Detuning and Saturation of Superconducting Devices: Formulation and Measurements

Saturation and detuning of high temperature superconducting (HTS) resonators and filters may occur due to the inherent nonlinear properties of the superconductor. In HTS transmission lines, these nonlinear properties introduce a dependence of the inductance and resistance per unit length on the current through the line and, if the line forms a resonator, this current dependence provokes changes in quality factor and/or resonant frequency with incident power. This paper derives equations for the dependence of the quality factor and resonant frequency of a nonlinear transmission line vs. source power and relates it to the circuit parameters of a nonlinear transmission line. The equations are verified with measurements in a 3.3 GHz YBa₂Cu₃O_7-x (YBCO) coplanar waveguide (CPW) resonator at 76 K and with simulations using harmonic balance.