Stability of the extended 3-D LOD-FDTD including lumped elements

Stability of the extended three-dimensional locally one-dimensional finite difference time domain (LOD-FDTD) including lumped elements is analyzed in this paper, and three common elements are investigated: resistor, capacitor, and inductor. The elements are inserted into the LOD-FDTD in the explicit, semi-implicit and implicit schemes. Stability analysis shows that the extended LOD-FDTD methods are unconditionally stable in the semi-implicit and implicit schemes, whereas, it is conditionally stable in the explicit scheme, and its stability criterion depends on both the values of the element and the mesh sizes. Finally, a simple microstrip circuit including an inductor is simulated in the extended LOD-FDTD to demonstrate the validity of the stability analysis.