Modeling and Simulation of a Microstrip-SQUID Amplifier
  Using a simple lumped-circuit model, we numerically study the dependence of the voltage gain and noise on the amplifier's parameters. Linear, quasi-linear, and nonlinear regimes are studied. We have shown that the voltage gain of the amplifier cannot exceed a characteristic critical value, which decreases with the increase of the input power. We have also shown that the spectrum of the voltage gain depends significantly on the level of the Johnson noise generated by the SQUID resistors. 
G.P. Berman, O.O. Chumak, D.I. Kamenev, D. Kinion, and V.I.   Tsifrinovich
cond-mat.supr-con quant-ph