Method of undetermined coefficients for circuits and filters using Legendre functions
Manbetova Z. Dunayev P. Yerzhan A. Imankul M. Zhazykbayeva Z. Seitova Z. Dzhanuzakova R. Karnakova G.
February 2025Institute of Advanced Engineering and Science
International Journal of Electrical and Computer Engineering
2025#15Issue 1846 - 854 pp.
This article presents a new way to implement matching networks and filters using the method of undetermined coefficients. A method is proposed for approximating the transmission coefficient of the synthesized filter, taking into account the required amplitude-frequency characteristics. To synthesize the filter, an approximating function (AF) was used using orthogonal Legendre polynomials, which is a mathematical description using a system of equations. Filter properties whose implementation is based on modified Legendre approximating functions usually depend on the interval on which they are defined and have the property that they are orthogonal on this interval. An example of seventh order filter synthesis using modified Legendre approximating functions is given. The filter circuit is implemented, the elements of the filter circuit are calculated based on the selected approximating modified function. The criteria used were minimization of the unevenness of the group delay time (GDT) and minimization of the complex approximation error for given values of the AF parameters. As a result, the number of filter elements, the group delay value and the complex approximation error are significantly reduced.
Complex approximation error , Matching-filtering circuits , Method of undetermined coefficients , Modified approximating function , Zero transfer
Text of the article Перейти на текст статьи
Department of Radio Engineering, Electronics and Telecommunications, Faculty of Energy, Saken Seifullin Kazakh Agrotechnical Research University, Astana, Kazakhstan
Department of Telecommunication Engineering, Institute of Communications and Space Engineering, Non-profit Joint Stock Company Almaty University of Power Engineering and Telecommunication named Gumarbek Daukeev, Almaty, Kazakhstan
Department of Radio Engineering, Electronics and Telecommunications, L.N. Gumilyov Eurasian National University, Astana, Kazakhstan
Department of Agricultural Engineering and Technology, Saken Seifullin Kazakh Agrotechnical Research University, Astana, Kazakhstan
Department Automation and Communication, M.Kh. Dulati Taraz Regional University, Taraz, Kazakhstan
Department of Radio Engineering
Department of Telecommunication Engineering
Department of Radio Engineering
Department of Agricultural Engineering and Technology
Department Automation and Communication
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026