Matrix d-tree method and its application for symbolic analysis of linear parametric circuits in frequency domain

Authors

  • Yuriy Shapovalov Lviv Polytechnic National University, Lviv, Ukraine
  • Dariya Bachyk Lviv Polytechnic National University, Lviv, Ukraine http://orcid.org/0000-0002-0535-0398
  • Ksenia Detsyk Lviv Polytechnic National University, Lviv, Ukraine
  • Roman Romaniuk Lviv Polytechnic National University, Lviv, Ukraine https://orcid.org/0009-0007-3541-6531
  • Ivan Shapovalov Queen’s University, Kingston, Canada

DOI:

https://doi.org/10.3103/S0735272722100041

Abstract

In this paper, the time of solving such SSLAR was reduced by using one of subcircuit methods, namely, topological d-tree method. The existing d-tree method is used for circuits with constant parameters; therefore, this paper proposes its modification under the name Matrix d-tree method that is extended to circuits with variable parameters. This involves the use of the notion of parametric matrix model y = 1/r, g = 1/L, and C of variables and constant elements of parametric circuit.

The d-tree method, both ordinary and matrix, provide a near-optimal taking out of similar terms in formed expressions. This result in a significant reduction of time required for their formation, decrease of the memory size required and the high operation speed of symbolic d-tree method as a whole. This leads to a significant extension of circuits admissible for analysis in terms of their complexity.

The analysis of simulation of parametric ladder circuits presented in this paper has shown a significant increase of admissible complexity of circuits using the matrix d-tree method as compared with the use of standard tools of MATLAB. This fact makes it possible to materially extend the application scope of FS-method in problems of statistical investigations or optimization of electronic devices that are simulated by linear parametric circuits.

References

  1. Y. Shapovalov, Symbolic Analysis of Linear Electrical Circuits in the Frequency Domain. Fixed and Variable Parameters. Lviv: LPNU, 2014.
  2. Y. Shapovalov, B. Mandziy, S. Mankovsky, “The peculiarities of analysis of linear parametric circuit performed by frequency-symbolic method,” Prz. Elektrotechniczny, vol. 86, no. 1, pp. 158–160, 2010, uri: https://www.infona.pl/resource/bwmeta1.element.baztech-article-BPOB-0026-0001/tab/summary.
  3. Y. Shapovalov, D. Bachyk, I. Shapovalov, “Matrix equation of L.A. Zadeh and its application to the analysis of the LPTV circuits,” in 19th International Conference Computational Problems of Electrical Engineering, 2018, pp. 1–5, doi: https://doi.org/10.1109/CPEE.2018.8506766.
  4. Y. Shapovalov, D. Bachyk, K. Detsyk, “Multivariate modelling of the LPTV circuits in the MAOPCs software environment,” Prz. Elektrotechniczny, vol. 98, no. 7, pp. 158–163, 2022, uri: http://pe.org.pl/abstract_pl.php?nid=13088&lang=1.
  5. 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.
  6. 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.
  7. P. Vanassche, G. Gielen, W. Sansen, “Symbolic modeling of periodically time-varying systems using harmonic transfer matrices,” IEEE Trans. Comput. Des. Integr. Circuits Syst., vol. 21, no. 9, pp. 1011–1024, 2002, doi: https://doi.org/10.1109/TCAD.2002.801098.
  8. V. P. Sigorskii, A. I. Petrenko, Fundamentals of Electronic Circuit Theory, [in Russian]. Kiev: Vyssh. Shkola, 1971.
  9. Y. Shapovalov, D. Bachyk, R. Romaniuk, I. Shapovalov, “Parametric matrix models of parametric circuits and their elements in frequency domain,” Radioelectron. Commun. Syst., vol. 64, no. 8, pp. 413–425, 2021, doi: https://doi.org/10.3103/S0735272721080021.
  10. Y. Shapovalov, D. Bachyk, K. Detsyk, R. Romaniuk, I. Shapovalov, “Frequency symbolic analysis of linear periodically time-variable circuits by sub-circuits method,” in 2022 23rd International Conference on Computational Problems of Electrical Engineering (CPEE), 2022, pp. 1–5, doi: https://doi.org/10.1109/CPEE56060.2022.9919673.
  11. F. Zhang, Matrix Theory: Basic Results and Techniques. Springer, 2011.
  12. H. Moore, MATLAB for Engineers. Pearson, 2014.
  13. V. P. Sigorskii, Mathematical Apparatus of Engineer, [in Russian]. Kiev: Tekhnika, 1977.
  14. Y. Shapovalov, “Analysis of linear periodically time-varying circuits by the frequency symbolic method with applying the D-trees method,” Przegląd Elektrotechniczny, vol. 1, no. 6, pp. 46–53, 2021, doi: https://doi.org/10.15199/48.2021.06.08.
  15. Y. O. Koval, L. V. Grinchenko, I. O. Milyutchenko, O. I. Rybin, Foundations of Circuit Theory. Textbook for Students, [in Ukrainian]. Kharkiv: CMIT, 2008.
Model of parametric long-distance line that contains l elementary parametric links

Published

2023-07-30

Issue

Vol. 65 No. 9 (2022)

Section

Research Articles