Finite element analysis of advanced multilayer capacitors

We establish a systematic methodology to design and analyse electromagnetic components such as advanced multilayer ceramic capacitors (MLCCs) using the nite element (FE) method. We employ a coupled formulation to compute the interaction between the electric and magnetic elds. Unlike a linear distribution of current assumed in the circuit model, an accurate electrostatic solution to model the entire advanced MLCCs (4×4×27=432 cells) is presented. The FE solution is used to compute the lumped parameters for a range of frequencies. These lumped parameters are then used to compute the parasitic elements of the MLCCs. We introduce two algorithms to e ciently analyse the behaviour of a capacitor with changing frequency. The lower frequency (much below the selfresonant frequency of the capacitor) algorithm separates the e ect of the electric and magnetic elds and reduces the computational e ort required to solve the FE problem, whereas, the high-frequency algorithm couples the e ect between the electric and the magnetic elds. We use these algorithms in conjunction with a new multiple scale technique to e ectively determine the small values of R, L and C in MLCCs. The formulation, the implementation, and the numerical results demonstrate the e cacy of the present FE formulation and establish a systematic methodology to design and analyse advanced electromagnetic components