We propose a new technique in this letter to design a $4 \times 8$ Butler matrix (BM) using a four-port network and variable phase shifters. This method helps the proposed BM to produce arbitrary output amplitudes for beam steering applications. It also contributes to reducing the size of its configuration. In addition to the two mentioned advantages, we can develop a $4\times 4$ BM, which generates unequal amplitudes. For validation, a single-layer $4\times 8$ BM with −21-dB Chebyshev distribution was designed and manufactured. We also used the high-frequency simulation structure (HFSS) software to simulate the proposed feed network and observed a good agreement between the simulation and measurement results.

中文翻译：

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4x 8 Butler 矩阵中任意幅值分布生成的新方法

我们在这封信中提出了一种新技术来设计一个 $4 \times 8$ 巴特勒矩阵 (BM) 使用四端口网络和可变移相器。这种方法有助于所提出的 BM 为波束控制应用产生任意输出幅度。它还有助于减小其配置的大小。除了上面提到的两个优点，我们还可以开发一个 $4\乘以4$ BM，产生不等的振幅。为了验证，单层 $4\乘以8$ 设计和制造了具有 -21-dB Chebyshev 分布的 BM。我们还使用高频仿真结构 (HFSS) 软件来仿真所提出的馈电网络，并观察到仿真和测量结果之间的良好一致性。