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We describe a circuit model for a flux-driven SQUID. This is useful fordeveloping insight into how these devices perform as active elements inparametric amplifiers. The key concept is that frequency mixing in aflux-pumped SQUID allows for the appearance of an effective negativeresistance. In the three-wave, degenerate case treated here, a negativeresistance appears only over a certain range of allowed input signal phase.This model readily lends itself to testable predictions of more complicatedcircuits.

The pumpistor: a linearized model of a flux-pumped SQUID for use as a negative-resistance parametric amplifier