In this work, a new lumped-network hybrid implicit-explicit finite-difference time-domain (LN-HIE-FDTD) method has been proposed. This method is derived from combining the 3D HIE-FDTD method with the Z-transform technique for the hybrid system including linear lumped networks. It possesses the advantage of deriving the updating equations immediately for complex circuits. The accuracy of the proposed method is verified from the comparison of calculated results given by the proposed method and the conventional lumped-network FDTD (LN-FDTD) method. The efficiency of the proposed method is verified from the comparison of the CPU time by the two methods. It is demonstrated that the proposed method is numerically efficient while time-saving. IntroductionThe finite-difference time-domain (FDTD) method has been widely applied in solving problems related to electromagnetism [1][2][3][4][5][6][7][8][9]. With the miniaturization of the hybrid microwave circuits, especially for thin-film structures [10,11], the thickness of the structures decreases to the micron level. It would be difficult for the conventional FDTD to analyze these problems for the time-step size is strictly limited by the stability condition. The small time-step size will significantly call for more calculating time and computational resources when the analysis object has fine scale dimensions compared with wavelength.To cope with this problem, the hybrid implicit-explicit FDTD algorithm (HIE-FDTD) has been proposed [12,13]. In the HIE-FDTD method, the maximum time-step size of the HIE-FDTD method is not strictly limited by the minimum space size. Thus, the stability condition is weaker than that of the conventional FDTD.Recently, the HIE-FDTD method has been used to calculate the hybrid system with lumped elements (LE-HIE-FDTD) and conductive media [14,15]. However, the LE-HIE-FDTD method is not good at calculating networks consisting of the arbitrary connection of several lumped elements [16]. In [14], a large number of schemes are needed to simulate the lumped network with multiple lumped elements. The Z-transform technique has been introduced to deal with this problem in the conventional FDTD method. In [17,18], the bilinear Z-transform is used to derive the transform, but its computational cost is higher because of the increased complexity. In [19], the direct Z-transform is used to deal with lumped loads,

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In this paper, the transmission line method (TLM) is applied to calculate the shielding effectiveness (SE) of a metallic enclosure with apertures. The cases of high-order modes and 2layer shield model are considered. The resonant frequency of the enclosure with installation of PCB is predicted by the perturbation method. Conclusions are drawn that the SE can be quickly calculated by the TLM and the SE of aperture array is higher than single one's. It is also worth noticing that a 2-layer enclosure is capable to improve the SE significantly. Also, Good agreement of the resonant frequency is obtained between simulated result by CST and calculated result by the perturbation method.

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