  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.
