Eigenmodes of coaxial quad-ridged waveguides. Theory





eigenmode, coaxial quad-ridged waveguide, electrodynamics boundary problem, integral equation technique, singularities at ridges, orthogonal basis functions, Gegenbauer polynomial, TEM mode, TE mode, ТМ mode, solutions convergence, residual error


The electrodynamics eigenmodes boundary problems’ solutions for the eigenmodes of coaxial quad-ridged waveguides are presented. These solutions have been obtained by integral equations technique utilizing the proposed system of orthogonal basis functions, which take correctly into account singular behavior of the field at the ridges’ edges. The formulas obtained provide possibilities to calculate cutoff wave numbers and electric and magnetic fields distributions for TEM, TE and TM modes in the presence of the ridges either on the inner or on the outer conducting cylinder. Analysis of the dependence of numerical solutions convergence for cutoff wave numbers on the number of basis functions and partial modes has been carried out. It has been shown that for calculation of cutoff wave numbers with residual error less than 0.1% it is enough to utilize the 7 proposed orthogonal basis functions and the 21 partial modes.


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