Numerical Dispersion of the ADI-FDTD Technique Including Lumped Models

The numerical dispersion characteristic of the extended ADI-FDTD algorithm including lumped models is systematically studied in this paper, and three common lumped models are investigated: resistor, capacitor and inductor, and their explicit, semi-implicit, and implicit temporal difference scheme are discussed. Theoretical results show that: (1) in the explicit and implicit case, the dispersion nature of a lumped resistor can be characterized by a series inductor and a series capacitor, respectively. (2) For capacitor, the dissipative nature of the explicit scheme can be replaced by a paralleling resistor. (3) If the semi-implicit or implicit scheme is applied to the lumped inductor, the dissipative inductor can be replaced by an equivalent circuit consisting of an inductor and a series resistor. Finally, a simple microstrip circuit including a lumped inductor is simulated to demonstrate the validity of the theoretical results.