Non-uniform Time-Step FLOD-FDTD Method for Multiconductor Transmission Lines Including Lumped Elements

This paper presents a novel non-uniform time-step (NUTS) fundamental locally one-dimensional (FLOD) finite-difference time-domain (FDTD) method for multiconductor transmission lines (MTLs) including lumped elements. The NUTS scheme adopts different (non-uniform) time steps for different periods during simulation, in order to reduce the large errors caused by unconditionally stable FDTD methods with uniform time step larger than Courant-Friedrichs-Lewy limit. It is found that NUTS scheme is potentially unstable for alternating-direction-implicit (ADI) FDTD method, but it is stable for LOD-FDTD method or its implementation based on fundamental (FLOD) scheme. The NUTS FLOD-FDTD method is useful to simulate MTLs with lumped elements including resistor, capacitor, and inductor in series and parallel connections. Moreover, the method based on multiple 1-D approach is also extended to incorporate lumped elements in cross connection to model near-field coupling between the MTLs. While the electric current density is commonly used for field-circuit coupling of parallel connected lumped elements, the magnetic current density will be utilized for field-circuit coupling of series and cross-connected lumped elements. Numerical results for MTLs with lumped elements in series, parallel, and cross connections are provided to show the trade-off between efficiency and accuracy of the proposed NUTS FLOD-FDTD method. Compared with the FLOD-FDTD method with uniform time step, the NUTS FLOD-FDTD method may achieve higher accuracy by using smaller time step for certain periods of simulation.