Coupled circuit-electromagnetic simulation with time domain integral equations

Time domain electromagnetic solvers are useful for simulating coupled circuit-electromagnetic (EM) problems involving integrated circuit packages and systems-on-chip, wherein effects of nonlinearities of circuit elements can be modeled accurately. The surface-based time domain integral equation (TDIE) approach has been gaining in popularity owing to its flexibility in modeling arbitrarily-shaped structures and its enhanced computational performance due to advances in fast solution methods. In this work, a generalized rigorous coupling scheme, to simultaneously simulate circuits with SPICE-like time-domain simulation, and EM interactions with a TDIE method, is presented. This approach enables direct solution of circuit-EM equations without the need for generating port models. The method permits both circuit and EM excitations and thereby has potential as a signal integrity and as an EMI/EMC modeling tool.