The article proposes to use to describe the polar equations of nonlinear resistive two-terminal corresponding differential equations. This simplifies the implementation of non-linear resistors based on analog-digital-analog element. Constant coefficients in the mathematical model are treated as constants of integration. Therefore, the element setting the desired current-voltage characteristic is accomplished by setting appropriate initial conditions.

Keywords: Non-linear element, a mathematical model, pole equation, the differential form

In this paper, we consider the problem of development of equivalent circuit of non-linear element with the current-voltage characteristic controlled either voltage or current, which can be modeled without any changes of scheme in accordance with design requirements. For solving the problem we use an analog-digital-analog element. The current-voltage characteristic of this element is determined by the program of the digital device work. To approximate the characteristics of non-linear elements we apply polynomials of varying degrees - segments of the Taylor series, Maclaurin, Lagrange, et al. In our opinion, the solution of such a problem is relevant.

Keywords: Synthesis schemes, non-linear circuits, equivalent transformations, analog-digital-analog element, non-linear resistance, controllable voltage source, Taylor series, Maclaurin, Lagrange polynomials

The paper gives the definition of reversibility, which can be used in the theory of linear circuits. To determine the conditions of the processes in reverse sequence selected linear second order circuit containing two reactive elements L and C. For a linear circuit at the time of switching current (or voltage ) can be written as the sum of two components : compulsory and free. Conditions for reversibility constrained component current (or voltage ) can be obtained a corresponding change of parameters independent sources of electrical energy. For a free component of the reversibility of the process can be achieved by changing the signs of the circuit elements in such a way that the signs of the roots of the characteristic equation is reversed . This switching can be realized if all the resistors in the multipole synthesized based on analog - digital-analog elements.

Keywords: A reversible process, electrical circuit, current, switching, multipole, input impedance, the characteristic equation