Improved FDTD formulation for high-order linear circuit based on matrix theory and modified integral transform

An improved finite-difference time-domain formulation using matrix theory and a modified integral transform is presented to address hybrid high-order linear lumped circuit and passive circuit problems. In the traditional hybrid FDTD method, a lumped circuit should be expressed firstly as an equation of current and voltage, and then this equation is discretised explicitly and substituted into Maxwell´s equations. In many cases, this equation cannot be derived and discretised easily. In the improved FDTD formulation, it is possible to analyse a passive circuit integrated with a general linear lumped circuit expressed as not only one equation but also as a set of equations according to Kirchhoff´s laws. When electromagnetic fields, current/current density and interior variables of a set of equations are defined as separated vector elements, a local iterative matrix expression connecting with each active circuit can be built. In order to make this formulation stable, a modified integral transform is given to improve the condition number of the matrix. Simulation shows that results from the improved FDTD formulation can effectively treat high-order linear lumped circuit expressed by a set of equations as well as by one equation.