  Linear parametric amplification is a key operation in information processing.
Our interest here is quantum-limited parametric amplification, $i.e.$,
amplification of quantum signals while adding the minimum amount of noise
allowed by quantum mechanics, which is essential for any viable implementation
of quantum information processing. We describe parametric amplifiers based on
the dispersive nonlinearity of Josephson junctions driven with appropriate
tones playing the role of pumps. We discuss two defining characteristics in the
architecture of these amplifiers: the number of modes occupied by the signal,
idler and pump waves and the number of independent ports through which these
waves enter into the circuit. The scattering properties of these amplifiers is
also reviewed. The main focus of this work are the computations of the dynamic
range and phase-space distributions of the fluctuations of the modes of the
amplifiers.
