The lumped network alternating direction implicit finite difference time domain (LN-ADI-FDTD) technique is proposed as an extension of the conventional ADI-FDTD method in this paper, which allows the lumped networks to be inserted into some ADI-FDTD cells. Based on the piecewise linear recursive convolution (PLRC) technique, the current expression of the loaded place can be obtained. Then, substituting the expression into the ADI-FDTD formulas, the difference equations including an arbitrary linear network are derived. For the sake of showing the validity of the proposed scheme, lumped networks are placed on the microstrip and the voltage across the road is computed by the lumped network finite difference time domain (LN-FDTD) method and LN-ADI-FDTD method, respectively. Moreover, the results are compared with those of obtained by using the circuital simulator ADS. The agreement among all the simulated results is achieved, and the extended ADI-FDTD method has been shown to overcome the Courant-Friedrichs-Lewy (CFL) condition.
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