The impedance matrix of an arbitrary multiport array antenna with Ohmic losses was studied. It was assumed that the partial current distributions in the array, corresponding to the alternate exciting one of its terminals while the other ones are open-circuited, are known. Consideration of the power balance in the lossy array antenna has allowed ascertaining that its impedance matrix is a sum of the radiation resistance matrix and loss resistance matrix, which are in general case complex Hermitian matrices and only in some particular cases can be real. The theoretical statements obtained are confirmed by two numerical examples, where analysis of two lossy dipole arrays was performed. In the first example, the dipoles were located above the imperfect ground, which served as a source of losses, and in the second example, the same dipoles were located in free space, and the embedded parasitic element was the source of losses. The results of the analysis showed that the asymmetric placement of energy absorbers in the array antennas leads to the appearance of imaginary parts in the matrices of radiation and loss resistances, which allow one to correctly predict the behavior of the array radiation efficiency during beam scanning.

中文翻译：

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有损阵列天线中的互阻抗特性

研究了具有欧姆损耗的任意多端口阵列天线的阻抗矩阵。假设已知阵列中的部分电流分布，该分布对应于其一个端子的交替励磁而另一个端子开路。考虑到有损阵列天线中的功率平衡，可以确定其阻抗矩阵是辐射电阻矩阵和损耗电阻矩阵的总和，它们通常是复数的埃尔米特矩阵，并且仅在某些特定情况下才是真实的。通过两个数值示例证实了所获得的理论结论，其中对两个有损偶极阵列进行了分析。在第一个示例中，偶极子位于不完善地面上方，这是损耗的来源，而在第二个示例中，相同的偶极子位于自由空间中，而嵌入的寄生元件是损耗的来源。分析结果表明，能量吸收器在阵列天线中的不对称放置会导致在辐射矩阵和损耗电阻中出现虚部，从而使人们能够正确预测波束扫描过程中阵列辐射效率的行为。