Three dimensional vector finite element analysis of microwave devices containing anisotropic materials

This thesis presents vector finite element solution methods for the electromagnetic fields in microwave devices containing anisotropic materials. The research focuses on microwave ferrite materials which represent a special case of anisotropy where the permeability tensor is Hermitian in the lossless case. Both two and three dimensional finite element computations are performed. Vector finite elements are used to avoid the occurrence of spurious nodes. In two dimensions, the propagation characteristics of ferrite loaded guiding structures are found and the resulting field patterns are presented. The three dimensional analysis computes the scattering parameters of microwave circulators. Circulators represent a common ferrite loaded microwave device that are often used in transmit/receive modules. The ferrite permeability tensor's dependance on externally applied bias fields results in a spatial inhomogeneity that is readily accommodated in the finite element method. Static bias fields are computed using a commercially available three dimensional nonlinear finite element solution procedure. The calculated static fields are then used in the high frequency analysis to compute the local permeability tensor within each tetrahedral finite element. Scattering parameters and field plots of the circulators are presented. The scattering parameters show good agreement with measured data. Including non-uniform static bias fields in the high-frequency analysis opens the door to design improvements based on shaped bias fields.