Primary frequency properties of LPTV circuits

Authors

DOI:

https://doi.org/10.3103/S0735272724100042

Keywords:

parametric circuits, linear periodically time-varying circuits, LPTV circuits, frequency symbolic method, transfer function, characteristic frequencies

Abstract

The paper considers primary frequency properties of parametric LPTV (linear periodically time-varying) circuits in steady state under the action of a harmonic input signal and periodic changes of parametric elements. Based on the representation of the transfer function by a finite Fourier series, an analytical expression for the output signal of a parametric circuit has been obtained. The conditions for the coincidence of pair harmonic components forming characteristic frequencies with amplification or attenuation effects have been investigated. A method for determining such frequencies has been proposed, and examples of its application in a synchronous detector, frequency converter, modulator, and in single-loop and dual-loop parametric amplifiers have been presented. The results obtained can be used to design radioelectronic devices with due regard for the parametric effects.

References

  1. Y. Shapovalov, D. Bachyk, K. Detsyk, R. Romaniuk, I. Shapovalov, “Analysis of complex linear periodically time-varying circuits by method of reduced matrix D-trees,” Radioelectron. Commun. Syst., vol. 66, no. 4, pp. 190–203, 2023, doi: https://doi.org/10.3103/S0735272723060018.
  2. Y. Shapovalov, S. Mankovskyy, D. Bachyk, A. Piwowar, Ł. Chruszczyk, D. Grzechca, “Machine learning use cases in the frequency symbolic method of linear periodically time-variable circuits analysis,” Appl. Sci., vol. 14, no. 17, p. 7926, 2024, doi: https://doi.org/10.3390/app14177926.
  3. N. Reiskarimian, L. Zhang, H. Krishnaswamy, “Linear periodically time-varying (LPTV) circuits enable new radio architectures for emerging wireless communication paradigms,” in Proceedings of the 54th Annual Design Automation Conference 2017, 2017, pp. 1–4, doi: https://doi.org/10.1145/3061639.3072954.
  4. G. Ptitcyn, M. S. Mirmoosa, A. Sotoodehfar, S. A. Tretyakov, “A tutorial on the basics of time-varying electromagnetic systems and circuits: Historic overview and basic concepts of time-modulation,” IEEE Antennas Propag. Mag., vol. 65, no. 4, pp. 10–20, 2023, doi: https://doi.org/10.1109/MAP.2023.3261601.
  5. A. Piwowar, D. Grabowski, “Modelling of the first-order time-varying filters with periodically variable coefficients,” Math. Probl. Eng., vol. 2017, pp. 1–7, 2017, doi: https://doi.org/10.1155/2017/9621651.
  6. B. Ho Eom, P. K. Day, H. G. LeDuc, J. Zmuidzinas, “A wideband, low-noise superconducting amplifier with high dynamic range,” Nat. Phys., vol. 8, no. 8, pp. 623–627, 2012, doi: https://doi.org/10.1038/nphys2356.
  7. A. Oppenheim, A. Willsky, S. H. Nawab, Signals and Systems. Upper Saddle River: Prentice Hall, 1996.
  8. Y. O. Koval, L. V. Grinchenko, I. O. Milyutchenko, O. I. Rybin, Foundations of Circuit Theory. Textbook for Students, [in Ukrainian]. Kharkiv: CMIT, 2008.
  9. I. S. Gonorovskiĭ, Radiotechnical Circuits and Signals, 5th ed. Moscow: Drofa, 2006.
  10. G. A. Korn, T. M. Korn, Mathematical Handbook for Scientists and Engineers, Revised ed. Mineola, NY: Dover Publications, 2000.
  11. A. A. Kharkevich, Fundamentals of Radio Engineering. Moscow: Fizmatlit, 2007.
  12. S. Faruque, Radio Frequency Modulation Made Easy. Cham: Springer International Publishing, 2017, doi: https://doi.org/10.1007/978-3-319-41202-3.
  13. Y. Shapovalov, “Multivariate modelling of the LPTV circuits in the MAOPCs software environment,” Przegląd Elektrotechniczny, vol. 1, no. 7, pp. 160–165, 2022, doi: https://doi.org/10.15199/48.2022.07.26.
LPTV circuit subjected to action of input harmonic signal and pumping power

Downloads

Published

2024-09-25

Issue

Vol. 67 No. 9 (2024): Circuit and Signal Theory

Section

Research Articles