Numerical determination of coaxial cable parameters in cryogenic environments for high-frequency active device noise modeling

This contribution presents an original mathematical method for numerically evaluating the noise parameters of a transmission line subject to an arbitrary thermal gradient. Compared with previous methods, this procedure permits to easily take into account possible variations of line parameters along the propagation direction due to very high thermal excursions. The principal application of the proposed method is coaxial cable modeling in noise figure measurement setups under cryogenic conditions: the connection cable or waveguide from the outside to the inside of the cryogenic vacuum chamber are subject to non-negligible thermal excursions. Under these conditions, significant de-embedding errors may arise if the cables are not correctly modeled, given the very low values of noise figure, which are commonly exhibited by in cryo-cooled devices. The behavior of transmission lines subject to thermal gradients is investigated through extensive 3D thermal and electromagnetic simulations. Simulated data are then input to a numerical algorithm for efficiently determining both scattering and noise parameters of coaxial cables actually used in a cryogenic probe station developed and realized in the facilities of the University of Rome Tor Vergata. A measurement campaign has been performed to validate the simulation-based approach. Subsequently, the numerical model has been used to de-embed the noise contribution of the coaxial cables from cryogenic NF50 measurements of a 70nm metamorphic high electron mobility transistor (mHEMT).