An improved FDTD formulation for general linear lumped microwave circuits based on matrix theory

An improved finite-difference time-domain (FDTD) formulation using the matrix theory is presented to analyze hybrid general linear lumped and distribution microwave circuits. Traditionally, since discrete current expressions of lumped circuits should be substituted into Maxwell´s equations explicitly, the different discrete formulations of Maxwell´s equations should be reconstructed when different active circuits are used. It will be much more difficult when high-order linear lumped circuits are considered in a hybrid system. In our improved formulation, a high-order linear lumped circuit is expressed by a serials of first-order modified integral transforms. When their interior variables together with electric fields, port voltage, and port current/current density of active circuits are considered as a vector, a local implicit and iterative matrix expression can be built. Compared with the traditional method, since our improved FDTD formulation is implicit, it easily combines with other active circuits built by the matrix method and decreases the condition number, is more stable, flexible, and general. Based on this formulation, the numerical stability and condition number are discussed. Simulation shows that the results by our improved FDTD formulation are in good agreement with that from commercial software.