Dielectric material optimization of filters and antennas using SIMP.

Abstract

Evidence in literature demonstrates that use of artificial composite materials provides for a greater potential in designing new electromagnetic/RF devices. However, existing studies dealing with design optimization for RF applications focused to a large extent on shape or geometry design only. So far, material and topology optimization has not been pursued primarily due to the challenges associated with the fabrication of inhomogeneous materials and the limited access to versatile and efficient analysis tools. There are very few examples in the literature on topology optimization of electrical devices and these have dealt with problem specific, restricted or semi-analytic tools for magneto-static applications. The goal of this thesis is to develop a general design method that draws from a broader class of design solutions as compared to conventional design methods and is capable of achieving topology and material designs for new electromagnetic devices that may yield much higher performance. In this dissertation, a topology optimization method based on the Solid Isotropic Material with Penalization Method (SIMP) is extended to develop full three-dimensional topology designs for electromagnetic scattering and radiation devices. The design problem is formulated in a non-linear optimization framework and is integrated with a fast full wave finite element - boundary integral (FE-BI) simulator. Sequential Linear Programming (SLP) is used to solve the optimization problem with the sensitivity analysis based on the adjoint variable method for complex variables. The sensitivity analysis is derived, verified and integrated into the simulator for the transmission coefficient and input impedance functions of FSS filters and patch antennas, respectively. The performance of high contrast composite material substrates supporting a patch antenna is studied before the proposed design procedure is presented. One such substrate is fabricated and measured using Micro Fabricated Co-Extrusion (MFCX). The capability of the proposed design method is demonstrated by three design examples. One of the examples refers to the dielectric material distribution for a spectral filter with bandpass behavior. In the second example, the dielectric material distribution of the substrate for a patch antenna subject to pre-specified bandwidth and miniaturization criteria is designed. The optimized design is post-processed via adaptive image filtering and is transformed into a two-material composite for manufacturability. The final substrate is manufactured using Thermoplastic Green Machining as a composite of Low Temperature Co-firing Ceramic (LTCC) filled with air. Finally, the same antenna is designed simultaneously for its patch topology and volumetric dielectric material distribution. Results from both the spectral filter and miniaturized antenna case studies 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.