Jump to ContentJump to Main Navigation
Show Summary Details

Metrology and Measurement Systems

The Journal of Committee on Metrology and Scientific Instrumentation of Polish Academy of Sciences

4 Issues per year

IMPACT FACTOR increased in 2015: 1.140

SCImago Journal Rank (SJR) 2015: 0.554
Source Normalized Impact per Paper (SNIP) 2015: 1.363
Impact per Publication (IPP) 2015: 1.260

Open Access
See all formats and pricing

Evaluation of Uncertainty of Phase Difference Determination in Presence of Bias

Lazar V. Saranovac
  • University of Belgrade, Faculty of Electrical Engineering, 11000 Belgrade, Serbia
  • Email:
/ Nada M. Vučijak
  • Elektrotehnički Institut DEC DOO, Kej 2. Oktobra 13, 23000 Zrenjanin, Serbia
  • Email:
Published Online: 2016-12-13 | DOI: https://doi.org/10.1515/mms-2016-0047


Determination of the phase difference between two sinusoidal signals with noise components using samples of these signals is of interest in many measurement systems. The samples of signals are processed by one of many algorithms, such as 7PSF, UQDE and MSAL, to determine the phase difference. The phase difference result must be accompanied with estimation of the measurement uncertainty. The following issues are covered in this paper: the MSAL algorithm background, the ways of treating the bias influence on the phase difference result, comparison of results obtained by applying MSAL and the other mentioned algorithms to the same real signal samples, and evaluation of the uncertainty of the phase difference.

Keywords: sinusoidal electrical signals; phase difference; bias; uncertainty of measurement; MSAL algorithm


  • [1] Svensson, S. (1999). Power measurement techniques for non-sinusoidal conditions. PhD thesis, Chalmers university of technology, Goteborg, Sweden.

  • [2] Rydler, K.E., Svensson, S., Tarasso, V. (2002). Voltage dividers with low phase angle errors for a wideband power measuring system. IEEE CPEM 2002, Conference Digest, 382-383.

  • [3] Voljč, B., Lindič, M., Pinter B., Kokalj, M., Svetik, Z., Lapuh, R. (2012). New design of coaxial current shunts for 50 A and 100 A. IEEE CPEM 2012, Conference Digest, 222-223.

  • [4] Mohns, E., Ramm, G., Kürten Ihlenfeld, W.G., Palafox, L., Moser, H. (2009). The PTB Primary Standard for Electrical AC Power. MAPAN - Journal of Metrology Society of India, 24(1), 15−19.

  • [5] Kokalj, M., Pinter, B., Lindič, M., Ziade, F. (2014). Development of coaxial adapter for calibration of EMC devices. IEEE CPEM 2014, Conference Digest, 586-587.

  • [6] Svensson, S., Rydler, K.E., Tarasso, V. (2004). Improved model and phase-angle verification of current shunts for AC and power measurements. IEEE CPEM 2004, Conference Digest, 82-83.

  • [7] Kokalj, M., Lindič, M., Voljč, B., Pinter, B., Svetik, Z., Lapuh, R. (2012). High accuracy signal parameter estimation algorithm for calibration of PMU devices. IEEE CPEM 2012, Conference Digest, 288-289.

  • [8] Tu, Y., Yang, H., Zhang, H., Liu, X. (2014). CMF Signal Processing Method Based on Feedback Corrected ANF and Hilbert Transformation. Measurement Science Review, 14 (1), 41-47. [Web of Science]

  • [9] So, H.C. (2005). A Comparative Study of Two Discrete - Time Phase Delay Estimators. IEEE Trans. Instrum. Meas., 54(6), 2501-2504.

  • [10] IEEE Standard 1241. (2010). Terminology and test methods for analog-to-digital converters.

  • [11] Ramos, P.M., Janeiro, F.M., Radil, T. (2010). Comparative analysis of three algorithms for two channel common frequency sinewave parameter estimation: ellipse fit, seven parameter sine fit and spectral sinc fit. Metrol. Meas. Syst., 17(2), 250-270. [Web of Science]

  • [12] Vučijak, N., Radojević, N. (2005). Three, Four and Seven Parameters Sine-fitting Algorithms Applied in Electric Power Calibrations. EUROCON 2005, Computer as a tool, 2, 1148-1150.

  • [13] Sedlaček, M., Krumpholc, M. (2005). Digital measurement of phase difference - a comparative study of DSP algorithms. Metrol. Meas. Syst., 12(4), 427-448.

  • [14] Vučijak, N.M., Saranovac, L.V. (2010). A Simple Algorithm for Estimation of Phase Difference between Two Sinusoidal Voltages. IEEE Trans. Instrum. Meas., 59(12), 3152-3158. [Web of Science]

  • [15] JCGM 100:2008 GUM 1995 with minor corrections „Evaluation of measurement data − Guide to the expression of uncertainty in measurement”, Joint Committee for Guides in Metrology.

  • [16] JCGM 200:2008 International Vocabulary of Metrology - Basic and General Concepts and Associated Terms (VIM), BIPM.

  • [17] Hegeduš, H., Mostarac, P., Malarić, R. (2011). Comparison of RMS Value Measurement Algorithms of Noncoherent Sampled Signals. Measurement Science Review, 11(3), 79−84. [Crossref]

  • [18] Novotny, M., Sedlacek, M. (2004). Measurement of RMS values of non-coherently sampled signals. Proc. of the 13th International Symposium on Measurements for Research and Industry Applications, IMEKO TC-4. Athens, Greece, 230−235.

  • [19] Kay, S.M. (1993). Fundamentals of Statistical Signal Processing-Estimation Theory. Englewood Clifs, NJ: Prentice-Hall.

  • [20] Pogliano, U. (2001). Use of Integrative Analog-to-Digital Converters for High-Precision Measurement of Electrical Power. IEEE Trans. Instrum. Meas., 50(5), 1315-1318.

  • [21] Çayci, H. (2011). Final report on key comparison EURAMET.EM-K5.1 (EURAMET Project No. 687): Comparison of 50/60 Hz power. Metrologia 48, Technical supplement 01009.

  • [22] Di Lillo, L., Laiz, H., Yasuda, E., Garcia, R. (2009). Sampling wattmeter at INTI. VIII Semetro, Brazil.

  • [23] Mohns, E., Ramm, G., Kürten Ihlenfeld, W.G., Palafox, L., Moser, H. (2009). The PTB Primary Standard for Electrical AC Power. MAPAN - Journal of Metrology Society of India. 24(1), 15-19.

  • [24] Tóth, E., Franco, A.M.R., Debatin, R.M. (2005). Power and Energy Reference System, Applying Dual- Channel Sampling. IEEE Trans. Instrum. Meas., 54(1), 404-408.

  • [25] Kürten Ihlenfeld, W.G., Mohns, E., Bachmair, H., Ramm, G., Moser, H. (2003). Evaluation of the Synchronous Generation and Sampling Technique. IEEE Trans. Instrum. Meas., 52(2), 371-374.

  • [26] Espel, P., Poletaeff, A., Bounouh, A. (2009). Characterisation of analogue-to-digital converters of a commercial digital voltmeter in the 20 Hz to 400 Hz frequency range. Metrologia, 46, 578-584.

  • [27] Lapuh, R., Voljč, B., Lindič, M. (2015). Evaluation of Agilent 3458A Time Jitter Performance, Two Sampling Voltmeters. IEEE Trans. Instrum. Meas., 64(6), 1331-1335.

  • [28] Kürten Ihlenfeld, W.G., Mohns, E. (2004). AC-dc transfer measurement of highest accuracy with synchronous analogue-to-digital conversion. Metrologia, 41, 111-115.

  • [29] Phillips, S., Eberhardt, K. (1997). Guidelines for Expressing the Uncertainty of Measurement Results Containing Uncorrected Bias. Journal of Research of the National Institute of Standards and Technology, 102, 577- 585.

About the article

Received: 2016-03-03

Accepted: 2016-06-08

Published Online: 2016-12-13

Published in Print: 2016-12-01

Citation Information: Metrology and Measurement Systems, ISSN (Online) 2300-1941, DOI: https://doi.org/10.1515/mms-2016-0047. Export Citation

© Polish Academy of Sciences. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. (CC BY-NC-ND 4.0)

Comments (0)

Please log in or register to comment.
Log in