Development and improvement of radio engineering devices, reduction of their design time period require development of effective methods of mathematical modeling of analysis and optimization of these devices technical parameters. The paper considers new mathematical models that describe such objects for which it is necessary to use algebraic equations along with differential ones. Kirchhoff's laws, component equations, equivalent transformations of currents and voltages gradually eliminating algebraic expressions from consideration are been used for the paper objectives solution. As a result of these transformations, the system which contains differential and algebraic relations is reduced to a form of differential equations in the Cauchy form. This allows applying well-developed methods and algorithms for the numerical solution of differential equations in further researches.

Keywords: mathematical modeling, optimization, electronic device, bipolar transistor, state space method, differential equations, regular search algorithms