多线直通-反射-传输线校准中的线长选择
The Choice of Line Lengths in Multiline Thru-Reflect-Line Calibration
AI总结：
本文通过非线性约束优化特征值问题，提出确定多线TRL校准中最优线长的严格方法，并给出基于稀疏标尺的近似选择方案，实验验证了该方法在高达150 GHz频率下能更均匀地分配校准不确定度。
摘要：
本文对矢量网络分析仪（VNA）多线直通-反射-传输线（TRL）校准中确定线标准最优长度的问题进行了分析和严格推导。通过多线TRL校准中特征值问题的非线性约束优化得到解。此外，我们提出了一种基于预定义稀疏标尺的近似最优长度选择简化方法。在线长计算的同时，我们讨论了满足带宽要求所需的线数。通过对不同材料和叠层的印刷电路板上的多个多线TRL校准套件进行测量，覆盖高达150 GHz的频率，验证了所提出的方法。基于阻抗标准基板测量导出的误差盒的测量蒙特卡罗不确定度分析表明，与商业校准套件相比，所提出的线长在校准不确定度上更均匀地分布在各线之间。针对各种应用提供了实际示例，包括有损和色散线，以及波导的分段解。
英文摘要：
This paper presents an analysis and rigorous procedure for determining the optimal lengths of line standards in multiline thru-reflect-line (TRL) calibration of vector network analyzers (VNAs). The solution is obtained through nonlinear constrained optimization of the eigenvalue problem in multiline TRL calibration. Additionally, we propose a simplified approach for near-optimal length selection based on predefined sparse rulers. Alongside the length calculation, we discuss the required number of lines to meet bandwidth requirements. The proposed methods are validated through measurements of multiple multiline TRL calibration kits on printed circuit boards of different materials and stackups, covering frequencies up to 150 GHz. A measurement-based Monte Carlo uncertainty analysis, using error boxes derived from impedance standard substrate measurements, demonstrates that the proposed line lengths distribute calibration uncertainty more evenly across lines compared to a commercial calibration kit. Practical examples are provided for various applications, including lossy and dispersive lines, as well as banded solutions for waveguides.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
