Topological metallic structure design for microwave applications using a modified interpolation scheme

In structural design for microwave applications, metallic structures generate the skin effect that critically affects the performance of microwave devices. In finite element analysis (FEA), highly refined mesh generation is necessary to take the skin effect into account. To avoid the expensive fine meshing and computing process, the condition of the perfect electrical conductor (PEC) or the impedance boundary condition has been generally used in FEA based topology optimization. In this study, we proposed a modified penalization formulation using the shifted sigmoid function for the interpolation of the electric permittivity of conductive materials and applied it to microwave structural design through the phase field design method. The proposed approach is available in case of applications to structural design composed of non-ferromagnetic metals. Based on the derived optimal shape, a simple post-processing scheme is employed only once to determine the clear boundary by eliminating the gray scale area for the purpose of manufacturing feasibility. The validity of the proposed design approach is discussed in three numerical examples allowing the change of the target operation frequency.