Abstract: The article analyzes three modified versions of the standard ellipse fitting algorithm (EFA), which enables the determination of the complex voltage ratio (CVR) for extremely small values of the phase shift angle when the input scattering matrix of sampled data is poorly conditioned. The novelty of the method is in the use of EFA twice for the sequence of samples shifted by the same angle value, but with opposite signs. The results of the numerical simulation tests are confirmed by the results of measurements carried out in the sampling system using the NI PXI 4461 data acquisition module.
B I B L I O G R A F I A[1]. R. Rybski, J. Kaczmarek and M. Koziol, “A High-Resolution PXI Digitizer for a Low-Value-Resistor Calibration System,” IEEE Trans. Instrum. Meas., vol.. 62, no. 6, pp. 1783-1788, June 2013, doi:
10.1109/TIM.2012.2225958P.
[2]. M. Ramos, F. M. Janeiro and T. Radil, “Comparison of impedance measurements in a DSP using ellipse-fit and seven-parameter sine-fit algorithms,” Measurement, vol. 42, no. 9, pp. 1370-1379, Nov. 2009, doi: 10.1016/j.measurement.2009.05.005
[3]. F. M. Janeiro, P. M. Ramos, M. Tlemcani and A. C. Serra, “Recent development on impedance measurements with DSP-based ellipse fitting algorithms,” IEEE Trans. Instrum. Meas., vol. 58, no. 5, pp. 1680-1689, May 2009, doi: 10.1109/TIM.2009.2014512
[4]. Frédéric Overney et al., Dual Josephson impedance bridge: towards a universal bridge for impedance metrology, Metrologia Vol. 57, Issue 6, 2020, doi: 10.1088/1681-7575/ab948d
[5]. K. Musioł, M. Kampik, A. Ziółek, J. Jursza, "Experiences with a new sampling-based four-terminal-pair digital impedance bridge", Measurement, 205 (2022) 112159, doi: 10.1016/j.measurement.2022.112159
[6]. M. Ortolano et al., "A Comprehensive Analysis of Error Sources in Electronic Fully Digital Impedance Bridges," in IEEE Transactions on Instrumentation and Measurement, vol. 70, pp. 1-14, 2021
[7]. S. Mašláň, M. Šíra, T. Skalická and T. Bergsten, "Four-Terminal Pair Digital Sampling Impedance Bridge up to 1MHz," in IEEE Transactions on Instrumentation and Measurement, vol. 68, no. 6, pp. 1860-1869, June 2019
[8]. K. Musioł, M. Kampik, “Metrological triangles in impedance comparisons”, Measurement, Volume 148, 2019
[9]. U. Pogliano, B. Trinchera and D. Serazio, Wideband digital phase comparator for high current shunts, Metrologia Vol. 49, Issue 3, 2012, doi:10.1088/0026-1394/49/3/349
[10]. F. Overney and B. Jeanneret, “Calibration of an LCR-Meter at Arbitrary Phase Angles Using a Fully Automated Impedance Simulator,” IEEE Trans. Instrum. Meas., vol. 66, no. 6, pp. 1516-1523, June 2017, doi: 10.1109/TIM.2017.2652500
[11]. M. Ortolano et al ”An international comparison of phase angle standards between the novel impedance bridges of CMI, INRIM and METAS” Metrologia 55 499, 2018
[12]. J. Konjevod, R. Malarić, M. Jurčević, P. Mostarac and M. Dadić, "Comparison of Digitizers for High-Precision Sampling Power Meters," in IEEE Transactions on Instrumentation and Measurement, vol. 69, no. 6, pp. 3719-3728, June 2020, doi: 10.1109/TIM.2019.2941260
[13]. B. Trinchera and D. Serazio, "A Power Frequency Modular Sampling Standard for Traceable Power Measurements: Comparison and Perspectives," in IEEE Transactions on Instrumentation and Measurement, vol. 71, pp. 1-8, 2022, Art no. 1500608, doi: 10.1109/TIM.2021.3132346
[14]. J. Kučera, J. Kováč, L. Palafox, R. Behr and L. Vojáčková, Characterization of a precision modular sinewave generator, Meas. Sci. Technol., Vol. 31, Issue 6, 2020, doi: 10.1088/1361-6501/ab6f2e
[15]. M. Kozioł, J. Kaczmarek, and R. Rybski, “Characterization of PXI-based generators for impedance measurement setups,” IEEE Trans. Instrum. Meas., vol. 68, pp. 1806–1813, 2019
[16]. J. Konjevod, R. Malarić, P. Mostarac, M. Jurčević, The AC amplitude and channel characterization of high-resolution digitizers, Measurement, Vol. 195, 2022, doi: 10.1016/j.measurement.2022.111144
[17]. K. Musioł,. Experimental Study of Digitizers Used in High-Precision Impedance Measurements, Energies 2022, 15, 4051, doi. 10.3390/en15114051
[18]. S. Maslan, M. Sira, V.N. Zachovalova, J. Streit, “Digital Sampling Setup for Measurement of Complex Voltage Ratio”, IEEE Trans. Instrum. Meas., vol. 66, no. 6, pp. 1355-1363, June 2017, doi: 10.1109/TIM.2017.2649899
[19]. J. Augustyn, M. Kampik, “Application of Ellipse Fitting Algorithm in Incoherent Sampling Measurements of Complex Ratio of AC Voltages”, IEEE Trans. Instrum. Meas., vol. 66, no. 6, pp. 1117-1123, June 2017, doi: 10.1109/TIM.2017.2662298
[20]. J. Augustyn and M. Kampik, “Improved Sine-Fitting Algorithms for Measurements of Complex Ratio of AC Voltages by Asynchronous Sequential Sampling,” IEEE Trans. Instrum. Meas., vol. 68, no. 6, pp.
1659–1665, Jun. 2019, doi: 10.1109/TIM.2018.2875901
[21]. K. Kanatani, Y. Sugaya, Y. Kanazawa, Ellipse Fitting for Computer Vision: Implementation and Applications, April 2016, Synthesis Lectures on Computer Vision 6(1):1-141, doi: 10.2200/S00713ED1V01Y201603COV008
[22]. J. Liang, P. Li, D. Zhou, H. C. So, D Liu, C. S. Leung & L. Sui, (2019). Robust ellipse fitting via alternating direction method of multipliers. Signal Processing, 164, 30-40, doi.org/10.1016/j.sigpro.2019.05.032
[23]. C. Panagiotakis and A. Argyros, Parameter-free Modelling of 2D Shapes with Ellipses, Pattern Recognition, vol.53, pp. 259-275, 2016, doi.org/10.1016/j.patcog.2015.11.004
[24]. W. Gander, G. Golub, R. Strebel, Fitting of circles and ellipses: Least squares solution, BIT 34, 558–578 (1994), doi: 10.1007/BF01934268
[25]. Z. A. Awan, and P. M. Ramos, “Improvement of phase difference estimation using modified ellipse fit method,” in Proc. I2MTC 2010, pp 78-81, May 2010
[26]. IEEE Standard for Terminology and Test Methods for Analog-to-Digital Converters, IEEE Standard 1241-2010, 2011, doi: 10.1109/IEEESTD.2011.5692956
[27]. R. Halíř, and J. Flusser, “Numerically stable direct least squares fitting of ellipses,” in Proc. WSCG’ 98, pp. 125-132, University of West Bohemia, Campus Bory, Czech Republic, Feb. 1998
[28]. N. J. Higham, Accuracy and stability of numerical algorithms, 2nd edition, Society for Industrial and Applied Mathematics, Philadelphia, 2002
[29]. J. Augustyn, M. Kampik and K. Musioł, "Investigation of Selected Reconstruction Algorithms Used for Determination of Complex Ratio of AC Voltages," in IEEE Transactions on Instrumentation and Measurement, vol. 70, pp. 1-9, 2021, Art no. 1503209, doi: 10.1109/TIM.2021.3071233
[30]. M. Kampik, K. Musioł, “Investigations of the high-performance source of digitally synthesized sinusoidal voltage for primary impedance metrology”, Measurement, Volume 168, 2021 
Pełny tekst 
DOI 
Web of Science