Recently, a circuits-based approach for modeling the mutual coupling of reconfigurable surfaces, which comprise sub-wavelength spaced passive scattering elements coupled with electronic circuits for enabling the reconfiguration of the surface, has been introduced. The approach is based on a finite-length discrete dipole representation of a reconfigurable surface, and on the assumption that the current distribution on each thin wire dipole is a sinusoidal function. Under these assumptions, the voltages at the ports of a multi-antenna receiver can be formulated in terms of the voltage generators at a multi-antenna transmitter through a transfer function matrix that explicitly depends on the mutual coupling and the tuning circuits through the mutual impedances between every pair of thin wire dipoles. In currently available works, the mutual impedances are formulated in an integral form. In this paper, we show that they can be formulated in a closed-form expression in terms of exponential integral functions.

翻译：最近，一种基于电路的建模方法被提出，用于描述可重构表面的互耦效应。该表面由亚波长间距的无源散射单元与电子电路耦合而成，以实现表面重构。该方法基于可重构表面的有限长离散偶极子表示，并假设每个细线偶极子上的电流分布呈正弦函数形式。在这些假设下，多天线接收机端口处的电压可通过传输矩阵用多天线发射机的电压源表示，该传输矩阵显式依赖于互耦及调谐电路，其具体形式由每对细线偶极子间的互阻抗决定。现有文献中，互阻抗通常以积分形式表述。本文证明，互阻抗可化为以指数积分函数表示的闭式表达式。