  One of the central challenges in the development of parametric amplifiers is
the control of the dynamic range relative to its gain and bandwidth, which
typically limits quantum limited amplification to signals which contain only a
few photons per inverse bandwidth. Here, we discuss the control of the dynamic
range of Josephson parametric amplifiers by using Josephson junction arrays. We
discuss gain, bandwidth, noise, and dynamic range properties of both a
transmission line and a lumped element based parametric amplifier. Based on
these investigations we derive useful design criteria, which may find broad
application in the development of practical parametric amplifiers.
