Developments of fundamental locally one-dimensional finite-difference time-domain methods for transmission lines and lumped elements

Abstract

This thesis presents the developments of fundamental locally one-dimensional finitedifference time-domain (FLOD-FDTD) methods for transmission lines and lumped elements. Unlike explicit FDTD method, the FLOD-FDTD method can use time step larger than Courant-Friedrichs-Lewy (CFL) limit. It also achieves higher efficiency and simplicity with matrix-operator-free right-hand sides (RHS) compared with the conventional LOD-FDTD method. The updating equations of the FLOD-FDTD method incorporating resistors, inductors and capacitors are derived. In addition to the three commonly used lumped elements, explicit FDTD method and FLOD-FDTD method incorporated with memristor are also developed. Memristor is regarded as the fourth lumped element which links charge and flux. The update equations are derived based on Maxwell's equations and the physical model given by Hewlett-Packard (HP) lab. Numerical examples including transmission lines and various lumped elements are provided to show the trade-off between efficiency and accuracy of the proposed 3-D FLOD-FDTD method.