The numerical stability of the extended alternating-direction-implicit-finite-difference-time-domain （ADI-FDTD） method including lumped models is analyzed. Three common lumped models are investigated： resistor, capacitor, and inductor, and three different formulations for each model are analyzed： the explicit, semi-implicit and implicit schemes. Analysis results show that the extended ADI-FDTD algorithm is not unconditionally stable in the explicit scheme case, and the stability criterion depends on the value of lumped models, but in the semi-implicit and implicit cases, the algorithm is stable. Finally, two simple microstrip circuits including lumped elements are simulated to demonstrate validity of the theoretical results.
