Detuning and Saturation of Superconducting Devices: Formulation and Measurements*

Abstract- 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 YBa2Cu307, (YBCO) coplanar waveguide (CPW) resonator at 76 K and with simulations using harmonic balance. Index Terms- Detuning, HTS, nonlinear transmission line, saturation, superconductor, superconducting resonator. I