Probabilistic Analysis of Tunability of Step-Edge Josephson Junction Arrays' Inductance in HTS Microwave Metamaterials

Josephson junction in superconductor circuits and metamaterials is modeled as a tunable inductance. The Josephson inductance is tunable by the bias current passing through it and can be tuned from an initial value to a very large value as much as one can push bias current near the critical current but not exceeding it. Tunability by bias current allows design of programmable metamaterials with flexible functions in microwave regime. In High-Temperature Superconductivity (HTS) tunable metamaterials, Josephson junctions should be used in series configuration to give usable tunable inductance. Each Step-Edge Josephson junction (SEJs) in HTS has a critical current that is dependent on its geometrical dimensions such as the width of the junction. In a practical fabrication process, the widths and critical currents will be distributed with a Gaussian Probability Distribution Function (PDF). This will decrease the tunability of the Josephson inductance of the array. We have calculated the tunability of an array with defined critical current distribution, in terms of probabilistic analysis.