r has to be devel- oped, taking into account the specific characteristics of this component. A complete modeling of the amplifier brings about a set of coupled differential equa- tions containing all the terms corresponding to every possible pump scheme, to a plurality of amplified channels, and to all the noise terms. We include such equations with a brief comment in Appendix D since there are situa- tions in which a more simplified model cannot be used. In such cases, a numerical solution of a more complete model has to be carried out. Here, in order to find a simpler model allowing us to investigate lumped Raman ampli- fiers potentialities, we will introduce the following approximations: The equations for the noise terms will be separated by the equations for the sig- nals eliminating the noise contribution from the signal equations (high signal to noise ratio condition). Stationary regime is assumed, that means that no time variation is induced in the amplifier parameters due to the signal modulation. We know that this is equiva- lent to neglecting the dynamic range compression due to the very short Raman response time. Backscattering of signal waves is neglected. All the RIN noise terms are neglected, thus eliminating also the RIN transfer from the pumps and the signal. Phonon-induced noise is neglected (that means that no useful signal is near the pump wavelengths). The undepleted pump approximation is used. It is worth noting that, under an architectural point of view, this means that the pumps are extracted from the line after the end of the active fiber. The useful signal is assumed to be a single narrowband channel. Just to be practical, we will analyze the approximated model in the case of a two back- propagating pumps. Eliminating all the relevant terms, the general equations of the Raman amplifier (see Appendix C) become Technology for Telecommunications: Optical Fibers, Amplifiers, and Passive Devices dli=+a,P, (j=1,2) (4.84) where the signal power flux is represented with P the pump power flux is i