In this work, we present a comprehensive analysis of port impedance effects on a signal coupled across two-port networks, derive an equation to evaluate the impedances for a specified coupling, and demonstrate two beam-shaping active array antenna prototypes to validate the theory. In this context, the generalized S-parameters are theoretically studied and verified through an example. Subsequently, a closed-form equation is derived to accurately evaluate the port impedances that enable the achievement of a desired magnitude and phase of the signal coupling across the two-port network. The meaningfulness of all the potential results and the additional capabilities of derived equations are then discussed. With this understanding, a general modeling procedure is formulated to achieve the simultaneous amplification and phase shifting only through the active devices, without resorting to any additional passive circuitry. As a proof of concept, two $1 \times 5$ active array antenna prototypes are developed and fabricated at 5 GHz: one for broadside radiation with a sidelobe level of less than −20 dB requirement, and the other for flat-top radiation beam between −10° and 30°. They are integrated with a $1 \times 5$ Wilkinson power divider that is designed for radiation pattern measurements, and the corresponding results agree reasonably well with the simulated counterparts and theory, thereby proving the developed concept. Such solutions demonstrate the inherent advantages of being low-loss, compact, and efficient, which are essential for the next generation of wireless systems.

中文翻译：

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端口阻抗对两端口网络的分析和影响及其在有源阵列天线开发中的应用

在这项工作中，我们对端口阻抗对跨两个端口网络耦合的信号的影响进行了全面分析，推导了一个方程式以评估指定耦合的阻抗，并演示了两个波束成形有源阵列天线原型以验证该理论。在这种情况下，通过实例对广义S参数进行了理论研究和验证。随后，导出一个封闭形式的方程式，以准确评估端口阻抗，从而实现跨两个端口网络的信号耦合的所需幅度和相位。然后讨论了所有潜在结果的意义以及派生方程的其他功能。有了这种认识，制定了通用建模程序，以仅通过有源器件实现同时放大和相移，而无需借助任何其他无源电路。作为概念证明，两个 1美元/次5美元 有源阵列天线原型是在5 GHz频率下开发和制造的：一种用于旁瓣电平低于-20 dB要求的宽边辐射，另一种用于-10°至30°之间的平顶辐射束。它们与 1美元/次5美元 专为辐射方向图测量而设计的Wilkinson功率分配器，其相应的结果与模拟的对应物和理论相当吻合，从而证明了所开发的概念。这样的解决方案展现出低损耗，紧凑和高效的内在优势，这对于下一代无线系统至关重要。