In this article, three frequency independent optical paths are designed and analyzed. A two-parabolic-mirror system and a four-parabolic-mirror system are studied and developed over 140–220 GHz to achieve precision complex permittivity measurements of a dielectric substrate. To achieve a wide plane wave zone for the center of the four-parabolic-mirror system, two 80-mm-length corrugated horns are designed and fabricated for the measurement systems. The Gaussicity of the corrugated horn is larger than 97.4%. For the multiple reflection model and direct wave model, two closed-form expressions of loss tangent are derived from the transmission parameters (insertion losses) of the measurement systems. Meanwhile, the resolution and uncertainty of loss tangent can be calculated according to the working frequency, the thickness of the wafer, the real part of the relative permittivity, and the $| {{S_{21}}} |$ measurement uncertainty. The complex permittivity of the Rogers/Duroid series PCB substrates, which are commonly used at microwave frequencies, and silicon wafers are measured in G-band.

中文翻译：

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亚太赫兹范围内介电基板的复介电常数测量

本文设计并分析了三种频率无关的光路。研究和开发了一个两抛物面镜系统和一个四抛物面镜系统，频率超过 140–220 GHz，以实现介电基板的精密复介电常数测量。为了实现四抛物面反射镜系统中心的宽平面波区，为测量系统设计并制造了两个 80 毫米长的波纹喇叭。波纹喇叭的高斯度大于97.4%。对于多次反射模型和直接波模型，从测量系统的传输参数（插入损耗）导出了损耗角正切的两个闭合表达式。同时，可以根据工作频率、晶圆厚度、相对介电常数的实部，以及 $| {{S_{21}}} |$ 测量不确定度。微波频率常用的Rogers/Duroid系列PCB基板和硅片的复介电常数在G波段测量。