A study of current basis functions for antenna modeling

The method of moments (MoM) remains one of the most popular methods to analyze antennas, or indeed, any perfect-electric-conductor (PEC) scattering problem. Since many antennas can be modeled as infinitely thin PEC surfaces, the electric field integral equation (EFIE) formulation has been used. Initially, the current basis function introduced by Rao, Wilton, and Glisson (1982) for PEC surfaces meshed with triangular patches was used. However it was noticed that for structures with both very small and very large features, the condition number of the resulting matrix was very large. This is unfortunate because many antennas fall into this category and because a large condition number may lead to problems in solving the linear system of equations. If a direct method is used to solve the matrix equation, a large condition number will lead to a large relative error between the exact solution and the calculated one. If an iterative method is used, a large condition number may mean that the iterative method will converge only very slowly. Nevertheless, in an effort to reduce the condition number, the RWG basis function was augmented with a loop basis function to form an alternative basis set. The effect of patch size and choice of basis set on the condition number are examined for a simple plate. The RWG basis function may also be augmented with a solenoidal basis function to create a higher order basis set. The effect of this higher order basis set on the convergence of the input impedance for a blade dipole is also examined.