Analysis of infinite antenna array by the method of piercing region

Abstract

The method of integral equation with a selection of overlapping regions has been used for solving electromagnetic problems in many papers. In accordance with this method, the cross-section of the considered structure is divided into overlapping regions, and a Fredholm second kind integral equation can be derived. However, in some electromagnetic problems one can not use the method of overlapping regions. To solve these problems (and other problems) the method of piercing region is proposed. In this method a piercing region is introduced, and a Fredholm second kind integral equation can be obtained.

The design of infinite antenna array in H and E plane is carried out by the method of integral equation with the separation of the piercing region (method of piercing region). The full-wave algorithm and the mathematical grounding of the method of piercing region are considered in details. For an antenna array in E plane an application of the Galerkin method eventually yields a system of linear algebraic equations, which is the same as with the method of overlapping regions. In H plane design case the final matrix equation is different.

Numerical results of the analysis of an infinite antenna array are considered in details, graphical material and tables are presented. The results agree well with the other available data. It is shown that the method of piercing region can be used for solving a wide class of electromagnetic problems.