Keywords
quasi-sinusoidal signal
higher harmonics
synchronous detection
error correction імпеданс
квазісинусоїдальний сигнал
вищі гармоніки
синхронне детектування
корекція похибок
How to Cite
Abstract
This article examines errors caused by the influence of higher harmonics during synchronous detection of step-approximated quasi-sinusoidal signals in electrical impedance meters and other devices. Numerical modeling of the synchronous detection process is performed in case of coinciding shapes of the input and reference detector’s signals. It is shown that when the number of approximation steps in the input and reference signals is equal, the dependence of the error on the phase of the input signal is periodic, with the period of error variation coinciding with the width of the signal step. An analytical expression is derived showing that the maximum error value decreases proportionally to the square of the number of signal approximation steps. Сhanging the shape of the reference signals of the detectors by varying the number of approximation steps is proposed to reduce the error. In this case, the error decreases proportionally to the square of the least common multiple of the numbers of steps in the input and reference signals. A combination of stage numbers that have no common factors are found to be an optional choice. It is demonstrated that the error under study can be reduced by several dozen times without narrowing the frequency range of the converted signals. An experimental determination of errors caused by the influence of higher harmonics was carried out, results of which confirmed the effectiveness of the proposed method for correcting these errors. References 13, figures 5, tables 3.
References
1. Sushrut H., Katlynne J. Smart DAC Sine-Wave Generation Circuit. Texas Instruments. SLAAE66. 12.2022. URL: https://www.ti.com/lit/pdf/slaae66 (accessed at 01.09.2025).
2. Cronin B. DDS Devices Generate High Phase Accumulator Quality Waveforms Simply, Efficiently, and Flexibly. Analog Dialogue 46-01. January 2012. URL: https://www.analog.com/media/en/analog-dialogue/volume-46/number-1/articles/dds-generates-high-quality-waveforms-efficiently.pdf (accessed at 01.09.2025).
3. Arozarena T.C. Development of a direct digital synthesis based generator. Universidad Pontificia Comillas. Madrid. 07.2019. URL: https://www.google.com/url?sa=t&source=web&rct=j&opi=89978449&url=https://repositorio.comillas.edu/xmlui/bitstream/handle/11531/35157/TFG_CorchadoArozarena%252CTeresa.pdf%3Fsequence%3D1%26isAllowed%3Dy&ved=2ahUKEwitqqCW97ePAxXaKhAIHd_9EDk4ChAWegQIFRAB&usg=AOvVaw1Mf1BI5KTrLTuLvNZh0Wby (accessed at 01.09.2025).
4. Grynevych F.B., Surdu М.N., Melnyk V.G., Sheremet L.P. On the construction of a synchronous-phase selective system for wide-band automatic AC bridges. Problemy tekhnicheskoi elektrodinamiki. 1978. Vyp. 68. Pp. 79-82. (Rus)
5. Surdu М.N., Melnyk V.G., Ornatsky О.А. On the selection of a method for calculating quasi-sinusoidal voltage parameters. In the book: Electrical Measurement Technique. Kyiv: Naukova Dumka, 1979. Pp. 41-48. (Rus)
6. Borschov P.І., Lameko О.L., Melnyk V.G. Reducing the influence of generator parameter deviations in precision quadrature bridges. Tekhnichna Elektrodynamika. 2024. No 1. Pp. 77-85. DOI: https://doi.org/10.15407/techned2024.01.077. (Ukr)
7. Surdu M., Lameko A., Surdu D., Kursin S. Wide frequency range quadrature bridge comparator. 16th International Congress of Metrology, Paris, France, 07 October 2013. Article no 11014. DOI: https://doi.org/10.1051/metrology/201311014.
8. Orozco L. Synchronous Detectors Facilitate Precision, Low-Level Measurements. Analog Dialogue 48-11. November 2014. URL: https://www.analog.com/media/en/analog-dialogue/volume-48/number-4/articles/synchronous-detectors-facilitate-precision.pdf (accessed at 04.09.2025).
9. Fourier series expansion of a function – a step approximation to a sinusoid. https://www.rotr.info/electronics/mcu/stm32_dac_synthesizer/stepf_expansion.htm (accessed at 01.09.2025).
10. Smith I.R. A Stepped-Waveform Approximation to a Sine Wave. International Journal of Electrical Engineering & Education. Vol. 1. Issue 1. DOI: https://doi.org/10.1177/002072096300100108.
11. Prudnikov A.P., Brychkov Yu.A., Marichev O.I. Integrals and series. Elementary functions. Moskva: Nauka, 1981. 800 p. (Rus)
12. Pimsut Y., Bauer S., Kraus M., Behr R., Kruskopf M., Kieler O., Palafox L. Development and implementation of an automated four-terminal-pair Josephson impedance bridge. Metrologia. 2024. Vol. 61. No 2. DOI: https://doi.org/10.1088/1681-7575/ad2539.
13. Surdu M.N., Lameko A.L., Mukharovsky M.Ya., Karpov I.V., Kursin S.N. Features of calibration of a two-channel vector voltmeter of a digital AC bridge. Ukrainskii metrologichnyi zhurnal. 2011. No 1. Pp. 25-30. (Rus)
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