Intercomparison of dielectric reference materials available for the calibration of an open-ended probe at different temperatures
Intercomparison of dielectric reference materials available for the calibration of an open-ended probe at different temperatures
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DOI：
10.1088/0957-0233/6/12/011
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发表时间：
1995-12-01
影响因子：
2.4
通讯作者：
Michelson, SC
中科院分区：
文献类型：
--
作者：
Evans, S;Michelson, SC
本文的前半部分展示了如何将最小二乘分析应用于双线性模型，该模型将用开放式探针观察到的未校正反射系数与探针孔径处介电材料的复介电常数联系起来。应选择大量参考材料，并从文献中不同精度的独立来源获得介电数据，并为双线性模型导出最佳拟合参数。然后就可以得到模型和参考数据之间的绝对残差‘和’：它们包含了数据、测量和模型中的误差。在论文的后半部分，用这种方法对17种不同材料的实验室测量结果进行了比较。频率范围从20 MHz到2 GHz，使用直径为7和22 mm的探针在+25℃和-20℃下比较残差。对于较小的探针，相对介电常数范围从1到80，对于任何100 MHz以上的材料，残余量很少超过+/-1 epsilon‘或epsilon’；对于较大的探头，残差在20兆赫以内是令人满意的，尽管不高达2兆赫。如果介电常数范围受到更多限制（这显然是模型的限制），则它们会显着减少；如果采用新的校准，而不是使用从+25℃测量确定的模型参数，则介电常数在-20℃时显着减少。
The first half of the paper shows how a least-squares analysis may be applied to a bilinear model relating the uncorrected reflection coefficients observed with an open-ended probe to the complex permittivities of dielectric materials at the probe aperture. A large number of reference materials should be chosen, with dielectric data available from independent sources of varying accuracy in the literature, and the best-fit parameters derived for the bilinear model. The absolute residuals in epsilon' and epsilon '' between the model and the reference data may then be obtained: they encompass errors in the data, in the measurements and in the model. Laboratory measurements on 17 different materials are intercompared in this way in the second half of the paper. The frequency range is from 20 MHz to 2 GHz and the residuals are compared at +25 degrees C and -20 degrees C using probe diameters of 7 and 22 mm. For the smaller probe and with a range of relative permittivities from 1 to 80, residuals rarely exceed +/-1 epsilon' or epsilon '' for any material from 100 MHz upwards; for the larger probe residuals are satisfactory down to 20 MHz though not up to 2 GHz. They are significantly reduced if the range of permittivities is more restricted (which is clearly a limitation of the model) and they are significantly reduced at -20 degrees C if a new calibration is adopted, rather than using the model parameters determined from measurements at +25 degrees C.