Incorporation of frequency-dependent multiport lumped networks into a hybrid time-domain finite-element solver

In modern circuit design, hybrid field-circuit solvers that combine a full-wave analysis and a lumped circuit simulation become indispensable for accurate characterization of complicated microwave circuits that include both distributive and lumped circuit subsystems. In some applications, lumped circuit might have been predesigned and characterized compactly in terms of frequency-dependent multiport network matrices which are often referred to as lumped networks. Recently, lumped networks have been incorporated into a finite-difference time-domain (FDTD) scheme [1] and a hybrid time-domain integral equation solver [2]. In this paper, we present an accurate and efficient algorithm to incorporate multiport lumped networks into a hybrid field-circuit solver based on the time-domain finite-element method (TDFEM) [3]. By casting its admittance matrix into the time-stepping equations, a lumped-network subsystem is formulated and then interfaced with the FEM subsystem through the FEM edges and the circuit subsystem through circuit nodes. The lumped-network port voltages are explicitly set to be the same as those computed from the FEM (or circuit) subsystem while its port currents are used as impressed current excitations along the associated FEM edges (or through the related circuit nodes). Finally, all the lumped-network port variables are eliminated to form a global system for only the FEM and circuit unknowns. The proposed algorithm provides a systematic and efficient scheme for incorporating lumped networks into the TDFEM analysis and thus significant extends the modeling capability and improves the simulation efficiency of the existing hybrid field-circuit solver.