A study of the symmetry of field patterns of elliptic horns fed by elliptic waveguides

Horn antennas are widely used as feeding systems in a variety of antennas in space communications and astronomy. While an elliptic horn fed by an elliptic waveguide is also known to exhibit symmetric field patterns, its theoretical treatment was always perceived as too time-consuming. With the availability of faster and larger digital computers, however, the computation of Mathieu functions, in terms of which the eigenmodes of elliptic waveguides can be expressed, is a practical undertaking. When the elliptic horn is operated in the frequency range, where only its dominant mode, TE(/sub c/11), is propagating, only a single set of expansion coefficients are in fact needed, as both Mathieu (ce/sub 1/) and modified Mathieu (Ce/sub 1/) functions share the same set of expansion coefficients. These expansion coefficients can be calculated once at the beginning of the computations, they are, read from the computer memory every time values of the Mathieu functions are needed. Taking advantage of this property considerably speeds up the calculations. The analysis presented follows the modified analysis of conical horns presented by Bornemann (see Microwave Opt. Technol. Lett., vol.10, p.91-94, Oct. 1995). The authors also show how the phase difference is computed.