Higher order mode impedances and cut-off frequencies of overmoded coaxial waveguides

Using both theoretical and experimental methods the critical geometrical ratios for effective higher order mode superposition in coaxial waveguides are identified for SDMA beam forming antenna applications. Higher order mode impedances are also important in the design of such antennas and a closed form expression for the power-voltage definition of impedance is derived together with estimates for the voltage-current and power-current forms. An industry standard finite element solver is used to confirm the accuracy of these formulations for a 60 mm radius overmoded coaxial waveguide. In the second part of the paper, the mode chart is used to design a coaxially fed, overmoded air-spaced coaxial waveguide "T" junction supporting the TEM, TE11 and TE21 modes. A Green's function based model of the input impedance of this junction establishes that the power-voltage characteristic impedance occurs naturally in calculations requiring absolute impedance values. Finally, this input impedance model, which includes higher order and evanescent mode propagation, is demonstrated to agree well with experimental data for this junction.