Abstract
Generally, with a surface magnetic current excitation, only the $\mathrm {TM}_{\mathrm {zmn}}$ modes are activated between the power/ground plate pair. As a result, the magnetic field only has azimuthal component while the longitude component is zero. To make full use of this quasi-2-D (Q-2D) property, a Q-2D finite-element time-domain (FETD) method combined with the basic 3-D triangular prism mesh elements is firstly proposed to solve the magnetic field wave equation. It is further noted that the higher order modes are confined in the proximity of the antipads (labeled as via domain) due to the exponential attenuation property along the propagating direction. Therefore, in the region sufficiently far from the antipad (marked as plate-pair domain), only the fundamental mode needs to be considered. In this way, a Q-2D FETD analysis is required in the via domain while in the plate-pair domain, only a 2-D FETD solver is needed. As a result, the proposed algorithm is actually a hybrid 2-D and Q-2D FETD method. Besides, to handle arbitrarily shaped antipads, the wave-port excitation is implemented, and the corresponding mode-based S-parameter extraction methodology is developed according to the orthogonal property of different eigenmodes. The efficiency, accuracy, and generality of the proposed approach are verified by several representative examples.
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