Numerical Analysis of Backed Cavity Archimedean Spiral Antenna

A method of calculating the radiation and directivity pattern of planar Archimedean printed spiral antenna backed with an arbitrarily shaped reflector is described. Application of the equivalence principle and the reaction concept of Rumsey leads to the variational formulation of the integral equation expressing the electric field in terms of equivalent currents. The method takes into account the 2-D nature of the strips making it possible to handle the problem of the kernel singularity using on exact analytical method in the case of self-reaction. In other cases the current is assumed to be tangential to the centre-line and constant over the width of the strip which can be approximated by its centre-line. The current and its divergence are approximated by a finite element method (1-D linear elements for the spiral and 2-D linear elements for the reflector). The electromagnetic field radiated by these currents is then calculated and integrated over total space in order to obtain the directivity of the antenna.