Построение и использование макромоделей линейных эквивалентных электрических схем
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 А.М. 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.