Извините, этот техт доступен только в “Американский Английский”. For the sake of viewer convenience, the content is shown below in the alternative language. You may click the link to switch the active language.
BUILDING AND USE OF MACROMODELS OF LINEAR EQUIVALENT ELECTRICAL CIRCUITS MODEL
Nikolay I. Borisov, National Research University Higher School of Economics, Moscow, nborisov@hse.ru
Alexandr D. Kasatkin, National Research University Higher School of Economics, Moscow, adkasatkin@hse.ru
Semyon A. Presnyakov, National Research University Higher School of Economics, Moscow, spresnyakov@hse.ru
Abstract
The task is to sharply reduce the complexity of analysis, multivariate analysis and parametric optimization of linear and linearized equivalent electrical circuits. The source of such schemes are not only linear electronic circuits, but also circuits formed on the basis of artificial electrical analogies. They can be formed on the basis of finite element methods and finite difference methods used in solving partial differential equations. The reduction in the complexity of computations is carried out by formal methods of transforming the model into a macromodel, which reflects only the input — output type relations of the original model. The e
ssence of the work lies in the formal transformation of the model of a linear or linearized equivalent electrical circuit, formed using artificial electrical analogies methods, into a macromodel, according to which the same output characteristics can be calculated with the same accuracy but with increased speed by several orders of magnitude. Algorithms for such transformations are given. Using a macromodel, one can calculate static characteristics, frequency characteristics, zeros and poles of system functions, dynamic characteristics, eigenvalues, and vectors of a macromodel matrix, which make it possible to determine the stability and stability margin of the original circuit using the first À.Ì. Lyapunov method, its resonant eigenfrequencies and the duration of the transition process, as well as partial derivatives of the above characteristics for a small number of variable circuit parameters to replace the optimization of the circuit with the methods of the 1st order with its optimization by the macro model. In addition, macromodels can be used to create a new element, constructional, and technological base for design. Macromodel can serve as an element of a model of a higher hierarchical level. Block hierarchical process of macromodelling is possible.
Keywords: macromodel, equivalent electrical circuit, finite element method, finite difference method, optimization.
References
1. Borisov N., Starykh V. (2017). Macromodeling of linear equivalent electrical circuits. The Sixth China-Russia Conference on Numerical Algebra with Applications (CRCNAA 2017). Moscow.
2. Borisov N., Shramkov I. (1990). Method for constructing phase macromodels of linear equivalent circuits. Mathematical modeling in CAD: Interinstitutional collection of scientific works. Moscow: Izd-e MIEM, pp. 169-178.
3. Borisov N. (1996). Research and development of methods for reducing the size and complexity of the tasks of analyzing and optimizing linear equivalent electrical circuits based on macromodelling in CAD: Abstract of dissertation for the Doctor of Technical Sciences degree. Moscow: MIEM.
4. Borisov N., Malina A. (2013). Development of methods for determining the frequency properties of linear electrical equivalent using macromodelling. Quality. Innovation. Education. No.3. Moscow, pp. 44-49.
5. Wilkinson J. (1970). Algebraic problem of eigenvalues. Trans. from English. Moscow: Nauka. 564 p.
6. Kublanovskaya V., Mikhailov V., Khazanov V. (1978). On the eigenvalue problem of an irregular matrix. Notes of the scientific seminar of the LOMI (Leningrad Branch of the Mathematical Institute named after V.A. Steklov of the Academy of Sciences of the USSR). Leningrad: Nauka, vol. 58, pp. 80-92.
7. Borisov N.I. (1990). Determination of the dynamic characteristics of linear schemes with multivariate analysis based on macromodelling. Intellectual integrated CAD of REE and LIC: Collection of scientific works. Moscow: Nauka, pp. 101-105.
8. Baskakov A., Borisov N. (2008). Algorithm for constructing a macromodel based on the idea of the method of determining quantities. New information technologies in automated systems: materials of the eleventh scientific and practical seminar. Moscow: MIEM, pp. 93-98.
9. Krohn G. (1972). The study of complex systems in parts – diakoptika. Moscow: Nauka, 542 p.
10. Batalov B., Egorov Yu., Rusakov S. (1982). Fundamentals of mathematical modeling of large integrated circuits on a computer. Moscow: Radio and communication, 167 p.
11. Abrameshin A., Borisov N., Kravchenko N., Malina A. (2013). The method of hierarchical macromodelling in problems of the analysis of linear electrical equivalent circuits in CAD. Quality. Innovation. Education. No. 11. Moscow, p. 40-46.
12. Borisov N., Vostrikov A., Kravchenko N., Malina A. (2014). Development of a reduction method for a linear equivalent electrical circuit model built in a uniform coordinate basis. Tekhnologii EMS [EMC Technologies. Vol. 51 (4). Moscow: Tekhnologii Publishing House, pp. 49-57.
Information about authors:
Nikolay I. Borisov, D.Sc., Professor, National Research University Higher School of Economics, Moscow, Russia
Alexandr D. Kasatkin, Engineer, National Research University Higher School of Economics, Moscow, Russia
Semyon A. Presnyakov, Assistant, National Research University Higher School of Economics, Moscow, Russia