theory. State publishing house of physical and mathematical literature, Moscow, USSR, 1958.

[20] G. Bushina, Second order curves. Publishing House of Khabarovsk state technical univerciry, Khabarovsk, Russia, 1995.

[21] A. Kirkinskij, Linear Algebra and Analytical Geometry.  Academic project, Moscow, Russia,  2006.