We describe a circuit model for a flux-driven SQUID. This is useful for developing insight into how these devices perform as active elements in parametric amplifiers. The key concept is that frequency mixing in a flux-pumped SQUID allows for the appearance of an effective negative resistance. In the three-wave, degenerate case treated here, a negative resistance appears only over a certain range of allowed input signal phase. This model readily lends itself to testable predictions of more complicated circuits.
@article{arxiv.1305.7051,
title = {The pumpistor: a linearized model of a flux-pumped SQUID for use as a negative-resistance parametric amplifier},
author = {K. M. Sundqvist and S. Kintaş and M. Simoen and P. Krantz and M. Sandberg and C. M. Wilson and P. Delsing},
journal= {arXiv preprint arXiv:1305.7051},
year = {2015}
}