Abstract
This paper presents a magnetically mixed Newmark-Leapfrog finite-difference time-domain (MNL-FDTD) method for efficient three-dimensional electromagnetic simulations of transient interactions between a spark channel of air-discharge electrostatic discharge (ESD) occurred at a short gap and its surrounding environment. The formulation is based on introducing the implicit Newmark-Beta method into the explicit leapfrog scheme of Yee's FDTD method directionally and magnetically. The stability condition of the algorithm does not include the mesh step in the channel direction, and therefore, is more relaxed than the Courant–Friedrichs–Lewy condition of the Yee scheme. For combined full-wave/circuit systems involving air-discharge ESD, both the sequential and simultaneous solutions are discussed in the context of MNL-FDTD. A stable direct linking of MNL-FDTD with SPICE is presented to include a discharge current characterized by arbitrary spark resistance. The relaxed stability is maintained in the combined systems. The presented method is verified with three spark resistance formulae. The accuracy, stability, and computational efficiency of the method are demonstrated in comparison with the conventional approaches in several numerical examples.
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