Harmonic Analysis for Finding the Optimum Working Point of High-Tc RF SQUID

High-Tc radio-frequency (RF) superconducting quantum interference devices (SQUIDs) are well understood and have been adequately expounded in theory, but in practice, it is not so easy to find the optimum working points for their low-noise operations. Starting from the basic equations describing the RF SQUID in nonhysteretic mode, a polynomial expression for its flux-to-voltage characteristic was deduced. For simplicity, the expansion was truncated to the first three harmonics in the flux quantum. The optimum working point is determined as the location of the maximum gradient of its transfer function. The analysis was compared with experimental flux-to-voltage characteristics of the RF SQUIDs with a step-edge junction, measured at 77 K for different settings of the readout electronics. Six typical kinds of the measured flux-to-voltage curves were fitted and analyzed with respect to their harmonics in the magnetic flux. The findings can be of referential value for automatically setting the working points of high-Tc RF SQUIDs in the practical applications.