# NUMERICAL CALCULATION OF EIGENFREQUENCIES OF A CYLINDRICAL WAVEGUIDE WITH AN ARBITRARY CROSS-SECTION

A new approach based on a strict formulation is considered, which allows to calculate the eigenfrequencies of a cylindrical waveguide with ideally conducting walls and an arbitrary cross-section. The problem is reduced to the solution of two equations – integral and integro-differential relative to the components of the current density flowing along the walls of the waveguide. It is shown that the equations obtained allow a sequential solution. An effective numerical algorithm for solving these equations using the collocation method is proposed. The algorithm is tested on the classical example of an infinite round waveguide with perfectly conducting walls. Matching between the numerical and theoretical values of eigenfrequencies within the error was found. An example of calculating the critical frequencies of a waveguide of a complex cross-section formed by the intersection of the parts of two circles is given.

**Authors:** D. A. Khodkov

**Direction:** Radiophysics

**Keywords:** Cylindrical waveguides, eigenfrequencies, system of integro-differential equations, numerical analysis

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