Finite element analysis of passive electromagnetic devices including lumped electrical circuit models

A methodology is presented for the development of electromagnetically-accurate models for multipart interconnect structures and, in general, passive electromagnetic devices that include embedded lumped elements. The proposed methodology utilizes a discrete state-space model for the electromagnetic device, generated through the application of the finite element method for the spatial discretization of Maxwell´s curl equations. The incorporation of lumped resistors, inductors and capacitors is effected through the direct stamping of the state-space voltage-current relationship for these elements in the matrices of the generated state-space form of the discrete electromagnetic model. The conditions necessary for the discrete model to be passive are discussed. The proposed methodology is demonstrated and validated through its application for the generation of models for a system of two coupled microstrip lines.