Eccentric circular coaxial waveguides has the advantage of changing the characteristic impedance by varying the lateral offset of the center conductor. This technique can be used for quarter wave matching element, which forms one of the sections in multi-section quarter wave transformer for broadband matching. The cut-off wavenumbers of eccentric circular coaxial waveguides are evaluated employing the Finite Element Method. Adaptive meshing has been employed to subdivide the cross-sectional region between the two conductors. The basic triangular element is employed for meshing since it best approximates the geometry.
A functional is derived for the homogeneous Helmholtz equation with the appropriate boundary condition and the solution is obtained using the Ritz method resulting in an eigenvalue problem. The symmetricity of the problem gives an advantage to analyze half of the domain of the problem, which in turn reduces the size of the matrix to half. Eccentric waveguides are analyzed using even and odd modes. This is incorporated in the problem by applying different boundary conditions for each mode respectively. The results are obtained after testing the convergence. The validity of the analysis has been justified by comparing the eigen values computed by the method presented in this paper with those of Finite difference method to validate the results. Effect of axial offset of inner conductor on the cutoff wavenumbers for different ratio of outer-to-inner radii has been determined.