Thermo-Mechanical EM Models for Broadband Cryogenic VNA Calibration Including Numerical Uncertainties Down to 4.2 K

Increasing demand for cryogenic electronics aimed at quantum sensors and computing technologies asks for accurate and quantifiable calibration methods and techniques. In this work, we present a structured approach to generate the nominal RF responses of standard artifacts, enabling wideband vector network analyzer (VNA) calibration algorithms, i.e., short, open, load, and reciprocal (SOLR), at cryogenic temperatures. Moreover, we present an EM simulation strategy to generate the perturbations in the artifacts’ responses based on mechanical fabrication tolerances and calculate an equivalent RF response uncertainty. Both the nominal and perturbed standard responses are computed at (user defined) cryogenic temperatures, by combining thermo-mechanical responses with the electromagnetic solver. A circuit simulator-based measurement model (MM) is used to compute the uncertainties of the cryogenic setups used in this work. Error contributions arising from the propagation of VNA noise, switch nonidealities, calibration artifacts uncertainties, temperature fluctuations, and temperature gradient over the interconnects are included in the MM. For validation, measured results of a coaxial air transmission line at 77 K and 4.2 K are presented and compared with 3-D EM simulation predictions. Finally, the measurement uncertainties are detailed in a budget analysis describing the individual contributions.