Please use this identifier to cite or link to this item: http://ena.lp.edu.ua:8080/handle/ntb/55981
Title: On the Adequacy of the Frequency-Symbolic Method for Linear Parametric Circuits Analysis
Other Titles: Про адекватність частотного символьного методу аналізу лінійних параметричних кіл
Authors: Шаповалов, Юрій
Shapovalov, Yuriy
Affiliation: Lviv Polytechnic National University
Bibliographic description (Ukraine): Shapovalov Y. On the Adequacy of the Frequency-Symbolic Method for Linear Parametric Circuits Analysis / Yuriy Shapovalov // Computational Problems of Electrical Engineering. — Lviv : Lviv Politechnic Publishing House, 2020. — Vol 10. — No 1. — P. 27–36.
Bibliographic description (International): Shapovalov Y. On the Adequacy of the Frequency-Symbolic Method for Linear Parametric Circuits Analysis / Yuriy Shapovalov // Computational Problems of Electrical Engineering. — Lviv : Lviv Politechnic Publishing House, 2020. — Vol 10. — No 1. — P. 27–36.
Is part of: Computational Problems of Electrical Engineering, 1 (10), 2020
Issue: 1
Issue Date: 24-Feb-2020
Publisher: Видавництво Львівської політехніки
Lviv Politechnic Publishing House
Place of the edition/event: Львів
Lviv
Keywords: circuit analysis computing
linear periodically time-variable circuits
frequency-symbolic method
frequency-symbolic models
approximations of transfer functions by Fourier polynomials
Number of pages: 10
Page range: 27-36
Start page: 27
End page: 36
Abstract: Частотний символьний метод (ЧС-метод) аналізу усталеного режиму лінійних параметричних кіл призначений для формування їх передавальних функцій у частотній області. Передавальні функції апроксимуються поліномами Фур’є та містять комплексну змінну, змінну час та параметри елементів кола у вигляді символів. Коефіцієнти таких поліномів Фур’є за ЧС-методом виступають невідомими у символьних системах лінійних алгебраїчних рівнянь (ССЛАР), і визначаються як їх розв’язки у символьному вигляді. Подано спосіб формування апроксимаційного виразу, який забезпечує адекватність обчислень. Наведено приклади та результати комп’ютерних експериментів. Основана на частотному символьному методі система функцій MAOPCs використовується при оптимальному проектуванні електронних пристроїв завадостійких скритних радіотехнічних систем з використанням кодових сигналів.
A frequency-symbolic method (FSmethod) of the analysis of steady-state mode of linear parametric circuits is intended for forming their transfer functions in the frequency domain. Transfer functions are approximated by Fourier polynomials and contain a complex variable, time variable and parameters of circuit elements in the form of symbols. The coefficients of such Fourier polynomials by the FS-method are unknown in the symbolic systems of linear algebraic equations (SSLAE), and are defined as their solutions in symbolic form. In the paper we present a method of forming an approximation expression which ensures the adequacy of calculations. Examples and results of computer experiments are given. The system of functions MAOPCs based on a frequency-symbolic method is used for the optimal design of electronic devices of noiseimmune hidden radio engineering systems using code signals.
URI: http://ena.lp.edu.ua:8080/handle/ntb/55981
Copyright owner: © Національний університет “Львівська політехніка”, 2020
References (Ukraine): [1] Yu. Shapovalov, B. Mandziy, and S. Mankovsky, “The peculiarities of analysis of linear parametric circuit performed by frequency-symbolic method”, Przeglad Elektrotechniczny, vol. 86, no. 1, pp. 158–160, 2010.
[2] Yu. Shapovalov and B. Mandziy, “Symbolic analysis of linear parametric circuits:: state of problems, content and directions of application”, Theoretical Electrical Engineering, issue 59, pp. 3–9, 2008.
[3] Yu. Shapovalov, Symbolic analysis of linear electrical circuits in the frequency domain. Fixed and variable parameters, Lviv, Lviv Polytechnic National University publication, p. 324, 2014.
[4] L. A. Zadeh, “Frequency Analysis of Variable Networks”, in Proc. IRE, vol. 38, issue 3, pp. 291–299, 1950.
[5] Solodov А. V. Linear automatic systems with variable parameters / А. V. Solodov, F. S. Petrov. – Moscow: Nauka, 1971. 620 p.
[6] I. Gonorovkiy, Radioengineering circuits and signals: Textbook for higher schools. М.: Radio and Communications, 4 rd ed., p. 512, 1986.
[7] S. Baskakov, Radioengineering circuits and signals, Textbook for higher schools, spec. “Radioengineering”, 2nd ed., М.: Vysshaia shkola, p. 448, 1988.
[8] М. А. Krasnoselskiy, G. М. Vainikko, P. P. Zabreiko, Ya. B. Rutitskiy, and V. Ya. Stetsenko, Approximate solution of operator equations, М.: Nauka, Main editorial office of physical and mathematical leterature, p. 456, 1969.
[9] К. Fletcher, Numerical methods based on the Galerkin method; transl. from Eng, М.: Mir, p. 352, 1988.
[10] Yu. Shapovalov, B. Mandziy and D. Bachyk “The system functions MAOPCs for analysis and optimization of linear periodically time-variable circuits based on the frequency symbolic method”, Przeglad Elektrotechniczny, vol. 91, no 7, pp. 39–42, 2015.
[11] Yu. Shapovalov, D. Bachyk, K. Detsyk, and R. Romaniuk, “Application of the Frequency Symbolic Method for the Analysis of Linear Periodically Time-Varying Circuits”, Przeglad Elektrotechniczny, vol. 96, no. 3, pp. 93–97. 2020.
References (International): [1] Yu. Shapovalov, B. Mandziy, and S. Mankovsky, "The peculiarities of analysis of linear parametric circuit performed by frequency-symbolic method", Przeglad Elektrotechniczny, vol. 86, no. 1, pp. 158–160, 2010.
[2] Yu. Shapovalov and B. Mandziy, "Symbolic analysis of linear parametric circuits:: state of problems, content and directions of application", Theoretical Electrical Engineering, issue 59, pp. 3–9, 2008.
[3] Yu. Shapovalov, Symbolic analysis of linear electrical circuits in the frequency domain. Fixed and variable parameters, Lviv, Lviv Polytechnic National University publication, p. 324, 2014.
[4] L. A. Zadeh, "Frequency Analysis of Variable Networks", in Proc. IRE, vol. 38, issue 3, pp. 291–299, 1950.
[5] Solodov A. V. Linear automatic systems with variable parameters, A. V. Solodov, F. S. Petrov, Moscow: Nauka, 1971. 620 p.
[6] I. Gonorovkiy, Radioengineering circuits and signals: Textbook for higher schools. M., Radio and Communications, 4 rd ed., p. 512, 1986.
[7] S. Baskakov, Radioengineering circuits and signals, Textbook for higher schools, spec. "Radioengineering", 2nd ed., M., Vysshaia shkola, p. 448, 1988.
[8] M. A. Krasnoselskiy, G. M. Vainikko, P. P. Zabreiko, Ya. B. Rutitskiy, and V. Ya. Stetsenko, Approximate solution of operator equations, M., Nauka, Main editorial office of physical and mathematical leterature, p. 456, 1969.
[9] K. Fletcher, Numerical methods based on the Galerkin method; transl. from Eng, M., Mir, p. 352, 1988.
[10] Yu. Shapovalov, B. Mandziy and D. Bachyk "The system functions MAOPCs for analysis and optimization of linear periodically time-variable circuits based on the frequency symbolic method", Przeglad Elektrotechniczny, vol. 91, no 7, pp. 39–42, 2015.
[11] Yu. Shapovalov, D. Bachyk, K. Detsyk, and R. Romaniuk, "Application of the Frequency Symbolic Method for the Analysis of Linear Periodically Time-Varying Circuits", Przeglad Elektrotechniczny, vol. 96, no. 3, pp. 93–97. 2020.
Content type: Article
Appears in Collections:Computational Problems Of Electrical Engineering. – 2020 – Vol. 10, No. 1



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