A characteristic mode (CM) method that relies on a global multi-trace formulation (MTF) of surface integral equations is proposed to compute the modes and the resonance frequencies of microstrip patch antennas with finite dielectric substrates and ground planes. Compared to the coupled formulation of electric field and Poggio-Miller-Chang-Harrington-Wu-Tsai integral equations, global MTF allows for more direct implementation of a sub-structure CM method. This is achieved by representing the coupling of the electromagnetic fields on the substrate and ground plane in the form of a numerical Green function matrix, which yields a more compact generalized eigenvalue equation. The resulting sub-structure CM method avoids the cumbersome computation of the multilayered medium Green function (unlike the CM methods that rely on mixed-potential integral equations) and the volumetric discretization of the substrate (unlike the CM methods that rely on volume-surface integral equations), and numerical results show that it is a reliable and accurate approach to predicting the modal behavior of electromagnetic fields on practical microstrip antennas.

翻译：提出了一种基于曲面积分方程全局多迹公式的特征模方法，用于计算具有有限介质基板和接地板的微带贴片天线的模式与谐振频率。相较于电场积分方程与Poggio-Miller-Chang-Harrington-Wu-Tsai积分方程的耦合公式，全局多迹公式能够更直接地实现子结构特征模方法。该方法通过将基板与接地板上的电磁场耦合表示为数值格林函数矩阵的形式，从而得到更紧凑的广义特征值方程。由此建立的子结构特征模方法避免了多层介质格林函数的繁琐计算（不同于依赖混合势积分方程的特征模方法）以及基板的体积离散化（不同于依赖体积-表面积分方程的特征模方法）。数值结果表明，该方法能够可靠且准确地预测实际微带天线电磁场的模式行为。