Topology Optimization of Dielectric Substrates for Filters and Antennas Using SIMP

In this paper a novel design procedure based on the integration of full wave Finite Element Analysis (FEA) and a topology design method employing Sequential Linear Programming (SLP) is introduced. The employed design method is the Solid Isotropic Material with Penahzation (SIMP) technique formulated as a general non-linear optimization problem. SLP is used to solve the optimization problem with the sensitivity analysis based on the adjoint variable method for complex variables. A key aspect of the proposed design method is the integration of optimization tools with a fast simulator based on the finite elementboundary integral (FE-BI) method. The capability of the design method is demonstrated by two design examples. First, we developed a metamaterial substrate with arbitrary material composition and subject to a pre-specified antenna bandwidth enhancement. The design is verified and its performance is evaluated via measurements and simulation. As a second example, the material distribution for a Thermo-Photovoltaic (TPV) filter subject to pre-specified bandwidth and compactness criteria is designed. Results show that the proposed design method is capable of designing full three-dimensional volumetric material textures and printed conductor topologies for filters and patch antennas with enhanced performance.