Mathematical Modeling of Complex Antenna System

The mathematical model of an antenna system as a set of dipoles array located above complex shape perfectly conducting reflector is offered. The general model is formulated as a compact system of rigorous integral equations. The Pocklington's integral equation for current distributions of dipoles is used. The technique for correct solving the Fredholm's integral equation of kind II for small thickness complex shape reflector and the method for numerical solving ill-posed equations are proposed. Using the correspondence of asymptotic solutions to 2D and 3D problems in antenna engineering leads to simple form of the model but only for limited cases, such as parallel polarization of dipoles to reflector axis and perpendicular plane for calculating the far-field pattern