The 2x-thru calibration often faces the problem that, at the highest measurement frequency f _max , the calibrated results exhibit spurious ripples or spikes that are clearly unphysical, such as violating passivity. Although being a common phenomenon, it has attracted little attention in the literature. In this article, the cause of this problem is identified, and a solution is proposed, which is to pre-extrapolate the S -parameters before carrying out the 2x-thru algorithm. Meanwhile, a novel extrapolation method, called the Sun–Earth–Moon (SEM) fitting, is proposed, which is shown to be able to provide a smooth extension of S -parameters for several GHz beyond f _max . The effectiveness of SEM extrapolation in reducing the spurious response at f _max is demonstrated by simulation and measurement examples. The results also indicate that with extrapolation, the calibration accuracy can be slightly improved even at lower frequencies. Comparison with three commercial 2x-thru tools reveals that the near- f _max problem shows up also in the industry-standard tools, indicating the potential of the proposed method for advancing the state-of-the-art.

中文翻译：

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用于提高 2x-thru 校准中近 f max 精度的 S 参数外推


2x-thru 校准经常面临这样的问题：在最高测量频率 f max 下，校准结果会出现明显不符合物理性质的寄生纹波或尖峰，例如违反无源性。尽管这是一种常见现象，但它在文献中却很少引起注意。在这篇文章中，找出了这个问题的原因，并提出了一个解决方案，即在执行 2x-thru 算法之前预先外推 S 参数。同时，提出了一种称为日地月（SEM）拟合的新型外推方法，该方法被证明能够在 f max 之外的几个 GHz 范围内提供 S 参数的平滑扩展。仿真和测量示例证明了 SEM 外推法在减少 f max 时的杂散响应方面的有效性。结果还表明，通过外推，即使在较低频率下，校准精度也可以略有提高。与三种商业 2x-thru 工具的比较表明，近 f max 问题也出现在行业标准工具中，表明所提出的方法具有推进最先进技术的潜力。