Numerical Analysis of Frequency Selective Surfaces

Open Access
Mehta, Nikhil N
Graduate Program:
Electrical Engineering
Master of Science
Document Type:
Master Thesis
Date of Defense:
July 31, 2010
Committee Members:
  • Raj Mittra, Thesis Advisor
  • dipole moment
  • characteristic basis functions
  • macro basis functions
  • non-planar FSS
The Method of Moments (MoM) is a numerical technique for solving the integro– differential field equations arising in computational electromagnetics (CEM) has evolved into a versatile and mature computational tool for solving a large variety of scattering problems involving arbitrary structures. However, the MoM requires knowledge of the Green’s function for the medium in which the scatterer is present, and special treatment is necessary to tackle the singularity issues that arise in the integral equation based on this Green’s function. To address these concerns, we introduce a new technique called the Dipole Moment method (DM) which uses the knowledge of the induced dipole moments in a small sphere under the influence of a plane wave. Although this method follows the matrix–based approach used in MoM to solve for the unknown currents induced on an object, it avoids the direct use of the Green’s function and hence is free from the singularity issues. The DM utilizes relatively large number of unknowns to solve the matrix equation compared to the conventional MoM. In order to improve the numerical efficiency of the DM method, we introduce a set of high-level macro basis functions, referred to herein as the Characteristic Basis Functions (CBFs). The use of CBFs leads to a well-conditioned interaction matrix whose size is substantially smaller than the size of the matrix required in DM or in conventional MoM for accurate solution. In particular, we introduce a numerically efficient technique based on a combination of the DM and CBFs to analyze doubly infinite periodic structures, also called as Frequency Selective Surfaces (FSSs). We also develop a new method based on the reciprocity principle, to calculate the reflection coefficient of the FSS. This method circumvents the need to integrate the current distribution on the FSS to find scattered far-fields from the array. We validate the numerical technique introduced in this thesis by comparing our results for the reflection coefficient of the FSS with those obtained from commercially available MoM–based codes, and show that it is able to analyze planar, non–planar and multi–layered FSSs.