Cataldo Giuseppe, Wollack Edward J, Barrentine Emily M, Brown Ari D, Moseley S Harvey, U-Yen Kongpop
NASA Goddard Space Flight Center, Greenbelt, Maryland 20771, USA.
Rev Sci Instrum. 2015 Jan;86(1):013103. doi: 10.1063/1.4904972.
A method is proposed and experimentally explored for in-situ calibration of complex transmission data for superconducting microwave resonators. This cryogenic calibration method accounts for the instrumental transmission response between the vector network analyzer reference plane and the device calibration plane. Once calibrated, the observed resonator response is analyzed in detail by two approaches. The first, a phenomenological model based on physically realizable rational functions, enables the extraction of multiple resonance frequencies and widths for coupled resonators without explicit specification of the circuit network. In the second, an ABCD-matrix representation for the distributed transmission line circuit is used to model the observed response from the characteristic impedance and propagation constant. When used in conjunction with electromagnetic simulations, the kinetic inductance fraction can be determined with this method with an accuracy of 2%. Datasets for superconducting microstrip and coplanar-waveguide resonator devices were investigated and a recovery within 1% of the observed complex transmission amplitude was achieved with both analysis approaches. The experimental configuration used in microwave characterization of the devices and self-consistent constraints for the electromagnetic constitutive relations for parameter extraction are also presented.
提出了一种用于超导微波谐振器复杂传输数据原位校准的方法，并进行了实验探索。这种低温校准方法考虑了矢量网络分析仪参考平面与器件校准平面之间的仪器传输响应。校准后，通过两种方法对观察到的谐振器响应进行详细分析。第一种方法是基于物理上可实现的有理函数的唯象模型，无需明确指定电路网络，就能提取耦合谐振器的多个谐振频率和宽度。第二种方法是使用分布式传输线电路的ABCD矩阵表示来根据特性阻抗和传播常数对观察到的响应进行建模。当与电磁模拟结合使用时，用这种方法可以确定动态电感分数，精度为2%。对超导微带和共面波导谐振器器件的数据集进行了研究，两种分析方法都实现了观察到的复传输幅度在1%以内的恢复。还介绍了在器件微波表征中使用的实验配置以及用于参数提取的电磁本构关系的自洽约束。
