title: Analysis and calibration techniques for superconducting resonators.
abstract: 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.
authors: NASA Goddard Space Flight Center, Greenbelt, Maryland 20771, USA.
authors: Giuseppe
authors: G
authors: Cataldo
authors: NASA Goddard Space Flight Center, Greenbelt, Maryland 20771, USA.
authors: Edward J
authors: EJ
authors: Wollack
authors: NASA Goddard Space Flight Center, Greenbelt, Maryland 20771, USA.
authors: Emily M
authors: EM
authors: Barrentine
authors: NASA Goddard Space Flight Center, Greenbelt, Maryland 20771, USA.
authors: Ari D
authors: AD
authors: Brown
authors: NASA Goddard Space Flight Center, Greenbelt, Maryland 20771, USA.
authors: S Harvey
authors: SH
authors: Moseley
authors: NASA Goddard Space Flight Center, Greenbelt, Maryland 20771, USA.
authors: Kongpop
authors: K
authors: U-Yen