A theoretical analysis of the erbium-doped fiber amplifier completely describes this device. This modeling is developed within the most attractive configurations : 1. 48im and O. 98im pump wavelengths. The original approach used to take into account the amplified spontaneous emission (ASE) enables us to fully characterize the amplifier at any pump and signal regime. Thus we may quantitavely predict the influence of optogeometrical parameters erbium distribution and spectroscopic properties pump and signal powers and wavelengths and amplifier lengths over the amplifier performances in terms of gains residual pump powers co- and counter-propagating ASE frequency components. The agreement between predictive calculations and experiments appears truly excellent. Moreover this original ASE modeling results in noise figures compelling with published experiments and this analysis may also be used for superfluorescent sources design. Due to its quantitative nature this numerical tool can be used for erbium-doped fiber optimization optimal set-up conditions for amplifier modules transmission link evaluations and network applications.