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SUMMARYWe establish a systematic methodology to design and analyse electromagnetic components such as advanced multilayer ceramic capacitors (MLCCs) using the ÿnite element (FE) method. We employ a coupled formulation to compute the interaction between the electric and magnetic ÿelds. 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 ÿelds 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 ÿelds. 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.

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