Propagation constant versus frequency curves are obtained after processing S-parameters measured to several lines differing only in length. The proposed method can be easily implemented once the thru-reflect-line (TRL) eigenvalues are calculated considering different combination of line pairs. The noticeable simplicity of the approach when compared to the original multiline algorithm makes it an attractive alternative to improve the determination of the complex propagation constant in practical applications by using experimental data collected to more than two lines. Here, applicability is demonstrated up to 110 GHz for printed circuit board (PCB) microstrip lines. Furthermore, it is provided an improved equation to determine the effective relative permittivity once the complex propagation constant is determined.

中文翻译：

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多线测量确定传播常数的差分法


在处理对仅长度不同的几条线测量的 S 参数后，获得传播常数与频率的关系曲线。一旦考虑不同的线对组合计算直通反射线（TRL）特征值，所提出的方法就可以很容易地实现。与原始多线算法相比，该方法明显简单，使其成为一种有吸引力的替代方案，可以通过使用收集到两条以上线路的实验数据来改进实际应用中复杂传播常数的确定。这里展示了高达 110 GHz 的印刷电路板 (PCB) 微带线的适用性。此外，提供了一种改进的方程，用于在确定复数传播常数后确定有效相对介电常数。