Hybrid finite element analysis of the effect of periodic loading at a perfectly conducting antenna reflector edge

The performance of antenna systems is often influenced by diffraction phenomena. Control over these diffracted fields can assume significant importance especially when compact antennas are designed. Considerable research has been devoted to the identification of suitable antenna reflector edge terminations in an attempt to minimise quiet zone ripple or field strength in the shadow zone. Hence a number of edge of configurations have been considered such as blended rolled edges, curved edges, and corrugated soft edges. Furthermore, the surface currents on the antenna reflector have been terminated gradually at the edges by tapering the conductivity of the reflector through the application of lossy materials even if in some antenna applications this is not desirable since it can adversely affect antenna noise temperature. The electromagnetic influence of some of the terminations described above cannot be easily quantified analytically. Consequently, the problem is solved by resorting to suitable numerical techniques. We present a hybrid technique which utilises a finite element/ boundary element method that models the electromagnetic behaviour of a perfectly conducting, arbitrarily shaped wedge loaded near its edge. The loading is considered to be periodic along the edge, hence the formulation is able to model the effect of the presence of hard surfaces. In particular, both geometrical and material periodic variations near the edge of the wedge are analysed using a Galerkin weighted residual finite element method (FEM) employing three dimensional edge elements and periodic weighting functions. In order to find the unique field solution everywhere in this geometrically complex and infinite problem region using finite computational resources, the finite element mesh is truncated by a boundary element surface on which the field solution is expanded in terms of cylindrical Floquet harmonics. The latter are appropriately chosen by taking into consideration the field solution of the canonical wedge problem. It is assumed that the geometrical structures under investigation are illuminated by a plane wave. The proposed technique is computationally efficient and hence it can be applied not only for the analysis but also for the optimisation of reflector antenna terminations.