  The advent of ultra-low noise microwave amplifiers revolutionized several
research fields demanding quantum-limited technologies. Exploiting a
theoretical bimodal description of a linear phase-preserving amplifier, in this
contribution we analyze some of the intrinsic properties of a model
architecture (i.e., an rf-SQUID based Josephson Traveling Wave Parametric
Amplifier) in terms of amplification and noise generation for key case study
input states (Fock and coherents). Furthermore, we present an analysis of the
output signals generated by the parametric amplification mechanism when thermal
noise fluctuations feed the device.
