In this paper, different configurations of phase-sensitive amplifiers (PSAs) built with periodically poled lithium niobate (PPLN) devices are theoretically and numerically investigated, focusing on their application for amplification in optical communications systems. Single- and dual-pump configurations of one-, two-, and four-mode PSAs are discussed. For each configuration, analytical expressions for the maximum and minimum gain of the amplifiers are provided, showing the influence of the power of the pump and signal waves, as well as the length and efficiency of the PPLN waveguide. The analytical expressions are numerically validated by solving the coupled differential equations describing the nonlinear interactions in the PPLN. The obtained results show that the gain of all PSA configurations exponentially increases with the power of the pump waves, and the length and efficiency of the PPLN device, whereas it is almost independent of the power of the signal wave. In addition, it is shown in this paper that PSA configurations where an intermediate interaction is necessary to generate waves at the second-harmonic band have a gain penalty of 6 dB. It is also shown that no significant difference in terms of gain bandwidth is observed for the single- and dual-pump configurations of two-mode PSAs with an intermediate interaction. Finally, it is shown that a four-mode PSA can only be implemented under very strict conditions, with no gain advantage over two-mode PSAs.