Wpływ liczby pobieranych próbek i ich usytuowania w okresie na błąd wyznaczania wartości skutecznej i średniej sygnału poliharmonicznego (Część II)

• Autorzy: Nowaczyk E. , Nowaczyk J.

Warianty tytułu

EN

Influence of the number of samples collected in a polyharmonic signal period on the root-mean-square or the average signal value calculated on their basis

• Języki publikacji: PL

Abstrakty

PL

W przentowanej pracy podano zależności matematyczne określające wartość skuteczną sygnału wyliczaną na podstawie próbek pobranych przez przetwornik niesynchroniczny. Przedstawiono wyniki badań modelu takiego przetwornika w środowisku MATLAB-a. Uzyskane rezultaty ilustrują wpływ parametrów sygnału poliharmonicznego i sposobu przeprowadzania próbkowania na błąd wyznaczenia wartości skutecznej i średniej bezwzględnej tego sygnału. W artykule zamieszczono przesłanki odnośnie prawidłowego wyboru częstotliwości próbkowania, a także zalecenia stosowania filtrów antyaliasingowych w torze przetwarzania. Stanowia one zdaniem autorów skuteczne remedium na zmniejszenie błędów omawianych w pracy.

EN

The paper produces an analysis of the accuracy of determination of the root-mean-square (rms) and average value at asynchronous signal sampling. It is an enlargement of the publication [1]. Mathematical equations determining the rms value for pure sine-wave and polyharmonic signals have been presented. The calculation of the average value has been based on the analysis carried out in a general way in many literature items, such as [6]. For both calculated kinds of values, tests were carried out by creating a model of asynchronous converter in MATLAB's environment and applying at its input a pure sine-wave signal or polyharmonic signals of different forms; at the same time the sampling frequency and the number of samples taken were changed. The obtained simulation results, representing the determination of the root-mean-square or average value with regard to the conventional true value, for exemplifying signal forms, have been presented in illustrations. They illustrate the effect of the number of samples taken, of the relative sampling frequency, of the moment of the first sample, and for polyhannonic signals also of harmonic contents, their numbers and phase shift. The phenomenon of result waving and particularly big errors for some ,,unlucky" harmonic numbers have been shown. It was noticed that as the number of the samples taken increases, the intervals are being narrowed where the calculated root-mean-square or average value can be found. However, with an increase of the sampling frequency there is need for drawing a larger and larger number of samples, in order to obtain results not differing from each other more than it is admissible (when calculating the root-mean-square value this occurs for a relative sampling frequency greater than four). If a signal contains, apart from the fundamental frequency, also harmonics ones (and this is always the case in practice), then in selecting sampling frequencies the greatest harmonic numbers should be kept in mind, including also the sum or the difference of their numbers. Neglecting this recommendation that results from Shannon's theorem, may lead to the result waving at a very low frequency and simultaneously with high amplitude. The result of taking a greater number of samples for calculations may be more departing from the correct one than with their smaller number. Application of antialiasing filters in the conversion line was proposed. These filters, damping high frequency components and possible noise enable one to obtain greater repeatability of the results. For the sampling of signals of approximately constant frequency, such as those of the power-line, it was recommended to select a sampling frequency close to an odd multiple of the rated frequency value of the sampled signal, both when calculating the average and the rms value. The presented paper points to the error sources resulting from the way of drawing of samples by sampling converters. It also contains main lines directed at practicians, connected with making use of the obtained results when applying these converters in measurements and automation.

Słowa kluczowe

EN

polyharmonic signal; measurements

• Wydawca: Komitet Metrologii i Aparatury Naukowej PAN
• Czasopismo: Metrology and Measurement Systems
• Rocznik: 2002
• Tom: Vol. 9, nr 4
• Strony: 413--432
• Opis fizyczny: Bibliogr. 20 poz., rys.

Twórcy

autor

Nowaczyk E.

• Politechnika Wrocławska, Zakład Pomiarowej i Medycznej Aparatury Elektronicznej

autor

Nowaczyk J.

• Politechnika Wrocławska, Zakład Pomiarowej i Medycznej Aparatury Elektronicznej

Bibliografia

• 1. Nowaczyk E., Nowaczyk J.: Wpływ liczby pobieranych próbek i ich usytuowania w okresie na wyznaczanie wartości skutecznej łub średniej sygnału poliharmonicznego, Metrology and Measurement Systems, vol. VIII, no. 3, 2001, pp. 271-287.
• 2. Howard J., Landgraf H.: Quadrature sampling phase detection. Review Sci. Instrum., vol. 65, no. 6, 1994, pp. 2130-2133.
• 3. Villa M., Feng T., Halamck J., Kasal M.: High-resolution digital quadrature detection. Review Sci. Instrum., vol. 67, no. 6, 1996, pp. 2123-2129.
• 4. Kirsten J., Fleming T.: Undersampling reduces data-acquisition costs for select applications. EDN. June 21, 1990, pp. 217-228.
• 5. Pogliano U.: Precision measurement of ac voltage below 20 Hz at IEN, IEEE Trans, on Instrum. and Meas., vol. 46, no. 2, April 1997, pp. 369-372.
• 6. Candy J. C., Temes G. C.: Oversampling Delta-Sigma data converters. IEEE Press, New York 1992.
• 7. Kollar I.: Bias of mean square value measurement based on quantized date. IEEE Trans, on Instrum. and Meas. vol. 43, no. 5, Oct. 1994, pp. 733-739.
• 8. Gray R., Stockham T.: Dithered quantizer. IEEE Trans, on Inform. Theory, vol. 38, no. 3, 1993, pp. 805-815.
• 9. Carbone P.: Quantative criteria for the design of dither-based quantizing systems, IEEE Trans, on Instrum. and Meas. vol. 46, no. 2, Jule 1997, pp. 656-659.
• 10. Wagdy M.: Effect of various dither forms on quantization errors of ideal A/D converters. IEEE Trans, on Instrum. and Meas. vol. 38, no. 4, 1989, pp. 850-855.
• 11. Harris F. J.: On the use of windows for harmonic analysis with the discrete Fourier transform, Proceeding of IEEE 66(1), Jan. 1978, pp. 51-83.
• 12. Asai T.: Precise interpolation for bandlimited digital signals based on sampling theorem incorporated with window functions. Transactions of the Institute of Electronics, Information and Communication Engineers A. vol. J 82-A, no. 8, Aug. 1999, pp. 1329-1342.
• 13. Leon C., Lopez A., Montano J. C., Monedero I.: Classification of disturbances in electrical signals using neural networks. Bio-Inspired Applications of Connectionism, 6th International Work-Conference on Artificial and Natural Neural Networks. IWANN 2001, Proceedings, Part II, Springer-Verlag, 2001, Berlin, Germany, pp. 728-737.
• 14. Leon C., Lopez A., Montano J. C., Elena J. M., Monedero I.: Neural network for detection and classification of disturbances in electrical signals. Proceedings of ihe IASTED International Conference Power and Energy Systems, IASTED/ACTA Press, 2000, Anaheim, CA, USA, pp. 529-534.
• 15. Dash P. K., Jena R. K., Salama M. A.: Power quality monitoring using an integrated Fourier linear combiner and fuzzy expert system, International Journal of Electrical Power & Enerev Svstems, vol. 21, no. 7, Oct. 1999, Elsevier, UK, pp. 497-506.
• 16. Oppenheim A. V., Schafer R., W.: Cyfrowe przetwarzanie sygnałów, WKiŁ, Warszawa 1979.
• 17. System Application Guide, Published by Analog Devices Inc., printed in USA, 1993.
• 18. Szabatin J.: Cyfrowe przetwarzanie sygnałów, WKiŁ, Warszawa, 2000.
• 19. Dahlquist G., Bjorek A.: Metody numeryczne, PWN, Warszawa, 1983.
• 20. Nowaczyk E., Nowaczyk J.: Ocena dokładnosci przetwarzania skutecznej wartości napięć zmiennych, XXXII Miedzyuczelniana Konferencja metrologów, Rzeszów-Jawor, 11-15.09.2000, t. II, s. 453-458.