Determination of the Parameters of a Linear N-Pole’s Elements from the Input Frequency Responses
Nikolay V. Korovkin, Aleksey GRISHENTSEV · Elektrichestvo · 2024
The article describes research and development of methods for solving the problem of determining the parameters of the elements of a linear N-pole from the input frequency responses. The solution of this problem is relevant for further development of the theory of linear electrical circuits and for a number of practical applications. Two methods for solving the noted problem have been developed. According to the first method, the problem is directly solved in the form of a system of nonlinear equations obtained on the basis of input frequency responses. In the framework of the second method, it is proposed to transform the initial system of nonlinear equations into a system of linear equations by replacing the unique products of the sought parameters with new variables. The main result of the research is the formulated and proven theorem about the number of independent equations and its corollary – a necessary criterion for solving the problem of determining the parameters of the elements of a linear N-pole from input frequency responses. Examples of calculations based on two selected basic circuit diagrams are given. The totality of the obtained results contributes to further development of the theoretical principles of linear electrical engineering and mathematical methods of electrical engineering. In addition, the developed solution methods and the necessary criterion for solving the inverse problem in the form of a theorem and its corollary can be useful in dealing with practical problems of circuit analysis and synthesis.