volume | PIER Journals

Abstract

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.

1. Taflove, A. and S. C. Hagness, "Computational Electrodynamics: The Finite-difference Time-domain Method," Artech House, Boston, MA, 2000.

2. Namiki, T., "A New FDTD algorithm based on alternating-direction implicit method," IEEE Trans. on Microw. Theory and Tech., Vol. 47, No. 10, 2003-2007, Oct. 1999.
doi:10.1109/22.795075

3. Zheng, F., Z. Chen, and J. Zhang, "Toward the development of a three-dimensional unconditionally stable finite-difference time-domain method," IEEE Trans. on Microw. Theory and Tech., Vol. 48, No. 9, 1550-1558, Sep. 2000.
doi:10.1109/22.868993

4. Pereda, J. A., F. Alimenti, P. Mezzanotte, L. Roselli, and R. Sorrentino, "A new algorithm for the incorporation of arbitrary linear lumped networks into FDTD simulators," IEEE Trans. on Microw. Theory and Tech., Vol. 47, No. 6, 943-949, Jun. 1999.
doi:10.1109/22.769330

5. Pereda, J. A., A. Vegas, and A. Prieto, "Study on the stability and numerical dispersion of the FDTD technique including lumped inductors," IEEE Trans. on Microw. Theory and Tech., Vol. 52, No. 3, 1052-1058, Mar. 2004.
doi:10.1109/TMTT.2004.823589

6. Kelly, D. F. and R. J. Luebbers, "Piecewise linear recursive convolution dispersive media using FDTD," IEEE Trans. on Antennas and Propag., Vol. 44, No. 6, 792-797, Jun. 1996.
doi:10.1109/8.509882

7. Lee, J. Y., J. H. Lee, and H. K. Jung, "Linear lumped loads in the FDTD method using piecewise linear recursive convolution method," IEEE Microwave Wireless Compon. Lett., Vol. 16, No. 4, 158-160, Apr. 2006.
doi:10.1109/LMWC.2006.872148

8. Chen, Z. H. and Q. X. Chu, "FDTD modeling of arbitrary linear lumped networks using piecewise linear recursive convolution technique," Progress In Electromagnetics Research, Vol. 73, 327-341, 2007.
doi:10.2528/PIER07042002

9. Abd EI-Raouf, H. E., W. Yu, and R. Mittra, "Application of the Z-transform technique to modeling linear lumped loads in the FDTD," Proc. Inst. Elect. Eng. | Microw. Antennas Propag., Vol. 151, No. 1, 67-70, Feb. 2004.
doi:10.1109/TMTT.2006.877058

10. Gonzalez, O., J. A. Pereda, A. Herrera, and A. vegas, "An extension of the lumped-network FDTD method to linear two-port lumped circuits," IEEE Trans. on Microw. Theory and Tech., Vol. 54, No. 7, 3045-3051, Jul. 2006.
doi:10.1109/TAP.2009.2021907

11. Gonzalez, O., A. Grande, J. A. Pereda, and A. vegas, "A study on the stability and numerical dispersion of the lumped-network FDTD method," IEEE Trans. on Antennas and Propag., Vol. 57, No. 7, 2023-2033, Jul. 2009.
doi:10.1080/09205071.2013.756375

12. Cui, Y. L., B. Chen, and Y. F. Mao, "Application of the Z-transform technique to modeling the linear lumped networks in the HIE-FDTD method," Journal of Electromagnetic Waves and Application, Vol. 27, No. 4, 529-538, 2013.
doi:10.1049/el:20060991

13. Fu, W. and E. L. Tan, "ADI-FDTD method including linear lumped networks," Electronics Letters, Vol. 42, No. 13, 728-729, Jun. 2006.

Dr. Fen Xia

Prof. Qing-Xin Chu

Dr. Yong-Dan Kong

Dr. Zhi-Yong Kang