Model-order reduction of finite-element approximations of passive electromagnetic devices including lumped electrical-circuit models

A methodology is presented for the development of reduced-order macromodels for multiport 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 model. The conditions necessary for the discrete model to be passive are discussed. The subsequent reduction of the discrete state-space model is effected through the application of a Krylov-subspace-based model-order reduction scheme that guarantees the passivity of the generated multiport macromodel, provided that the original state-space model is passive. The proposed methodology is demonstrated and validated through its application for the generation of reduced-order macromodels for a coaxial cable circuit and a microstrip directional coupler circuit.