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On the theory of spherical waves in GTEM cells: higher-order modes in unloaded cells

The recent theory for the formulation of closed form solutions for spherical TEM-waves in GTEM cells is conveniently extended to the analysis of higher order modes. The well-known common spherical and cylindrical functions are agreeably combined and used to determine higher order mode field distributions in the cell. It is shown that by distinguishing the dominant mode from the secondary modes and applying boundary conditions adapted to the geometrical form of the cell, substantial simplifications of the analysis can be achieved. The analysis is based upon the coupled field formulation between the upper and the lower regions of the cell. Both fields are directly matched together through the Maxwell surface boundary conditions. In this way, the determination of higher order modes is reduced to the solution of a transcendental equation for the particular case of symmetric cells. For asymmetric cells, however, the points-matching principle is applied.