come the gain of one of the two stages. Thus, the result already known for electronic amplifiers is obtained also for optical amplifiers: the first stage has to be designed with a low noise factor, while the design of the second stage is mainly driven by the need of a high output power, since the noise factor contributes to the overall noise divided by the whole amplifier gain. Starting from Equation 4.79, it is also possible to face another type of design problem related to the fact that the design of the whole transmission system dictates requirements for the subsystems and in particular for optical amplifiers. Such requirements in general consists in the input and in the output power, with the condition that such input power pushes the amplifier sufficiently deep in saturation to be stable against the input signal or the environmental fluctuations. Moreover, the system design also dictates the value of the intrastage loss, since it depends on the dispersion compensation and on what are the other optical components that have to fit between the two stages. In this condition, minimizing the noise means of course to reduce NF1 as much as pos- sible, increasing the population inversion and reducing the system nonidealities, but also Telecommunication Networks means to distribute the overall gain between the two stages determining G1 and G2 SO that our is minimum. This problem can be solved by expressing Equation 4.79 as a function of one of the unknown gains using G = G1aG2 and the expression (Equation 4.74) of NF. Indicating with y the population inversion of the two stages, the expression of the noise variance transforms in the following equation: (4.80) Equation 4.80 can be minimized with respect to G2 to obtain the optimum gain distribu- tion in a two-stage amplifier. The result can be written as G2 = V(Y,G/(Y1Ga2 +y2-12a2)). This equation, with realistic amplifier parameters, simply tells us that the gain of the second stage has to be very small with respect to the gain of the first and, in the limit of small 