Input Impedance and Gain of a Gigahertz Amplifier Using a DC SQUID in a   Quarter Wave Resonator
  Due to their superior noise performance, SQUIDs are an attractive alternative to high electron mobility transistors for constructing ultra-low-noise microwave amplifiers for cryogenic use. We describe the use of a lumped element SQUID inductively coupled to a quarter wave resonator. The resonator acts as an impedance transformer and also makes it possible for the first time to accurately measure the input impedance and intrinsic microwave characteristics of the SQUID. We present a model for input impedance and gain, compare it to the measured scattering parameters, and describe how to use the model for the systematic design of low-noise microwave amplifiers with a wide range of performance characteristics. 
Lafe Spietz, Kent Irwin, and Jose Aumentado