Design and characterization of a superconducting nonlinear reference device

We describe the design, fabrication, and testing of a superconducting passive nonlinear reference device that has a calculable phase relationship between the fundamental RF drive signal and resulting higher order harmonic components. We show this passive device to be a useful standard for verifying the phase calibration of nonlinear vector network analyzers, as the magnitude and phase of the third-order product are found directly from independent measurements of the field-dependent surface impedance. Microwave power-dependent measurements of coplanar waveguide (CPW) resonators fabricated from thin film high-T_c superconductor materials yield the transmission line resistance and inductance per unit length as a function of rf current. With these values and the line geometry we computed both the nonlinear surface impedance of the material and the phase and magnitude of the third-order product of a traveling wave in a quasi-linear transmission line. To demonstrate our CPW reference device, we measured both the magnitude and the phase of third-harmonic components generated in a number of 133 mm long meander transmission lines using a commercial nonlinear vector network analyzer. We demonstrate agreement to within 10 degrees between the measured and the predicted phase for third-harmonic signals relative to the fundamental.