Accurate simulation of a spherical reflector antenna by the complex point source-dual series approach

For a 2-D problem, an efficient and accurate analysis can be done by combining the complex-point source (CPS) method to simulate a directive feed field, and a dual-series-equations (DSE) based on regularization technique. A circular-cylindrical reflector fed by a complex point E and H-polarized line sources was considered. DSEs were formulated in terms of trigonometric functions, with the static part analytically inverted based on the Riemann-Hilbert problem solution. The resulting matrix equations were of the Fredholm 2-nd kind. A remarkable feature of this equation is that it can be solved numerically with a guaranteed accuracy and small CPU time expenditures.