Mathematical Modeling and Experimental Research of Microwave Waveguide Taking into Account Boundary Value Problems on the Geometric Middle of the Domain

Summary: The article presents mathematical modeling and experimental study of microwave waveguide taking into account boundary value problems on the geometric middle of the domain. For the first time, general classes of local and nonlocal boundary value problems on the geometric middle of the domain for three-dimensional Bianchi-type equations for the electromagnetic field of microwave rectangular waveguide are investigated. New mathematical models of the electromagnetic field of microwave rectangular waveguide operating in the frequency range of 4,9-7,05 GHz are developed taking into account the nonlinearity of the medium, wave types and effective algorithms for solving the models are proposed, which made it possible to improve the electrical, magnetic, structural and operational parameters and characteristics of microwave rectangular waveguide. For E-type and H-type waves, 3D models of the distribution of electromagnetic field strengths in elementary regions of rectangular waveguide are developed. Experimental devices and functional circuits for measuring the parameters of the microwave path, including the electric and magnetic fields of a rectangular waveguide in a nonlinear state of the medium, were developed, and the parameters of the microwave rectangular waveguide were experimentally determined. Comparison of theoretical and experimental results of the electric and magnetic field strengths showed that the relative error for these parameters is 4%. This proved the adequacy of the theoretical and experimental results obtained. The proposed work differs from the existing [1-5] works in that, in this work, for the first time, the factor that the studied microwave waveguide is filled with nonlinear media is taken into account.