DOI: https://doi.org/10.20535/RADAP.2018.72.13-22

### Generalized Mathematical Model of Thin Asymmetric Inductive Diaphragm in Rectangular Waveguide

O. S. Zakharchenko, S. Ye. Martynyuk, P. Ya. Stepanenko

#### Abstract

Introduction. A significant number of microwave devices are constructed with applying the investigation results of thin asymmetric inductive diaphragm in rectangular waveguide. Increasing the requirements for the characteristics of these devices stipulates necessity to review the possibilities of existing electromagnetic methods in relation to increasing the accuracy of generalized scattering matrices calculation of this diaphragm. To obtain the high accuracy results of generalized scattering matrices calculation, a further study of integral equations method is represent considerable practical interest.
Mathematical model of diaphragm. An accurate novel solution for general scattering matrix of infinitely thin asymmetric one-sided diaphragm in rectangular waveguide has been obtained. The problem is formed as the system of integral equations along the number of waves which is incident on the diaphragm. By applying the Galerkin’s method, each integral equation is reduced to system of linear algebraic equations relatively to coefficients of tangential electric field decomposition in diaphragm window by series of coordinate functions. The joint solution of all equations gives the distribution of tangential electric field in diaphragm window which is further used for finding the generalized scattering matrix.
Numerical results. Two approaches for finding the coupling coefficients of coordinate functions of diaphragm window and eigen functions of waveguide are investigated. An estimation of limiting possibilities of developed realization of the integral equations method at approximation of tangential electric field in diaphragm window by series of eigen scalar functions has been carried out. It is shown that the calculated results of module and phase of fundamental wave transmission coefficient through diaphragm slowly go to exact values when the order of linear algebraic equation system is increased.
Conclusions. The results of diaphragm investigation by using this algorithm have not only independent value but can be used to verify the accuracy of calculating the electromagnetic parameters of thin waveguide structures by using the general methods for solving electromagnetic problems, for example, FDTD. It is supposed that the results obtained in this work can be used in developing fast and high-precision calculation algorithms for frequency responses of multi-stage asymmetric waveguide structures.

#### Keywords

generalised scattering matrix; infinitely thin asymmetric inductive diaphragm; rectangular waveguide

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