A COMPARATIVE ANALYSIS OF THE GRAPHO-ANALYTICAL METHODS OF RESEARCH OF ELECTRIC CIRCUITS

Konkina Maria Sergeevna, postgraduate student, Penza State University (40 Krasnaya street, Penza, Russia), myzochka@list.ru
Medvedeva Svetlana Nikolaevna, candidate of technical sciences, associate professor, acting head of sub-department of applied and business informatics, Penza branch of K. G. Razumovsky Moscow State University of Technologies and Management (First Cossack University) (6 Volodarskogo street, Penza, Russia), sn-medvedeva@yandex.ru

519.171, 621.317.3

10.21685/2307-5538-2018-2-3

Background. The object of study is graphic or topological methods of calculation of electric circuits. There are many types of graphs: graphs Mason, Coates, current, potential-current graph, potential of the signal graphs, etc. All graphs are characterized by clarity and constitute one of the ways of the system of linear equations. The aim of this work is justification of selection of one of the types of graphs for analysis of electrical circuits.
Materials and methods. The study used non-metric section of mathematics, which is based upon a topological approach to the study of processes and phenomena. The obtained results are consistent with the basic provisions of the theory of graphs and algebraic methods to quickly obtain mathematical expressions, is extremely convenient from the point of view of subsequent analysis.
Results. Studied various types of graphs, each defined by its characteristics. It is revealed that the set of characteristics for the analysis of electric circuits more convenient are generalized signal graphs, which combine the strengths of the counts of Mason and Coates, and free from inherent disadvantages. All varieties of signal graphs are special cases of the generalized signal graphs.
Conclusions. It is shown that the generalized signal graphs are the most convenient for the analysis of electric circuits, due to the greater informational content and visibility of relationships between parameters of the electrical circuit.

graph, the determinant of the graph, a topological formula, potentialcurrent graph, potential of the signal graph, the generalized signal graph