Abstract
The stability of the four-step alternating direction implicit finite-difference time-domain (ADI-FDTD) method including lumped elements is studied. Three common lumped elements are investigated: resistor, capacitor and inductor, and three different formulations for each element are analyzed: the explicit, semi-implicit, and implicit schemes. Analysis 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 element. Finally, a simple microstrip circuit including a lumped resistor is simulated to demonstrate the validity of the theoretical results.
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