Electric field singularities at sharp edges of planar conductors

The electric field behavior around printed conductors with a polygonal contour, as used in antennas and microwave circuit components, is investigated. The diffraction problem posed by these geometries involves edge and vertex conditions as well as boundary conditions. These can collectively be described by means of a simple singularity function that gives the distribution of zeros of the electric field on the flat conductor surfaces and of its singularities along the conductor edges. The analysis is based on solving the vector Helmholtz equation for the plane-sector perfect conductor in a conical coordinate system, and the static case is derived from a limit process. The values of the singularity function for the electric field components are explicitly reported for the more commonly encountered 90° and 270° sectors and for 90° bitriangular antennas. Systematic extension to sectors of arbitrary aperture, to composite configurations, and to their polygonal combinations is also indicated