Methodologies for transient simulation of hybrid electromagnetic/circuit systems with multiple time scales

This work presents methodologies to facilitate the efficient cosimulation of electromagnetic/circuit systems while exploiting the multiple time scales that are often present in the numerical simulation of such systems. Three distinct approaches are presented to expedite such a simulation process, with the common theme that the methodologies should allow for the ability to utilize different timesteps in the simulation procedure for the different components appearing in a hybrid system.;The first contribution involves a direct representation of each of Maxwell's curl equations in terms of SPICE-equivalent circuit stamps. This provides for a full-wave, circuit-compatible description of a distributed structure that can very naturally be incorporated into a circuit simulation environment. This capability can be applied to circuit simulations of distributed structures, or it can facilitate the detailed simulation of an electrically small structure with full electromagnetic accuracy.;The second contribution allows for the utilization of different numerical integration schemes and timesteps in the simulation of hybrid structures via a domain decomposition approach. By introducing a novel scheme to combine finite-difference time-domain simulation with SPICE-like circuit simulation, it is shown that the timestep used in the lumped circuit portions need not be limited by the Courant-Friedrichs-Lewy (CFL) limit which governs the timestep used in distributed portions. Additionally, the use of the Crank-Nicolson integration scheme is investigated for the simulation of transmission line structures, and an efficient methodology is proposed by combining the Crank-Nicolson integration of transmission lines and standard integration of circuits.;Finally, the third contribution in this work involves efficient simulation of circuits involving multirate signals with widely separated time scales. An efficient representation of multirate signals is found by introducing a different time variable for each time scale in order to overcome the significant oversampling of such signals that arises from more traditional, univariate representations. This representation is then directly applied to the simulation of transmission line structures. It is found that the resulting methodologies provide for a significant speedup in the overall simulation time.