| The finite element method is applied to simulate frequency-domain electromagnetic behaviors of multilayer transmission lines and multilayer circuit components that are commonly used in microwave, RF circuits, integrated circuits, and electronic circuit packaging and interconnects. Some difficulties encountered in numerical simulations are tackled with special treatments. First, a generalized eigenvalue problem for inhomogeneous multilayer transmission lines is formulated with the full-wave finite element method. Computationally efficient solvers are employed to solve the eigenvalue problem, which make the fast full-wave field solution possible for hundreds of thousands or even millions of unknowns. Several issues in the simulation are discovered and discussed. Second, the full-wave field solution of transmission lines is used to extract distributed circuit parameters that are useful in circuit designs. A traditional 2-D quasi-TEM finite element method is also extended to handle anisotropic materials in the transmission line analysis. Third, the 3-D full-wave finite element method is applied to analyze circuit components on multilayer boards. The first-order absorbing boundary condition is used to truncate the simulation domain, and the eigenfunction expansion method is used to connect the circuit component to signal inputs and outputs. A new E-H type eigenfunction expansion formulation is used for inhomogeneous port boundary conditions. Various types of planar structures are calculated with the 3-D finite element method. Fourth, a domain decomposition algorithm is developed to reduce the computational efforts in the 3-D multilayer circuit component simulation. The domain decomposition algorithm is further accelerated by a new order-reduction method using modal field basis functions on intersubdomain surfaces and port surfaces. Examples show that the accelerated domain decomposition algorithm greatly improves the performance of the finite element simulation for large multilayer circuit problems. Last, conclusion and possible future research topics are discussed. General computer programs implementing the ideas of this dissertation have been written. Various types of structures are simulated and the results are verified to validate the formulations and their code implementations. |
