Analysis and calibration techniques for superconducting resonators

TL;DR

This paper introduces a new in-situ calibration method for superconducting microwave resonators, enabling precise analysis of resonator responses and accurate extraction of physical parameters, validated through experiments on microstrip and coplanar-waveguide devices.

Contribution

It presents a novel cryogenic calibration technique and two analysis approaches for superconducting resonators, improving parameter extraction accuracy and enabling detailed response analysis.

Findings

Calibration accuracy within 1% of complex transmission amplitude

Kinetic inductance fraction determined with 2% accuracy

Effective analysis of coupled resonators without explicit circuit models

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.