Cryogenic On-chip In Situ S-parameter Calibration using Superconducting Coplanar Waveguides

Published

July 16, 2025

Author(s)

Jeremy Thomas, Johannes Hoffmann, Nathan Flowers-Jacobs, Anna Fox, Nicholas Jungwirth, Raegan Johnson, Paul Dresselhaus, Samuel Benz

Abstract

This article presents a new multiimpedance-state line (MISL) in situ scattering parameter (S-parameter) calibration technique using on-chip superconducting transmission lines at 4 K that enables cryogenic calibration in a fixed signal path without the need for cryogenic switches or a cryogenic probe station. The method uses coplanar waveguide (CPW) models based on various impedance states of niobium (Nb), which has zero dc resistance below 9 K and a monotonically increasing resistance from 10 K to room temperature. The different impedance states are accessed by heating the 4 K stage of a cryostat and injecting up to 245 mA of current into the line. Using these states, we solve for the unknowns in an eight-term error model through a least-squares analysis. We first validate the MISL calibration technique by comparing it with short-open-load-reciprocal (SOLR) calibrated measurements in a cryogenic probe station, finding transmission agreement within 0.2 dB and uncertainty overlap for nearly all frequencies up to 26.5 GHz. We then apply the method to calibrate Nb CPWs with and without embedded Josephson junctions (JJs), using a fixed wire bonded connection, and without the use of cryogenic switches or movable probes. Strong agreement with the CPW models is demonstrated, with uncertainty overlap and differences below 0.1 dB up to 4.6 GHz without JJs and up to 2.4 GHz with JJs; resonances cause interruptions beyond these frequencies.

Citation

IEEE Transactions on Microwave Theory and Techniques

Volume

73

Issue

11

Pub Type

Journals

Download Paper

https://doi.org/10.1109/TMTT.2025.3585803

Local Download

Keywords

Superconducting circuits, cryogenic calibration, microwave metrology, S-parameters, Josephson junctions

Citation

Thomas, J. , Hoffmann, J. , Flowers-Jacobs, N. , Fox, A. , Jungwirth, N. , Johnson, R. , Dresselhaus, P. and Benz, S. (2025), Cryogenic On-chip In Situ S-parameter Calibration using Superconducting Coplanar Waveguides, IEEE Transactions on Microwave Theory and Techniques, [online], https://doi.org/10.1109/TMTT.2025.3585803, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=958908 (Accessed February 18, 2026)