Fiber laser for on-board Lidar applications (EDFL) are still in steadily progress. Due to limited peak power available from laser diodes at 1550 nm, Erbium Doped Fiber Amplifier (EDFA) are required. So, the design of such eye-safe laser emitters is based on an in-depth modelling of the EDFA. This paper presents a non-linear model including physical processes such as excited state absorption, pair-induced quenching and homogenous upconversion. All needed measurements have been made to fit the theoretical data without using fitting parameters. Taking into account the complex medium susceptibility of the EDFA allows us to specify precisely its behavior in wavelength, power and phase, with respect to various forms of signals used in a Doppler LIDAR. The experimental characterization of dynamic phase variations, at the output of the EDFA, has been successfully carried out, for the first time at our knowledge.