Scientific paper ID 1890 : 2019/3

The mathematical model of the electrical circuits is represented in various forms: by the impulse response, the transfer function, in form of a system of integral-differential equations. The task of circuit synthesis is to immediately solve the equations and determine the parameters of the elements, in provided physical realizability.

In case with random changes and uncertainties of the input signal, the circuit synthesis task may be incorrect. Then, an optimal by complexity and precise mathematical model of the circuit that is also physically realizable is needed.

The work proposes an approach for the synthesis of an electric circuit under conditions of random changes of the input impact. The variation method is used, defining a functional describing qualitative synthesis criteria. According to the theory of variance calculus, the necessary conditions for the extrema of the functional are determined. Expression for the transfer function of the synthesized circuit, which depends on both the optimization parameter and the random changes of the input signal.

The proposed methodology defines the transfer function of the first order frequency circuit in a single input signal. Сalculations are made in Mathcad environment. The accuracy of the method has been assessed. The error between the actual and calculated values of the transfer function parameters is in the range of 0.1%.