Six-stage split-step FDTD method including lumped resistors and its stability analysis

Abstract

The stability of the six-stage split-step finite-difference time-domain (SS-FDTD) method including lumped resistors is studied. In particular, three different formulations for the lumped resistors are analyzed: the explicit, semi-implicit, and implicit schemes. Then, the numerical stability of the extended six-stage SS-FDTD method including lumped resistors is analyzed by combining the von Neumann method with the Jury criterion, and the results show that the proposed method is unconditionally stable in the semi-implicit and implicit schemes, whereas it is conditionally stable in the explicit scheme, which its stability is related to both the mesh size and values of the resistance. Finally, a simple microstrip circuit including a lumped resistor is simulated to demonstrate the validity of the theoretical results.